Kernel-Based Least Squares Temporal Difference With Gradient Correction

Recursive Least-Squares Temporal Difference With Gradient Correction

Since the late 1980s, temporal difference (TD) learning has dominated the research area of policy evaluation algorithms. However, the demand for the avoidance of TD defects, such as low data-efficiency and divergence in off-policy learning, has inspired the studies of a large number of novel TD-based approaches. Gradient-based and least-squares-based algorithms comprise the major part of these new approaches. This paper aims to combine advantages of these two categories to derive an efficient policy evaluation algorithm with O ( n ² ) per-time-step runtime complexity. The least-squares-based framework is adopted, and the gradient correction is used to improve convergence performance. This paper begins with the revision of a previous O ( n ³ ) batch algorithm, least-squares TD with a gradient correction (LS-TDC) to regularize the parameter vector. Based on the recursive least-squares technique, an O ( n ² ) counterpart of LS-TDC called RC is proposed. To increase data efficiency, we generalize RC with eligibility traces. An off-policy extension is also proposed based on importance sampling. In addition, the convergence analysis for RC as well as LS-TDC is given. The empirical results in both on-policy and off-policy benchmarks show that RC has a higher estimation accuracy than that of RLSTD and a significantly lower runtime complexity than that of LSTDC.

Actor-Critic Learning Control Based on -Regularized Temporal-Difference Prediction With Gradient Correction

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.