n-Step Temporal Difference Learning with Optimal n

TL;DR

This paper introduces a model-free stochastic optimization method to find the optimal n in n-step TD learning, demonstrating convergence and superior performance over existing algorithms on benchmark RL tasks.

Contribution

It adapts SPSA for discrete optimization to determine the optimal n in n-step TD, with proven convergence and improved results over OCBA.

Findings

SDPSA converges to the optimal n almost surely.

SDPSA outperforms OCBA on benchmark RL tasks.

The method effectively finds the optimal n for various initializations.

Abstract

We consider the problem of finding the optimal value of n in the n-step temporal difference (TD) learning algorithm. Our objective function for the optimization problem is the average root mean squared error (RMSE). We find the optimal n by resorting to a model-free optimization technique involving a one-simulation simultaneous perturbation stochastic approximation (SPSA) based procedure. Whereas SPSA is a zeroth-order continuous optimization procedure, we adapt it to the discrete optimization setting by using a random projection operator. We prove the asymptotic convergence of the recursion by showing that the sequence of n-updates obtained using zeroth-order stochastic gradient search converges almost surely to an internally chain transitive invariant set of an associated differential inclusion. This results in convergence of the discrete parameter sequence to the optimal n in n-step TD. Through experiments, we show that the optimal value of n is achieved with our SDPSA algorithm for arbitrary initial values. We further show using numerical evaluations that SDPSA outperforms the state-of-the-art discrete parameter stochastic optimization algorithm Optimal Computing Budget Allocation (OCBA) on benchmark RL tasks.