Finite-Time Performance Bounds and Adaptive Learning Rate Selection for Two Time-Scale Reinforcement Learning

TL;DR

This paper derives finite-time performance bounds for two time-scale reinforcement learning algorithms, introduces an adaptive learning rate scheme based on Lyapunov functions, and demonstrates improved convergence in experiments.

Contribution

It provides the first finite-time bounds for two time-scale stochastic approximation algorithms and proposes an adaptive learning rate method that enhances convergence speed.

Findings

Adaptive learning rate significantly improves convergence.

Finite-time bounds are established for fixed learning rates.

Experimental results show better performance than polynomial decay rules.

Abstract

We study two time-scale linear stochastic approximation algorithms, which can be used to model well-known reinforcement learning algorithms such as GTD, GTD2, and TDC. We present finite-time performance bounds for the case where the learning rate is fixed. The key idea in obtaining these bounds is to use a Lyapunov function motivated by singular perturbation theory for linear differential equations. We use the bound to design an adaptive learning rate scheme which significantly improves the convergence rate over the known optimal polynomial decay rule in our experiments, and can be used to potentially improve the performance of any other schedule where the learning rate is changed at pre-determined time instants.