Actor-Critic Learning Control Based on <inline-formula> <tex-math notation="LaTeX">$\ell_{2}$ </tex-math> </inline-formula>-Regularized Temporal-Difference Prediction With Gradient Correction

Abstract

Actor-critic based on the policy gradient (PG-based AC) methods have been widely studied to solve learning control problems. In order to increase the data efficiency of learning prediction in the critic of PG-based AC, studies on how to use recursive least-squares temporal difference (RLS-TD) algorithms for policy evaluation have been conducted in recent years. In such contexts, the critic RLS-TD evaluates an unknown mixed policy generated by a series of different actors, but not one fixed policy generated by the current actor. Therefore, this AC framework with RLS-TD critic cannot be proved to converge to the optimal fixed point of learning problem. To address the above problem, this paper proposes a new AC framework named critic-iteration PG (CIPG), which learns the state-value function of current policy in an on-policy way and performs gradient ascent in the direction of improving discounted total reward. During each iteration, CIPG keeps the policy parameters fixed and evaluates the resulting fixed policy by -regularized RLS-TD critic. Our convergence analysis extends previous convergence analysis of PG with function approximation to the case of RLS-TD critic. The simulation results demonstrate that the -regularization term in the critic of CIPG is undamped during the learning process, and CIPG has better learning efficiency and faster convergence rate than conventional AC learning control methods.

Deep reinforcement learning using least‐squares truncated temporal‐difference

“…Xu et al propose an actor-critic algorithm using Recursive Least-Squares Temporal Difference (λ) as the critic, which is the recursive version of LSTD [20]. There are some other leastsquares-based actor-critic algorithms [21,22]. However, to the best of our knowledge, most of these methods are designed for benchmark tasks with low-dimensional feature vectors (state inputs).…”