Discounted Reinforcement Learning is Not an Optimization Problem

Discounted reinforcement learning is fundamentally incompatible with function approximation for control in continuing tasks. It is not an optimization problem in its usual formulation, so when using function approximation there is no optimal policy. We substantiate these claims, then go on to address some misconceptions about discounting and its connection to the average reward formulation. We encourage researchers to adopt rigorous optimization approaches, such as maximizing average reward, for reinforcement learning in continuing tasks.