Actor-critic is implicitly biased towards high entropy optimal policies

TL;DR

This paper demonstrates that a simple actor-critic algorithm inherently favors high entropy optimal policies, enabling convergence without explicit regularization, exploration, or mixing assumptions, even from a single trajectory.

Contribution

It reveals the implicit high entropy bias of actor-critic methods and introduces tools for analyzing mixing times and implicit regularization effects.

Findings

The algorithm prefers high entropy policies even without explicit regularization.

Convergence to optimal policies occurs without mixing assumptions or exploration strategies.

The analysis decouples actor and critic concerns using mirror descent and provides bounds on mixing times.

Abstract

We show that the simplest actor-critic method -- a linear softmax policy updated with TD through interaction with a linear MDP, but featuring no explicit regularization or exploration -- does not merely find an optimal policy, but moreover prefers high entropy optimal policies. To demonstrate the strength of this bias, the algorithm not only has no regularization, no projections, and no exploration like $\epsilon$-greedy, but is moreover trained on a single trajectory with no resets. The key consequence of the high entropy bias is that uniform mixing assumptions on the MDP, which exist in some form in all prior work, can be dropped: the implicit regularization of the high entropy bias is enough to ensure that all chains mix and an optimal policy is reached with high probability. As auxiliary contributions, this work decouples concerns between the actor and critic by writing the actor update as an explicit mirror descent, provides tools to uniformly bound mixing times within KL balls of policy space, and provides a projection-free TD analysis with its own implicit bias which can be run from an unmixed starting distribution.