Humans trade off viewing time and movement duration to improve visuomotor accuracy in a fast reaching task

Dissecting Bayes: Using influence measures to test normative use of probability density information derived from a sample

Bayesian decision theory (BDT) is frequently used to model normative performance in perceptual, motor, and cognitive decision tasks where the possible outcomes of actions are associated with rewards or penalties. The resulting normative models specify how decision makers should encode and combine information about uncertainty and value-step by step-in order to maximize their expected reward. When prior, likelihood, and posterior are probabilities, the Bayesian computation requires only simple arithmetic operations: addition, etc. We focus on visual cognitive tasks where Bayesian computations are carried out not on probabilities but on (1) probability density functions and (2) these probability density functions are derived from samples. We break the BDT model into a series of computations and test human ability to carry out each of these computations in isolation. We test three necessary properties of normative use of pdf information derived from a sample-accuracy, additivity and influence. Influence measures allow us to assess how much weight each point in the sample is assigned in making decisions and allow us to compare normative use (weighting) of samples to actual, point by point. We find that human decision makers violate accuracy and additivity systematically but that the cost of failure in accuracy or additivity would be minor in common decision tasks. However, a comparison of measured influence for each sample point with normative influence measures demonstrates that the individual's use of sample information is markedly different from the predictions of BDT. We will show that the normative BDT model takes into account the geometric symmetries of the pdf while the human decision maker does not. An alternative model basing decisions on a single extreme sample point provided a better account for participants' data than the normative BDT model.

Sensorimotor Uncertainty of Immersive Virtual Reality Environments for People in Pain: Scoping Review

INTRODUCTION

Decision making and action execution both rely on sensory information, and their primary objective is to minimise uncertainty. Virtual reality (VR) introduces uncertainty due to the imprecision of perceptual information. The concept of "sensorimotor uncertainty" is a pivotal element in the interplay between perception and action within the VR environment. The role of immersive VR in the four stages of motor behaviour decision making in people with pain has been previously discussed. These four processing levels are the basis to understand the uncertainty that a patient experiences when using VR: sensory information, current state, transition rules, and the outcome obtained.

METHODS

This review examines the different types of uncertainty that a patient may experience when they are immersed in a virtual reality environment in a context of pain. Randomised clinical trials, a secondary analysis of randomised clinical trials, and pilot randomised clinical trials related to the scope of Sensorimotor Uncertainty in Immersive Virtual Reality were included after searching.

RESULTS

Fifty studies were included in this review. They were divided into four categories regarding the type of uncertainty the intervention created and the stage of the decision-making model.

CONCLUSIONS

Immersive virtual reality makes it possible to alter sensorimotor uncertainty, but studies of higher methodological quality are needed on this topic, as well as an exploration into the patient profile for pain management using immersive VR.

Utterance planning under message uncertainty: evidence from a novel picture-naming paradigm

Language researchers view utterance planning as implicit decision-making: producers must choose the words, sentence structures, and various other linguistic features to communicate their message. To date, much of the research on utterance planning has focused on situations in which the speaker knows the full message to convey. Less is known about circumstances in which speakers begin utterance planning before they are certain about their message. In three picture-naming experiments, we used a novel paradigm to examine how speakers plan utterances before a full message is known. In Experiments 1 and 2, participants viewed displays showing two pairs of objects, followed by a cue to name one pair. In an Overlap condition, one object appeared in both pairs, providing early information about one of the objects to name. In a Different condition, there was no object overlap. Across both spoken and typed responses, participants tended to name the overlapping target first in the Overlap condition, with shorter initiation latencies compared with other utterances. Experiment 3 used a semantically constraining question to provide early information about the upcoming targets, and participants tended to name the more likely target first in their response. These results suggest that in situations of uncertainty, producers choose word orders that allow them to begin early planning. Producers prioritize message components that are certain to be needed and continue planning the rest when more information becomes available. Given similarities to planning strategies for other goal-directed behaviors, we suggest continuity between decision-making processes in language and other cognitive domains.

Tapping on a target: dealing with uncertainty about its position and motion

Reaching movements are guided by estimates of the target object's location. Since the precision of instantaneous estimates is limited, one might accumulate visual information over time. However, if the object is not stationary, accumulating information can bias the estimate. How do people deal with this trade-off between improving precision and reducing the bias? To find out, we asked participants to tap on targets. The targets were stationary or moving, with jitter added to their positions. By analysing the response to the jitter, we show that people continuously use the latest available information about the target's position. When the target is moving, they combine this instantaneous target position with an extrapolation based on the target's average velocity during the last several hundred milliseconds. This strategy leads to a bias if the target's velocity changes systematically. Having people tap on accelerating targets showed that the bias that results from ignoring systematic changes in velocity is removed by compensating for endpoint errors if such errors are consistent across trials. We conclude that combining simple continuous updating of visual information with the low-pass filter characteristics of muscles, and adjusting movements to compensate for errors made in previous trials, leads to the precise and accurate human goal-directed movements.

Developmental changes in impulse control: Trial-by-trial EMG dissociates the evolution of impulse strength from its subsequent suppression

Goal-oriented behavior can be disrupted by irrelevant information that automatically activates incorrect responses. While behavioral errors reveal response capture in such situations, they are only the tip of the iceberg. Additional subliminal activations of the incorrect responses (partial errors) can be revealed on correctly responded trials thanks to electromyography (EMG). In the current study, for the first time, EMG recorded in children was combined with distributional analyses. This allowed to investigate the properties of incorrect response activations and to highlight developmental changes in impulse control. A sample of 114 children aged 6-14 years was studied. Children performed a Simon task in which the irrelevant stimulus-position automatically activates a response that might be compatible or incompatible with the correct one. On incompatible trials, the automatic response activation must be overcome by controlled response selection. As previously observed in adults, our approach revealed the presence of an automatic EMG activation of the incorrect response elicited by the irrelevant stimulus dimension. Further, it revealed another independent source at the origin of incorrect response activations: the tendency to guess for response alternation. Both sources increased the frequency of early incorrect EMG activations, indicating impulsive responding. In addition, the influence of both sources decreased with increasing age. Thus, development is marked by improved ability to manage distractibility on the one hand and decreased tendency to rely on a guessing strategy on the other.

Exploration of sensory-motor tradeoff behavior in Parkinson's disease

While slowness of movement is an obligatory characteristic of Parkinson's disease (PD), there are conditions in which patients move uncharacteristically fast, attributed to deficient motor inhibition. Here we investigate deficient inhibition in an optimal sensory-motor integration framework, using a game in which subjects used a paddle to catch a virtual ball. Display of the ball was extinguished as soon as the catching movement started, segregating the task into a sensing and acting phase. We analyzed the behavior of 9 PD patients (ON medication) and 10 age-matched controls (HC). The switching times (between sensing and acting phase) were compared to the predicted optimal switching time, based on the individual estimates of sensory and motor uncertainties. The comparison showed that deviation from predicted optimal switching times were similar between groups. However, PD patients showed a weaker correlation between variability in switching time and sensory-motor uncertainty, indicating a reduced propensity to generate exploratory behavior for optimizing goal-directed movements. Analysis of the movement kinematics revealed that PD patients, compared to controls, used a lower peak velocity of the paddle and intercepted the ball with greater velocity. Adjusting the trial duration to the time for the paddle to stop moving, we found that PD patients spent a smaller proportion of the trial duration for observing the ball. Altogether, the results do not show the premature movement initiation and truncated sensory processing that we predicted to ensue from deficient inhibition in PD.

Compensative movement ameliorates reduced efficacy of rapidly-embodied decisions in humans

Dynamic environments, such as sports, often demand rapid decision-making and motor execution. The concept of embodied decision refers to the mutual link between both processes, but little is known about how these processes are balanced under severe time constraints. We address this problem by using a baseball-like hitting paradigm with and without Go/No-go judgment; participants were required to hit (Go) a moving target in the strike area or not to hit (No-go) other targets. We found that Go/No-go judgments were effective with regard to task performance, but efficacy was lost below the time constraint of 0.5 seconds mainly due to a reduction in judgment accuracy rather than movement accuracy. However, either slowing movement initiation in Go trials or canceling the movement in progress in No-go trials improved judgment accuracy. Our findings suggest that embodied decision efficacy is limited in split-second periods, but compensation is possible by changing ongoing movement strategies.

Contrasting contributions of movement onset and duration to self-evaluation of sensorimotor timing performance

Movement execution is not always optimal. Understanding how humans evaluate their own motor decisions can give us insights into their suboptimality. Here, we investigated how humans time the action of synchronizing an arm movement with a predictable visual event and how well they can evaluate the outcome of this action. On each trial, participants had to decide when to start (reaction time) and for how long to move (movement duration) to reach a target on time. After each trial, participants judged the confidence they had that their performance on that trial was better than average. We found that participants mostly varied their reaction time, keeping the average movement duration short and relatively constant across conditions. Interestingly, confidence judgements reflected deviations from the planned reaction time and were not related to planned movement duration. In two other experiments, we replicated these results in conditions where the contribution of sensory uncertainty was reduced. In contrast to confidence judgements, when asked to make an explicit estimation of their temporal error, participants' estimates were related in a similar manner to both reaction time and movement duration. In summary, humans control the timing of their actions primarily by adjusting the delay to initiate the action, and they estimate their confidence in their action from the difference between the planned and executed movement onset. Our results highlight the critical role of the internal model for the self‐evaluation of one's motor performance.

The computational cost of active information sampling before decision-making under uncertainty

Humans often seek information to minimize the pervasive effect of uncertainty on decisions. Current theories explain how much knowledge people should gather before a decision, based on the cost-benefit structure of the problem at hand. Here, we demonstrate that this framework omits a crucial agent-related factor: the cognitive effort expended while collecting information. Using an active sampling model, we unveil a speed-efficiency trade-off whereby more informative samples take longer to find. Crucially, under sufficient time pressure, humans can break this trade-off, sampling both faster and more efficiently. Computational modelling demonstrates the existence of a cost of cognitive effort which, when incorporated into theoretical models, provides a better account of people's behaviour and also relates to self-reported fatigue accumulated during active sampling. Thus, the way people seek knowledge to guide their decisions is shaped not only by task-related costs and benefits, but also crucially by the quantifiable computational costs incurred.

Reaching for known unknowns: Rapid reach decisions accurately reflect the future state of dynamic probabilistic information

Everyday tasks such as catching a ball appear effortless, but in fact require complex interactions and tight temporal coordination between the brain's visual and motor systems. What makes such interceptive actions particularly impressive is the capacity of the brain to account for temporal delays in the central nervous system-a limitation that can be mitigated by making predictions about the environment as well as one's own actions. Here, we wanted to assess how well human participants can plan an upcoming movement based on a dynamic, predictable stimulus that is not the target of action. A central stationary or rotating stimulus determined the probability that each of two potential targets would be the eventual target of a rapid reach-to-touch movement. We examined the extent to which reach movement trajectories convey internal predictions about the future state of dynamic probabilistic information conveyed by the rotating stimulus. We show that movement trajectories reflect the target probabilities determined at movement onset, suggesting that humans rapidly and accurately integrate visuospatial predictions and estimates of their own reaction times to effectively guide action.

Human decision making anticipates future performance in motor learning

It is well-established that people can factor into account the distribution of their errors in motor performance so as to optimize reward. Here we asked whether, in the context of motor learning where errors decrease across trials, people take into account their future, improved performance so as to make optimal decisions to maximize reward. One group of participants performed a virtual throwing task in which, periodically, they were given the opportunity to select from a set of smaller targets of increasing value. A second group of participants performed a reaching task under a visuomotor rotation in which, after performing a initial set of trials, they selected a reward structure (ratio of points for target hits and misses) for different exploitation horizons (i.e., numbers of trials they might be asked to perform). Because movement errors decreased exponentially across trials in both learning tasks, optimal target selection (task 1) and optimal reward structure selection (task 2) required taking into account future performance. The results from both tasks indicate that people anticipate their future motor performance so as to make decisions that will improve their expected future reward.

The Visual Perception of Material Properties Affects Motor Planning in Prehension: An Analysis of Temporal and Spatial Components of Lifting Cups

The current study examined the role of visually perceived material properties in motor planning, where we analyzed the temporal and spatial components of motor movements during a seated reaching task. We recorded hand movements of 14 participants in three dimensions while they lifted and transported paper cups that differed in weight and glossiness. Kinematic- and spatial analysis revealed speed-accuracy trade-offs to depend on visual material properties of the objects, in which participants reached slower and grabbed closer to the center of mass for stimuli that required to be handled with greater precision. We found grasp-preparation during the first encounters with the cups was not only governed by the anticipated weight of the cups, but also by their visual material properties, namely glossiness. After a series of object lifting, the execution of reaching, the grip position, and the transportation of the cups from one location to another were preeminently guided by the object weight. We also found the planning phase in reaching to be guided by the expectation of hardness and surface gloss. The findings promote the role of general knowledge of material properties in reach-to-grasp movements, in which visual material properties are incorporated in the spatio-temporal components.

Optimizing motor decision-making through competition with opponents

Although optimal decision-making is essential for sports performance and fine motor control, it has been repeatedly confirmed that humans show a strong risk-seeking bias, selecting a risky strategy over an optimal solution. Despite such evidence, the ideal method to promote optimal decision-making remains unclear. Here, we propose that interactions with other people can influence motor decision-making and improve risk-seeking bias. We developed a competitive reaching game (a variant of the “chicken game”) in which aiming for greater rewards increased the risk of no reward and subjects competed for the total reward with their opponent. The game resembles situations in sports, such as a penalty kick in soccer, service in tennis, the strike zone in baseball, or take-off in ski jumping. In five different experiments, we demonstrated that, at the beginning of the competitive game, the subjects robustly switched their risk-seeking strategy to a risk-averse strategy. Following the reversal of the strategy, the subjects achieved optimal decision-making when competing with risk-averse opponents. This optimality was achieved by a non-linear influence of an opponent’s decisions on a subject’s decisions. These results suggest that interactions with others can alter human motor decision strategies and that competition with a risk-averse opponent is key for optimizing motor decision-making.

Sub-optimality in motor planning is not improved by explicit observation of motor uncertainty

To make optimal decisions under risk, one must correctly weight potential rewards and penalties by the probabilities of receiving them. In motor decision tasks, the uncertainty in outcome is a consequence of motor uncertainty. When participants perform suboptimally as they often do in such tasks, it could be because they have insufficient information about their motor uncertainty: with more information, their performance could converge to optimal as they learn their own motor uncertainty. Alternatively, their suboptimal performance may reflect an inability to make use of the information they have or even to perform the correct computations. To discriminate between these two possibilities, we performed an experiment spanning two days. On the first day, all participants performed a reaching task with trial-by-trial feedback of motor error. At the end of the day, their aim points were still typically suboptimal. On the second day participants were divided into two groups one of which repeated the task of the first day and the other of which repeated the task but were intermittently given additional information summarizing their motor errors. Participants receiving additional information did not perform significantly better than those who did not.

Human representation of multimodal distributions as clusters of samples

Behavioral and neuroimaging evidence shows that human decisions are sensitive to the statistical regularities (mean, variance, skewness, etc.) of reward distributions. However, it is unclear what representations human observers form to approximate reward distributions, or probability distributions in general. When the possible values of a probability distribution are numerous, it is cognitively costly and perhaps unrealistic to maintain in mind the probability of each possible value. Here we propose a Clusters of Samples (CoS) representation model: The samples of the to-be-represented distribution are classified into a small number of clusters and only the centroids and relative weights of the clusters are retained for future use. We tested the behavioral relevance of CoS in four experiments. On each trial, human subjects reported the mean and mode of a sequentially presented multimodal distribution of spatial positions or orientations. By varying the global and local features of the distributions, we observed systematic errors in the reported mean and mode. We found that our CoS representation of probability distributions outperformed alternative models in accounting for subjects’ response patterns. The ostensible influence of positive/negative skewness on the over/under estimation of the reported mean, analogous to the “skewness preference” phenomenon in decisions, could be well explained by models based on CoS.

Life is full of uncertainties: An action may yield multiple possible consequences and a percept may imply multiple possible causes. To survive, humans and animals must compensate for the uncertainty in the environment and in their own perceptual and motor systems. However, how humans represent probability distributions to fulfill probabilistic computations for perception and action remains elusive. The number of possible values in a distribution is vast and grows exponentially with the dimension of the distribution. It would be costly, if not impossible, to maintain the probability of each possible value. Here we propose a sparse representation of probability distributions, which can reduce an arbitrary distribution to a small set of coefficients while still keeping important global and local features of the original distribution. Our experiments provide preliminary evidence for the use of such representations in human cognition.

Uncertainty modulated exploration in the trade-off between sensing and acting

Many sensorimotor activities have a time constraint for successful completion. In this case, any time devoted to sensory processing is at the expense of time available for motor execution. Earlier studies have explored how this competition between sensory processing and motor execution is resolved by using experimental designs that segregate the sensing and acting phase of the task. It was found that participants switch from the sensing to the acting stage such that the overall (sensorimotor) uncertainty in the outcome of the task is minimized. An unexplained observation in these studies is the substantial variability in switching times. We investigated the variability in switching time by correlating it with the underlying sensorimotor uncertainty. To this end, we used a modified version of the virtual ball catching paradigm proposed by Faisal & Wolpert (2009). Subjects were instructed to catch a ball, but as soon as they initiated their movement the ball disappeared. We extended the range of horizontal velocities and used two different start positions of the ball to quantify the dependence of sensory uncertainty on ball velocity. Velocity dependence of sensory uncertainty allowed us to manipulate sensory uncertainty and hence the sensorimotor uncertainty. We found that the variability in switching times is correlated with two factors. Firstly, variability in switching times is greater when variation in switching time has only minimal effects on sensorimotor uncertainty. Secondly, variability in switching times is greater when the sensorimotor uncertainty is larger. Our results suggest that the variability in switching time reflects an uncertainty-driven exploratory process.

Gaze Behaviors During Serve Returns in Tennis: A Comparison Between Intermediate- and High-Skill Players

The authors studied gaze behaviors in high- and intermediate-skill tennis players while they performed tennis serve returns. Participants returned 40 serves in 4 serve locations while wearing a mobile eye tracker. The ball's flight path was deconstructed into 3 distinct locations (i.e., ball before bouncing on surface, the bounce area, and ball after bouncing on surface), and gaze behaviors along with quiet-eye (QE) onset and durations were recorded. Results revealed that (a) high-skill players exhibited better return shots than their lower skill counterparts, (b) high-skill players and high-score shots were characterized by longer fixation durations on the ball at prebounce, and (c) longer QE durations were observed for high-skill players and high-score shots. Findings provide valuable insight into the relationship between gaze behaviors, QE, and performance in fast-pace interceptive sports.

Rational Inference of Beliefs and Desires From Emotional Expressions

We investigated people's ability to infer others' mental states from their emotional reactions, manipulating whether agents wanted, expected, and caused an outcome. Participants recovered agents' desires throughout. When the agent observed, but did not cause the outcome, participants' ability to recover the agent's beliefs depended on the evidence they got (i.e., her reaction only to the actual outcome or to both the expected and actual outcomes; Experiments 1 and 2). When the agent caused the event, participants' judgments also depended on the probability of the action (Experiments 3 and 4); when actions were improbable given the mental states, people failed to recover the agent's beliefs even when they saw her react to both the anticipated and actual outcomes. A Bayesian model captured human performance throughout (rs ≥ .95), consistent with the proposal that people rationally integrate information about others' actions and emotional reactions to infer their unobservable mental states.

Dynamic combination of sensory and reward information under time pressure

When making choices, collecting more information is beneficial but comes at the cost of sacrificing time that could be allocated to making other potentially rewarding decisions. To investigate how the brain balances these costs and benefits, we conducted a series of novel experiments in humans and simulated various computational models. Under six levels of time pressure, subjects made decisions either by integrating sensory information over time or by dynamically combining sensory and reward information over time. We found that during sensory integration, time pressure reduced performance as the deadline approached, and choice was more strongly influenced by the most recent sensory evidence. By fitting performance and reaction time with various models we found that our experimental results are more compatible with leaky integration of sensory information with an urgency signal or a decision process based on stochastic transitions between discrete states modulated by an urgency signal. When combining sensory and reward information, subjects spent less time on integration than optimally prescribed when reward decreased slowly over time, and the most recent evidence did not have the maximal influence on choice. The suboptimal pattern of reaction time was partially mitigated in an equivalent control experiment in which sensory integration over time was not required, indicating that the suboptimal response time was influenced by the perception of imperfect sensory integration. Meanwhile, during combination of sensory and reward information, performance did not drop as the deadline approached, and response time was not different between correct and incorrect trials. These results indicate a decision process different from what is involved in the integration of sensory information over time. Together, our results not only reveal limitations in sensory integration over time but also illustrate how these limitations influence dynamic combination of sensory and reward information.

Collecting more information seems beneficial for making most of the decisions we face in daily life. However, the benefit of collecting more information critically depends on how well we can integrate that information over time and how costly time is. Here we investigate how humans determine the amount of time to spend on collecting sensory information in order to make a perceptual decision when the reward for making a correct choice decreases over time. We show that sensory integration over time is not perfect and further deteriorates with time pressure. However, we also find evidence that when the cost of time has to be considered, decision processes are influenced by limitations in sensory integration.

Unifying Speed-Accuracy Trade-Off and Cost-Benefit Trade-Off in Human Reaching Movements

Two basic trade-offs interact while our brain decides how to move our body. First, with the cost-benefit trade-off, the brain trades between the importance of moving faster toward a target that is more rewarding and the increased muscular cost resulting from a faster movement. Second, with the speed-accuracy trade-off, the brain trades between how accurate the movement needs to be and the time it takes to achieve such accuracy. So far, these two trade-offs have been well studied in isolation, despite their obvious interdependence. To overcome this limitation, we propose a new model that is able to simultaneously account for both trade-offs. The model assumes that the central nervous system maximizes the expected utility resulting from the potential reward and the cost over the repetition of many movements, taking into account the probability to miss the target. The resulting model is able to account for both the speed-accuracy and the cost-benefit trade-offs. To validate the proposed hypothesis, we confront the properties of the computational model to data from an experimental study where subjects have to reach for targets by performing arm movements in a horizontal plane. The results qualitatively show that the proposed model successfully accounts for both cost-benefit and speed-accuracy trade-offs.

Rapid target foraging with reach or gaze: The hand looks further ahead than the eye

Real-world tasks typically consist of a series of target-directed actions and often require choices about which targets to act on and in what order. Such choice behavior can be assessed from an optimal foraging perspective whereby target selection is shaped by a balance between rewards and costs. Here we evaluated such decision-making in a rapid movement foraging task. On a given trial, participants were presented with 15 targets of varying size and value and were instructed to harvest as much reward as possible by either moving a handle to the targets (hand task) or by briefly fixating them (eye task). The short trial duration enabled participants to harvest about half the targets, ensuring that total reward was due to choice behavior. We developed a probabilistic model to predict target-by-target harvesting choices that considered the rewards and movement-related costs (i.e., target distance and size) associated with the current target as well as future targets. In the hand task, in comparison to the eye task, target choice was more strongly influenced by movement-related costs and took into account a greater number of future targets, consistent with the greater costs associated with arm movement. In both tasks, participants exhibited near-optimal behaviour and in a constrained version of the hand task in which choices could only be based on target positions, participants consistently chose among the shortest movement paths. Our results demonstrate that people can rapidly and effectively integrate values and movement-related costs associated with current and future targets when sequentially harvesting targets.

Many natural tasks involve a series of decisions about which target to acquire next, either with our gaze or hand. We examined the factors influencing such decisions using a task in which targets of varying value and size are sequentially acquired by eye or hand movements. By developing a probabilistic model of decision-making behavior we show that eye movement decisions are made in isolation, independent of potential future targets, and are primarily determined by target value. In contrast, hand movement decisions consider multiple future targets and are strongly shaped by movement-related costs. By examining decision-making in sequential actions, our results and model represent a significant advance over previous work that has focused primarily on decisions about single actions.

Exploring the quiet eye in archery using field- and laboratory-based tasks

The ‘quiet eye’ (QE)—a period of extended gaze fixation on a target—has been reported in many tasks that require accurate aiming. Longer quiet eye durations (QEDs) are reported in experts compared to non-experts and on successful versus less successful trials. The QE has been extensively studied in the field; however, the cognitive mechanisms underlying the QE are not yet fully understood. We investigated the QEDs of ten expert and ten novice archers in the field and in the laboratory using a computer-based archery task. The computer task consisted of shooting archery targets using a joystick. Random ‘noise’ (visual motion perturbation) was introduced at high and low levels to allow for the controlled examination of the effects of task complexity and processing demands. In this computer task, we also tested an additional group of ten non-archers as controls. In both field and computer tasks, eye movements were measured using electro-oculography. The expert archers exhibited longer QED compared to the novice archers in the field task. In the computer task, the archers again exhibited longer QEDs and were more accurate compared to non-archers. Furthermore, expert archers showed earlier QE onsets and longer QEDs during high noise conditions compared to the novices and non-archers. Our findings show skill-based effects on QED in field conditions and in a novel computer-based archery task, in which online (visual) perturbations modulated experts’ QEDs. These longer QEDs in experts may be used for more efficient programming in which accurate predictions are facilitated by attention control.

The effects of payoff manipulations on temporal bisection performance

There is growing evidence that alterations in reward rates modify timing behavior demonstrating the role of motivational factors in interval timing behavior. This study aimed to investigate the effects of manipulations of rewards and penalties on temporal bisection performance in humans. Participants were trained to classify experienced time intervals as short or long based on the reference durations. Two groups of participants were tested under three different bias conditions in which either the relative reward magnitude or penalty associated with correct or incorrect categorizations of short and long reference durations was manipulated. Participants adapted their choice behavior (i.e., psychometric functions shifted) based on these payoff manipulations in directions predicted by reward maximization. The signal detection theory-based analysis of the data revealed that payoff contingencies affected the response bias parameter (B″) without altering participants' sensitivity (A') to temporal distances. Finally, the response time (RT) analysis showed that short categorization RTs increased, whereas long categorization RTs decreased as a function of stimulus durations. However, overall RTs did not exhibit any modulation in response to payoff manipulations. Taken together, this study provides additional support for the effects of motivational variables on temporal decision-making.

Archerfish fast-start decisions can take an additional variable into account

The analysis of saccadic decision-making tasks with two or four alternatives has shown what appears to be a general hallmark of decision-making: adding more alternatives decreases speed and accuracy. In their everyday lives, however, animals often select among many more than two options and under heavy constraints on speed and accuracy. Here we analyse a rapid decision made by hunting archerfish. As in the classical saccadic tasks, the fish must first estimate sensory information: based on an estimate of horizontal speed, azimuthal direction and initial height of falling prey, the fish must quickly select a suitable fast-start to arrive at the right place at the right time. Our results suggest that the fast-start decisions of archerfish are surprisingly robust with respect to adding a further decision-relevant variable. We show that the fish can appropriately account for vertical speed as an independent further variable - but the need to do so does not affect speed or accuracy of the decisions. Our findings suggest novel ways by which rapid and yet complex decisions could be balanced against increasing complexity.

Information sampling behavior with explicit sampling costs

The decision to gather information should take into account both the value of information and its accrual costs in time, energy and money. Here we explore how people balance the monetary costs and benefits of gathering additional information in a perceptual-motor estimation task. Participants were rewarded for touching a hidden circular target on a touch-screen display. The target's center coincided with the mean of a circular Gaussian distribution from which participants could sample repeatedly. Each "cue" - sampled one at a time - was plotted as a dot on the display. Participants had to repeatedly decide, after sampling each cue, whether to stop sampling and attempt to touch the hidden target or continue sampling. Each additional cue increased the participants' probability of successfully touching the hidden target but reduced their potential reward. Two experimental conditions differed in the initial reward associated with touching the hidden target and the fixed cost per cue. For each condition we computed the optimal number of cues that participants should sample, before taking action, to maximize expected gain. Contrary to recent claims that people gather less information than they objectively should before taking action, we found that participants over-sampled in one experimental condition, and did not significantly under- or over-sample in the other. Additionally, while the ideal observer model ignores the current sample dispersion, we found that participants used it to decide whether to stop sampling and take action or continue sampling, a possible consequence of imperfect learning of the underlying population dispersion across trials.

Why Don't We Move Slower? The Value of Time in the Neural Control of Action

To want something now rather than later is a common attitude that reflects the brain's tendency to value the passage of time. Because the time taken to accomplish an action inevitably delays task achievement and reward acquisition, this idea was ported to neural movement control within the "cost of time" theory. This theory provides a normative framework to account for the underpinnings of movement time formation within the brain and the origin of a self-selected pace in human and animal motion. Then, how does the brain exactly value time in the control of action? To tackle this issue, we used an inverse optimal control approach and developed a general methodology allowing to squarely sample infinitesimal values of the time cost from experimental motion data. The cost of time underlying saccades was found to have a concave growth, thereby confirming previous results on hyperbolic reward discounting, yet without making any prior assumption about this hypothetical nature. For self-paced reaching, however, movement time was primarily valued according to a striking sigmoidal shape; its rate of change consistently presented a steep rise before a maximum was reached and a slower decay was observed. Theoretical properties of uniqueness and robustness of the inferred time cost were established for the class of problems under investigation, thus reinforcing the significance of the present findings. These results may offer a unique opportunity to uncover how the brain values the passage of time in healthy and pathological motor control and shed new light on the processes underlying action invigoration.

SIGNIFICANCE STATEMENT

Movement time is a fundamental characteristic of neural motor control, but the principles underlying its formation remain little known. This work addresses that question within the inverse optimal control framework where the challenge is to uncover what optimality criterion underlies a system's behavior. Here we rely on the "cost of time" theory that finds its roots into the brain's tendency to discount the actual value of future reward. It asserts that the time elapsed until action completion entails a cost, thereby making slow moves nonoptimal. By means of a thorough theoretical analysis, the present article shows how to sample the infinitesimal values of the time cost without prior assumption about its hypothetical nature and emphasizes its sigmoidal shape for reaching.

Human representation of visuo-motor uncertainty as mixtures of orthogonal basis distributions

In many laboratory visuo-motor decision tasks, subjects compensate for their own visuo-motor error, earning close to the maximum reward possible. To do so, they must combine information about the distribution of possible error with values associated with different movement outcomes. The optimal solution is a potentially difficult computation that presupposes knowledge of the probability density function (pdf) of visuo-motor error associated with each possible planned movement. It is unclear how the brain represents such pdfs or computes with them. In three experiments, we used a forced-choice method to reveal subjects' internal representations of their spatial visuo-motor error in a speeded reaching movement. Although subjects' objective distributions were unimodal, close to Gaussian, their estimated internal pdfs were typically multimodal and were better described as mixtures of a small number of distributions differing only in location and scale. Mixtures of a small number of uniform distributions outperformed other mixture distributions, including mixtures of Gaussians.

Risky visuomotor choices during rapid reaching in childhood

Many everyday actions are implicit gambles because imprecisions in our visuomotor systems place probabilities on our success or failure. Choosing optimal action strategies involves weighting the costs and gains of potential outcomes by their corresponding probabilities, and requires stable representations of one's own imprecisions. How this ability is acquired during development in childhood when visuomotor skills change drastically is unknown. In a rewarded rapid reaching task, 6‐ to 11‐year‐old children followed ‘risk‐seeking’ strategies leading to overly high point‐loss. Adults' performance, in contrast, was close to optimal. Children's errors were not explained by distorted estimates of value or probability, but may reflect different action selection criteria or immature integration of value and probability information while planning movements. These findings provide a starting point for understanding children's risk‐taking in everyday visuomotor situations when suboptimal choices can be dangerous. Moreover, children's risky visuomotor decisions mirror those reported for non‐motor gambles, raising the possibility that common processes underlie development across decision‐making domains.

Acquisition, representation, and transfer of models of visuo-motor error

We examined how human subjects acquire and represent models of visuo-motor error and how they transfer information about visuo-motor error from one task to a closely related one. The experiment consisted of three phases. In the training phase, subjects threw beanbags underhand towards targets displayed on a wall-mounted touch screen. The distribution of their endpoints was a vertically elongated bivariate Gaussian. In the subsequent choice phase, subjects repeatedly chose which of two targets varying in shape and size they would prefer to attempt to hit. Their choices allowed us to investigate their internal models of visuo-motor error distribution, including the coordinate system in which they represented visuo-motor error. In the transfer phase, subjects repeated the choice phase from a different vantage point, the same distance from the screen but with the throwing direction shifted 45°. From the new vantage point, visuo-motor error was effectively expanded horizontally by √2. We found that subjects incorrectly assumed an isotropic distribution in the choice phase but that the anisotropy they assumed in the transfer phase agreed with an objectively correct transfer. We also found that the coordinate system used in coding two-dimensional visuo-motor error in the choice phase was effectively one-dimensional.

Quickly making the correct choice

In daily life, unconscious choices guide many of our on-going actions. Such choices need to be made quickly, because the options change as the action progresses. We confirmed that people make reasonable choices when they have to quickly decide between two alternatives, and studied the basis of such decisions. The task was to tap with their finger on as many targets as possible within 2 min. A new target appeared after every tap, sometimes accompanied by a second target that was easier to hit. When there was only one target, subjects had to find the right balance between speed and accuracy. When there were two targets, they also had to choose between them. We examined to what extent subjects switched to the target that was easier to hit when it appeared some time after the original one. Subjects generally switched to the easier target whenever doing so would help them hit more targets within the 2-min session. This was so, irrespective of whether the different delays were presented in separate sessions or were interleaved within one session. Whether or not they switched did not depend on how successful they were at hitting the targets on earlier attempts, but it did depend on the position of the finger at the moment that the easy target appeared. We conclude that people have continuous access to reasonable estimates of how long various movement options would take and of how precise the endpoints are likely to be, given the instantaneous circumstances.

Balancing out dwelling and moving: optimal sensorimotor synchronization

Sensorimotor synchronization is a fundamental skill involved in the performance of many artistic activities (e.g., music, dance). After a century of research, the manner in which the nervous system produces synchronized movements remains poorly understood. Typical rhythmic movements involve a motion and a motionless phase (dwell). The dwell phase represents a sizable fraction of the rhythm period, and scales with it. The rationale for this organization remains unexplained and is the object of this study. Twelve participants, four drummers (D) and eight nondrummers (ND), performed tapping movements paced at 0.5-2.5 Hz by a metronome. The participants organized their tapping behavior into dwell and movement phases according to two strategies: 1) Eight participants (1 D, 7 ND) maintained an almost constant ratio of movement time (MT) and dwell time (DT) irrespective of the metronome period. 2) Four participants increased the proportion of DT as the period increased. The temporal variabilities of both the dwell and movement phases were consistent with Weber's law, i.e., their variability increased with their durations, and the longest phase always exhibited the smallest variability. We developed an optimal statistical model that formalized the distribution of time into dwell and movement intervals as a function of their temporal variability. The model accurately predicted the participants' dwell and movement durations irrespective of their strategy and musical skill, strongly suggesting that the distribution of DT and MT results from an optimization process, dependent on each participant's skill to predict time during rest and movement.

Neural coding of uncertainty and probability

Organisms must act in the face of sensory, motor, and reward uncertainty stemming from a pandemonium of stochasticity and missing information. In many tasks, organisms can make better decisions if they have at their disposal a representation of the uncertainty associated with task-relevant variables. We formalize this problem using Bayesian decision theory and review recent behavioral and neural evidence that the brain may use knowledge of uncertainty, confidence, and probability.

How much to trust the senses: likelihood learning

Our brain often needs to estimate unknown variables from imperfect information. Our knowledge about the statistical distributions of quantities in our environment (called priors) and currently available information from sensory inputs (called likelihood) are the basis of all Bayesian models of perception and action. While we know that priors are learned, most studies of prior-likelihood integration simply assume that subjects know about the likelihood. However, as the quality of sensory inputs change over time, we also need to learn about new likelihoods. Here, we show that human subjects readily learn the distribution of visual cues (likelihood function) in a way that can be predicted by models of statistically optimal learning. Using a likelihood that depended on color context, we found that a learned likelihood generalized to new priors. Thus, we conclude that subjects learn about likelihood.

Perceptual decision processes flexibly adapt to avoid change-of-mind motor costs

The motor system is tightly linked with perception and cognition. Recent studies have shown that even anticipated biophysical action costs associated with competing response options can be incorporated into decision-making processes. As a result, choices associated with high energy costs are less likely to be selected. However, some action costs may be harder to predict. For example, a person choosing among apples at a grocery store may change his or her mind suddenly about which apple to put into the cart. This change of mind may be reflected in motor output as the initial decision triggers a motor response toward a Granny Smith that is subsequently redirected toward a Red Delicious. In the present study, to examine how motor costs associated with changes of mind affect perceptual decision making, participants performed a difficult random dot–motion discrimination task in which they had to indicate the direction of motion by reaching to one of two response options. Although each response box was always equidistant from the starting position, the physical distance between the two response options was varied. We found that when the boxes were far apart from one another, and thus changes of mind incurred greater redirection motor costs, change-of-mind frequency decreased while latency to initiate movement increased. This occurred even when response box distance varied randomly from trial to trial and was cued only 1 s before each trial began. Thus, we demonstrated that observers can dynamically adjust perceptual decision-making processes to avoid high motor costs incurred by a change of mind.

Decoupling speed and accuracy in an urgent decision-making task reveals multiple contributions to their trade-off

A key goal in the study of decision making is determining how neural networks involved in perception and motor planning interact to generate a given choice, but this is complicated due to the internal trade-off between speed and accuracy, which confounds their individual contributions. Urgent decisions, however, are special: they may range between random and fully informed, depending on the amount of processing time (or stimulus viewing time) available in each trial, but regardless, movement preparation always starts early on. As a consequence, under time pressure it is possible to produce a psychophysical curve that characterizes perceptual performance independently of reaction time, and this, in turn, makes it possible to pinpoint how perceptual information (which requires sensory input) modulates motor planning (which does not) to guide a choice. Here we review experiments in which, on the basis of this approach, the origin of the speed-accuracy trade-off becomes particularly transparent. Psychophysical, neurophysiological, and modeling results in the "compelled-saccade" task indicate that, during urgent decision making, perceptual information-if and whenever it becomes available-accelerates or decelerates competing motor plans that are already ongoing. This interaction affects both the reaction time and the probability of success in any given trial. In two experiments with reward asymmetries, we find that speed and accuracy can be traded in different amounts and for different reasons, depending on how the particular task contingencies affect specific neural mechanisms related to perception and motor planning. Therefore, from the vantage point of urgent decisions, the speed-accuracy trade-off is not a unique phenomenon tied to a single underlying mechanism, but rather a typical outcome of many possible combinations of internal adjustments within sensory-motor neural circuits.

One and done? Optimal decisions from very few samples

In many learning or inference tasks human behavior approximates that of a Bayesian ideal observer, suggesting that, at some level, cognition can be described as Bayesian inference. However, a number of findings have highlighted an intriguing mismatch between human behavior and standard assumptions about optimality: People often appear to make decisions based on just one or a few samples from the appropriate posterior probability distribution, rather than using the full distribution. Although sampling-based approximations are a common way to implement Bayesian inference, the very limited numbers of samples often used by humans seem insufficient to approximate the required probability distributions very accurately. Here, we consider this discrepancy in the broader framework of statistical decision theory, and ask: If people are making decisions based on samples--but as samples are costly--how many samples should people use to optimize their total expected or worst-case reward over a large number of decisions? We find that under reasonable assumptions about the time costs of sampling, making many quick but locally suboptimal decisions based on very few samples may be the globally optimal strategy over long periods. These results help to reconcile a large body of work showing sampling-based or probability matching behavior with the hypothesis that human cognition can be understood in Bayesian terms, and they suggest promising future directions for studies of resource-constrained cognition.

When money is not enough: awareness, success, and variability in motor learning

When performing a skill such as throwing a dart, many different combinations of joint motions suffice to hit the target. The motor system adapts rapidly to reduce bias in the desired outcome (i.e., the first-order moment of the error); however, the essence of skill is to produce movements with less variability (i.e., to reduce the second-order moment). It is easy to see how feedback about success or failure could sculpt performance to achieve this aim. However, it is unclear whether the dimensions responsible for success or failure need to be known explicitly by the subjects, or whether learning can proceed without explicit awareness of the movement parameters that need to change. Here, we designed a redundant, two-dimensional reaching task in which we could selectively manipulate task success and the variability of action outcomes, whilst also manipulating awareness of the dimension along which performance could be improved. Variability was manipulated either by amplifying natural errors, leaving the correlation between the executed movement and the visual feedback intact, or by adding extrinsic noise, decorrelating movement and feedback. We found that explicit, binary, feedback about success or failure was only sufficient for learning when participants were aware of the dimension along which motor behavior had to change. Without such awareness, learning was only present when extrinsic noise was added to the feedback, but not when task success or variability was manipulated in isolation; learning was also much slower. Our results highlight the importance of conscious awareness of the relevant dimension during motor learning, and suggest that higher-order moments of outcome signals are likely to play a significant role in skill learning in complex tasks.

How the required precision influences the way we intercept a moving object

Do people perform a given motor task differently if it is easy than if it is difficult? To find out, we asked subjects to intercept moving virtual targets by tapping on them with their fingers. We examined how their behaviour depended on the required precision. Everything about the task was the same on all trials except the extent to which the fingertip and target had to overlap for the target to be considered hit. The target disappeared with a sound if it was hit and deflected away from the fingertip if it was missed. In separate sessions, the required precision was varied from being quite lenient about the required overlap to being very demanding. Requiring a higher precision obviously decreased the number of targets that were hit, but it did not reduce the variability in where the subjects tapped with respect to the target. Requiring a higher precision reduced the systematic deviations from landing at the target centre and the lag-one autocorrelation in such deviations, presumably because subjects received information about smaller deviations from hitting the target centre. We found no evidence for lasting effects of training with a certain required precision. All the results can be reproduced with a model in which the precision of individual movements is independent of the required precision, and in which feedback associated with missing the target is used to reduce systematic errors. We conclude that people do not approach this motor task differently when it is easy than when it is difficult.

Testing whether humans have an accurate model of their own motor uncertainty in a speeded reaching task

In many motor tasks, optimal performance presupposes that human movement planning is based on an accurate internal model of the subject's own motor error. We developed a motor choice task that allowed us to test whether the internal model implicit in a subject's choices differed from the actual in isotropy (elongation) and variance. Subjects were first trained to hit a circular target on a touch screen within a time limit. After training, subjects were repeatedly shown pairs of targets differing in size and shape and asked to choose the target that was easier to hit. On each trial they simply chose a target – they did not attempt to hit the chosen target. For each subject, we tested whether the internal model implicit in her target choices was consistent with her true error distribution in isotropy and variance. For all subjects, movement end points were anisotropic, distributed as vertically elongated bivariate Gaussians. However, in choosing targets, almost all subjects effectively assumed an isotropic distribution rather than their actual anisotropic distribution. Roughly half of the subjects chose as though they correctly estimated their own variance and the other half effectively assumed a variance that was more than four times larger than the actual, essentially basing their choices merely on the areas of the targets. The task and analyses we developed allowed us to characterize the internal model of motor error implicit in how humans plan reaching movements. In this task, human movement planning – even after extensive training – is based on an internal model of human motor error that includes substantial and qualitative inaccuracies.

When you play darts, which part of the dartboard do you aim at? The tiny bull's eye is worth 50 points. The 20-point section is much larger. If you're not very good at dart throwing you may want to take that into account. Your choice of target depends not on how good you are but on how good you think you are – your internal model of your own motor error distribution. If you think you hit exactly where you aim, you should aim at the bull's eye. If you assume you have less error in the horizontal direction, you would tend to choose vertically elongated targets over horizontally elongated ones. Previous work in movement planning hints that people have accurate models of their own motor error; we test this hypothesis. People first practiced speeded reaching to touch targets. We then asked them to choose between targets of varying shapes and sizes. Their pattern of choices allows us to estimate their internal models of their own motor error and compare them to their actual motor error distributions. We found – in contrast to previous work – that people's models of their own motor ability were markedly inaccurate.

Very slow search and reach: failure to maximize expected gain in an eye-hand coordination task

We examined an eye-hand coordination task where optimal visual search and hand movement strategies were inter-related. Observers were asked to find and touch a target among five distractors on a touch screen. Their reward for touching the target was reduced by an amount proportional to how long they took to locate and reach to it. Coordinating the eye and the hand appropriately would markedly reduce the search-reach time. Using statistical decision theory we derived the sequence of interrelated eye and hand movements that would maximize expected gain and we predicted how hand movements should change as the eye gathered further information about target location. We recorded human observers' eye movements and hand movements and compared them with the optimal strategy that would have maximized expected gain. We found that most observers failed to adopt the optimal search-reach strategy. We analyze and describe the strategies they did adopt.

A model of reward- and effort-based optimal decision making and motor control

Costs (e.g. energetic expenditure) and benefits (e.g. food) are central determinants of behavior. In ecology and economics, they are combined to form a utility function which is maximized to guide choices. This principle is widely used in neuroscience as a normative model of decision and action, but current versions of this model fail to consider how decisions are actually converted into actions (i.e. the formation of trajectories). Here, we describe an approach where decision making and motor control are optimal, iterative processes derived from the maximization of the discounted, weighted difference between expected rewards and foreseeable motor efforts. The model accounts for decision making in cost/benefit situations, and detailed characteristics of control and goal tracking in realistic motor tasks. As a normative construction, the model is relevant to address the neural bases and pathological aspects of decision making and motor control.

Knowing how much you don't know: a neural organization of uncertainty estimates

How we estimate uncertainty is important in decision neuroscience and has wide-ranging implications in basic and clinical neuroscience, from computational models of optimality to ideas on psychopathological disorders including anxiety, depression and schizophrenia. Empirical research in neuroscience, which has been based on divergent theoretical assumptions, has focused on the fundamental question of how uncertainty is encoded in the brain and how it influences behaviour. Here, we integrate several theoretical concepts about uncertainty into a decision-making framework. We conclude that the currently available evidence indicates that distinct neural encoding (including summary statistic-type representations) of uncertainty occurs in distinct neural systems.

Motor control is decision-making

Motor behavior may be viewed as a problem of maximizing the utility of movement outcome in the face of sensory, motor and task uncertainty. Viewed in this way, and allowing for the availability of prior knowledge in the form of a probability distribution over possible states of the world, the choice of a movement plan and strategy for motor control becomes an application of statistical decision theory. This point of view has proven successful in recent years in accounting for movement under risk, inferring the loss function used in motor tasks, and explaining motor behavior in a wide variety of circumstances.

The effect of sensory uncertainty due to amblyopia (lazy eye) on the planning and execution of visually-guided 3D reaching movements

BACKGROUND

Impairment of spatiotemporal visual processing in amblyopia has been studied extensively, but its effects on visuomotor tasks have rarely been examined. Here, we investigate how visual deficits in amblyopia affect motor planning and online control of visually-guided, unconstrained reaching movements.

METHODS

Thirteen patients with mild amblyopia, 13 with severe amblyopia and 13 visually-normal participants were recruited. Participants reached and touched a visual target during binocular and monocular viewing. Motor planning was assessed by examining spatial variability of the trajectory at 50-100 ms after movement onset. Online control was assessed by examining the endpoint variability and by calculating the coefficient of determination (R(2)) which correlates the spatial position of the limb during the movement to endpoint position.

RESULTS

Patients with amblyopia had reduced precision of the motor plan in all viewing conditions as evidenced by increased variability of the reach early in the trajectory. Endpoint precision was comparable between patients with mild amblyopia and control participants. Patients with severe amblyopia had reduced endpoint precision along azimuth and elevation during amblyopic eye viewing only, and along the depth axis in all viewing conditions. In addition, they had significantly higher R(2) values at 70% of movement time along the elevation and depth axes during amblyopic eye viewing.

CONCLUSION

Sensory uncertainty due to amblyopia leads to reduced precision of the motor plan. The ability to implement online corrections depends on the severity of the visual deficit, viewing condition, and the axis of the reaching movement. Patients with mild amblyopia used online control effectively to compensate for the reduced precision of the motor plan. In contrast, patients with severe amblyopia were not able to use online control as effectively to amend the limb trajectory especially along the depth axis, which could be due to their abnormal stereopsis.

Visual extrapolation under risk: human observers estimate and compensate for exogenous uncertainty

Humans commonly face choices between multiple options with uncertain outcomes. Such situations occur in many contexts, from purely financial decisions (which shares should I buy?) to perceptuo-motor decisions between different actions (where should I aim my shot at goal?). Regardless of context, successful decision-making requires that the uncertainty at the heart of the decision-making problem is taken into account. Here, we ask whether humans can recover an estimate of exogenous uncertainty and then use it to make good decisions. Observers viewed a small dot that moved erratically until it disappeared behind an occluder. We varied the size of the occluder and the unpredictability of the dot's path. The observer attempted to capture the dot as it emerged from behind the occluded region by setting the location and extent of a 'catcher' along the edge of the occluder. The reward for successfully catching the dot was reduced as the size of the catcher increased. We compared human performance with that of an agent maximizing expected gain and found that observers consistently selected catcher size close to this theoretical solution. These results suggest that humans are finely tuned to exogenous uncertainty information and can exploit it to guide action.