Understanding the impact of entropy on policy optimization

TL;DR

This paper investigates how entropy regularization influences policy optimization in reinforcement learning, revealing that higher entropy can smooth the optimization landscape and facilitate learning, but also highlighting the complexity of designing universal algorithms.

Contribution

The paper introduces new visualization tools for the optimization landscape and demonstrates that entropy acts as a regularizer, affecting the geometry of policy optimization.

Findings

Higher entropy can make the landscape smoother and connect local optima.

Policy optimization remains challenging despite access to exact gradients.

Entropy regularization influences the geometry of the optimization process.

Abstract

Entropy regularization is commonly used to improve policy optimization in reinforcement learning. It is believed to help with \emph{exploration} by encouraging the selection of more stochastic policies. In this work, we analyze this claim using new visualizations of the optimization landscape based on randomly perturbing the loss function. We first show that even with access to the exact gradient, policy optimization is difficult due to the geometry of the objective function. Then, we qualitatively show that in some environments, a policy with higher entropy can make the optimization landscape smoother, thereby connecting local optima and enabling the use of larger learning rates. This paper presents new tools for understanding the optimization landscape, shows that policy entropy serves as a regularizer, and highlights the challenge of designing general-purpose policy optimization algorithms.