A unified view of entropy-regularized Markov decision processes
This work provides a unified theoretical foundation for entropy-regularized RL algorithms, addressing convergence issues for researchers and practitioners in reinforcement learning.
The paper tackles the problem of entropy-regularized average-reward reinforcement learning in Markov decision processes by proposing a general framework based on linear programming, showing that conditional entropy regularization leads to a dual problem resembling Bellman optimality equations, and proving convergence for TRPO while identifying potential non-convergence in some policy gradient methods.
We propose a general framework for entropy-regularized average-reward reinforcement learning in Markov decision processes (MDPs). Our approach is based on extending the linear-programming formulation of policy optimization in MDPs to accommodate convex regularization functions. Our key result is showing that using the conditional entropy of the joint state-action distributions as regularization yields a dual optimization problem closely resembling the Bellman optimality equations. This result enables us to formalize a number of state-of-the-art entropy-regularized reinforcement learning algorithms as approximate variants of Mirror Descent or Dual Averaging, and thus to argue about the convergence properties of these methods. In particular, we show that the exact version of the TRPO algorithm of Schulman et al. (2015) actually converges to the optimal policy, while the entropy-regularized policy gradient methods of Mnih et al. (2016) may fail to converge to a fixed point. Finally, we illustrate empirically the effects of using various regularization techniques on learning performance in a simple reinforcement learning setup.