Variational actor-critic algorithms^*,,^**

¹ Department of Mathematics and Halicioğlu Data Science Institute, University of California, San Diego, La Jolla, California, USA
² Department of Mathematics, Stanford University, Stanford, California, USA

^*** Corresponding author: yuhuazhu@stanford.edu

Received: 2 August 2021
Accepted: 13 January 2023

Abstract

We introduce a class of variational actor-critic algorithms based on a variational formulation over both the value function and the policy. The objective function of the variational formulation consists of two parts: one for maximizing the value function and the other for minimizing the Bellman residual. Besides the vanilla gradient descent with both the value function and the policy updates, we propose two variants, the clipping method and the flipping method, in order to speed up the convergence. We also prove that, when the prefactor of the Bellman residual is sufficiently large, the fixed point of the algorithm is close to the optimal policy.