Evidence for Hyperbolic Temporal Discounting of Reward in Control of Movements

Suppose that the purpose of a movement is to place the body in a more rewarding state. In this framework, slower movements may increase accuracy and therefore improve the probability of acquiring reward, but the longer durations of slow movements produce devaluation of reward. Here we hypothesize that the brain decides the vigor of a movement (duration and velocity) based on the expected discounted reward associated with that movement. We begin by showing that durations of saccades of varying amplitude can be accurately predicted by a model in which motor commands maximize expected discounted reward. This result suggests that reward is temporally discounted even in timescales of tens of milliseconds. One interpretation of temporal discounting is that the true objective of the brain is to maximize the rate of reward—which is equivalent to a specific form of hyperbolic discounting. A consequence of this idea is that the vigor of saccades should change as one alters the intertrial intervals between movements. We find experimentally that in healthy humans, as intertrial intervals are varied, saccade peak velocities and durations change on a trial-by-trial basis precisely as predicted by a model in which the objective is to maximize the rate of reward. Our results are inconsistent with theories in which reward is discounted exponentially. We suggest that there exists a single cost, rate of reward, which provides a unifying principle that may govern control of movements in timescales of milliseconds, as well as decision making in timescales of seconds to years.