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Within a rational framework, a decision-maker selects actions based on the reward-maximization principle, which stipulates that they acquire outcomes with the highest value at the lowest cost. Action selection can be divided into two dimensions: selecting an action from various alternatives, and choosing its vigor, i.e., how fast the selected action should be executed. Both of these dimensions depend on the values of outcomes, which are often affected as more outcomes are consumed together with their associated actions. Despite this, previous research has only addressed the computational substrate of optimal actions in the specific condition that the values of outcomes are constant. It is not known what actions are optimal when the values of outcomes are non-stationary. Here, based on an optimal control framework, we derive a computational model for optimal actions when outcome values are non-stationary. The results imply that, even when the values of outcomes are changing, the optimal response rate is constant rather than decreasing. This finding shows that, in contrast to previous theories, commonly observed changes in action rate cannot be attributed solely to changes in outcome value. We then prove that this observation can be explained based on uncertainty about temporal horizons; e.g., the session duration. We further show that, when multiple outcomes are available, the model explains probability matching as well as maximization strategies. The model therefore provides a quantitative analysis of optimal action and explicit predictions for future testing.

Optimal response vigor and choice under non-stationary outcome values