An Analysis of Measure-Valued Derivatives for Policy Gradients

TL;DR

This paper explores the Measure-Valued Derivative as a low-variance, unbiased gradient estimator for policy gradients in reinforcement learning, applicable to both differentiable and non-differentiable function approximators.

Contribution

It introduces and empirically evaluates the Measure-Valued Derivative estimator as a versatile alternative to likelihood-ratio and reparametrization tricks in policy gradient methods.

Findings

Achieves comparable performance to existing methods in various action space dimensions.

Can be used with non-differentiable function approximators.

Offers low variance and unbiased gradient estimates.

Abstract

Reinforcement learning methods for robotics are increasingly successful due to the constant development of better policy gradient techniques. A precise (low variance) and accurate (low bias) gradient estimator is crucial to face increasingly complex tasks. Traditional policy gradient algorithms use the likelihood-ratio trick, which is known to produce unbiased but high variance estimates. More modern approaches exploit the reparametrization trick, which gives lower variance gradient estimates but requires differentiable value function approximators. In this work, we study a different type of stochastic gradient estimator - the Measure-Valued Derivative. This estimator is unbiased, has low variance, and can be used with differentiable and non-differentiable function approximators. We empirically evaluate this estimator in the actor-critic policy gradient setting and show that it can reach comparable performance with methods based on the likelihood-ratio or reparametrization tricks, both in low and high-dimensional action spaces. With this work, we want to show that the Measure-Valued Derivative estimator can be a useful alternative to other policy gradient estimators.