A Deeper Look at Discounting Mismatch in Actor-Critic Algorithms

We investigate the discounting mismatch in actor-critic algorithm implementations from a representation learning perspective. Theoretically, actor-critic algorithms usually have discounting for both actor and critic, i.e., there is a γt term in the actor update for the transition observed at time t in a trajectory and the critic is a discounted value function. Practitioners, however, usually ignore the discounting (γt) for the actor while using a discounted critic. We investigate this mismatch in two scenarios. In the first scenario, we consider optimizing an undiscounted objective (γ=1) where γt disappears naturally (1t=1). We then propose to interpret the discounting in critic in terms of a bias-variance-representation trade-off and provide supporting empirical results. In the second scenario, we consider optimizing a discounted objective (γ<1) and propose to interpret the omission of the discounting in the actor update from an auxiliary task perspective and provide supporting empirical results.