Bayesian deterministic decision making: a normative account of the operant matching law and heavy-tailed reward history dependency of choices

How do animals weigh conflicting information about reward sources over time? Comparing dynamic averaging models

Optimal foraging theory suggests that animals make decisions which maximize their food intake per unit time when foraging, but the mechanisms animals use to track the value of behavioral alternatives and choose between them remain unclear. Several models for how animals integrate past experience have been suggested. However, these models make differential predictions for the occurrence of spontaneous recovery of choice: a behavioral phenomenon in which a hiatus from the experimental environment results in animals reverting to a behavioral allocation consistent with a reward distribution from the more distant past, rather than one consistent with their most recently experienced distribution. To explore this phenomenon and compare these models, three free-operant experiments with rats were conducted using a serial reversal design. In Phase 1, two responses (A and B) were baited with pellets on concurrent variable interval schedules, favoring option A. In Phase 2, lever baiting was reversed to favor option B. Rats then entered a delay period, where they were maintained at weight in their home cages and no experimental sessions took place. Following this delay, preference was assessed using initial responding in test sessions where levers were presented, but not baited. Models were compared in performance, including an exponentially weighted moving average, the Temporal Weighting Rule, and variants of these models. While the data provided strong evidence of spontaneous recovery of choice, the form and extent of recovery was inconsistent with the models under investigation. Potential interpretations are discussed in relation to both the decision rule and valuation functions employed.

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.