Bayesian methods applied to the generalized matching law

Undermatching Is a Consequence of Policy Compression

The matching law describes the tendency of agents to match the ratio of choices allocated to the ratio of rewards received when choosing among multiple options (Herrnstein, 1961). Perfect matching, however, is infrequently observed. Instead, agents tend to undermatch or bias choices toward the poorer option. Overmatching, or the tendency to bias choices toward the richer option, is rarely observed. Despite the ubiquity of undermatching, it has received an inadequate normative justification. Here, we assume agents not only seek to maximize reward, but also seek to minimize cognitive cost, which we formalize as policy complexity (the mutual information between actions and states of the environment). Policy complexity measures the extent to which the policy of an agent is state dependent. Our theory states that capacity-constrained agents (i.e., agents that must compress their policies to reduce complexity) can only undermatch or perfectly match, but not overmatch, consistent with the empirical evidence. Moreover, using mouse behavioral data (male), we validate a novel prediction about which task conditions exaggerate undermatching. Finally, in patients with Parkinson's disease (male and female), we argue that a reduction in undermatching with higher dopamine levels is consistent with an increased policy complexity.SIGNIFICANCE STATEMENT The matching law describes the tendency of agents to match the ratio of choices allocated to different options to the ratio of reward received. For example, if option a yields twice as much reward as option b, matching states that agents will choose option a twice as much. However, agents typically undermatch: they choose the poorer option more frequently than expected. Here, we assume that agents seek to simultaneously maximize reward and minimize the complexity of their action policies. We show that this theory explains when and why undermatching occurs. Neurally, we show that policy complexity, and by extension undermatching, is controlled by tonic dopamine, consistent with other evidence that dopamine plays an important role in cognitive resource allocation.

Entropy-based metrics for predicting choice behavior based on local response to reward

For decades, behavioral scientists have used the matching law to quantify how animals distribute their choices between multiple options in response to reinforcement they receive. More recently, many reinforcement learning (RL) models have been developed to explain choice by integrating reward feedback over time. Despite reasonable success of RL models in capturing choice on a trial-by-trial basis, these models cannot capture variability in matching behavior. To address this, we developed metrics based on information theory and applied them to choice data from dynamic learning tasks in mice and monkeys. We found that a single entropy-based metric can explain 50% and 41% of variance in matching in mice and monkeys, respectively. We then used limitations of existing RL models in capturing entropy-based metrics to construct more accurate models of choice. Together, our entropy-based metrics provide a model-free tool to predict adaptive choice behavior and reveal underlying neural mechanisms.

Meta-analyses and effect sizes in applied behavior analysis: A review and discussion

For more than four decades, researchers have used meta-analyses to synthesize data from multiple experimental studies often to draw conclusions that are not supported by individual studies. More recently, single-case experimental design (SCED) researchers have adopted meta-analysis techniques to answer research questions with data gleaned from SCED experiments. Meta-analyses enable researchers to answer questions regarding intervention efficacy, generality, and condition boundaries. Here we discuss meta-analysis techniques, the rationale for their adaptation with SCED studies, and current indices used to quantify the effect of SCED data in applied behavior analysis.

In search of a definition of reinforcer value: Some successes and failures of the multiplicative hyperbolic model

The concept of 'value' has enjoyed a central position in many theoretical accounts of choice behaviour. Several definitions of 'value' are contrasted in this paper, and one particular approach is defended, whereby value is defined as a dimensionless intervening variable. This definition is a cornerstone of the multiplicative hyperbolic model of choice (MHM), which was proposed twenty years ago as a modification of Mazur's (1987) hyperbolic model of delay discounting. This paper reviews some of the merits and shortcomings of MHM, and suggests some ways in which MHM might be extended and improved. A formal link between 'value' and the related concept of 'response strength' is suggested, and revisions of the model are proposed which may enable it to accommodate several behavioural phenomena not considered in the original formulation. Broadening the scope of MHM comes at the cost of adding to its burden of free parameters, and it is emphasised that addition of any new parameters needs empirical justification. The status of value as a dimensionless intervening variable is upheld; however it is noted that a growing body of empirical evidence for links between neurobiological phenomena and value suggests that interpretation of value as a hypothetical construct may be warranted.