Expected Policy Gradients for Reinforcement Learning

TL;DR

Expected Policy Gradients (EPG) unify stochastic and deterministic policy gradients, reducing variance and improving performance in reinforcement learning across continuous and discrete actions.

Contribution

The paper introduces EPG, a novel framework that generalizes policy gradients, providing analytical methods for various policies and demonstrating superior empirical results.

Findings

EPG reduces gradient estimate variance.

EPG outperforms existing methods in control tasks.

A new policy gradient theorem unifies stochastic and deterministic approaches.

Abstract

We propose expected policy gradients (EPG), which unify stochastic policy gradients (SPG) and deterministic policy gradients (DPG) for reinforcement learning. Inspired by expected sarsa, EPG integrates (or sums) across actions when estimating the gradient, instead of relying only on the action in the sampled trajectory. For continuous action spaces, we first derive a practical result for Gaussian policies and quadratic critics and then extend it to a universal analytical method, covering a broad class of actors and critics, including Gaussian, exponential families, and policies with bounded support. For Gaussian policies, we introduce an exploration method that uses covariance proportional to the matrix exponential of the scaled Hessian of the critic with respect to the actions. For discrete action spaces, we derive a variant of EPG based on softmax policies. We also establish a new general policy gradient theorem, of which the stochastic and deterministic policy gradient theorems are special cases. Furthermore, we prove that EPG reduces the variance of the gradient estimates without requiring deterministic policies and with little computational overhead. Finally, we provide an extensive experimental evaluation of EPG and show that it outperforms existing approaches on multiple challenging control domains.