Entropic Regularization of Markov Decision Processes
This work addresses instability in reinforcement learning for agents interacting with unknown environments, offering a novel regularization approach that unifies actor-critic architectures, though it is incremental by extending prior KL divergence methods to a broader family.
The paper tackles the instability in reinforcement learning when system dynamics and rewards are unknown by proposing a unified framework using a broader family of f-divergences, specifically α-divergences, for entropic regularization, which provides closed-form policy improvement steps and dual objectives for policy evaluation, with asymptotic analysis showing effects on standard problems.
An optimal feedback controller for a given Markov decision process (MDP) can in principle be synthesized by value or policy iteration. However, if the system dynamics and the reward function are unknown, a learning agent must discover an optimal controller via direct interaction with the environment. Such interactive data gathering commonly leads to divergence towards dangerous or uninformative regions of the state space unless additional regularization measures are taken. Prior works proposed bounding the information loss measured by the Kullback-Leibler (KL) divergence at every policy improvement step to eliminate instability in the learning dynamics. In this paper, we consider a broader family of $f$-divergences, and more concretely $α$-divergences, which inherit the beneficial property of providing the policy improvement step in closed form at the same time yielding a corresponding dual objective for policy evaluation. Such entropic proximal policy optimization view gives a unified perspective on compatible actor-critic architectures. In particular, common least-squares value function estimation coupled with advantage-weighted maximum likelihood policy improvement is shown to correspond to the Pearson $χ^2$-divergence penalty. Other actor-critic pairs arise for various choices of the penalty-generating function $f$. On a concrete instantiation of our framework with the $α$-divergence, we carry out asymptotic analysis of the solutions for different values of $α$ and demonstrate the effects of the divergence function choice on common standard reinforcement learning problems.