Beyond the Policy Gradient Theorem for Efficient Policy Updates in Actor-Critic Algorithms

TL;DR

This paper introduces a novel policy update method in Actor-Critic algorithms that improves unlearning speed and guarantees convergence, addressing limitations of traditional policy gradient updates in reinforcement learning.

Contribution

It proposes a new policy update based on cross-entropy loss, proves its convergence to global optimality, and compares it analytically and empirically with standard methods.

Findings

The new update accelerates unlearning in policy optimization.

It guarantees convergence to the global optimum under standard assumptions.

Empirical results validate theoretical improvements over traditional policy gradients.

Abstract

In Reinforcement Learning, the optimal action at a given state is dependent on policy decisions at subsequent states. As a consequence, the learning targets evolve with time and the policy optimization process must be efficient at unlearning what it previously learnt. In this paper, we discover that the policy gradient theorem prescribes policy updates that are slow to unlearn because of their structural symmetry with respect to the value target. To increase the unlearning speed, we study a novel policy update: the gradient of the cross-entropy loss with respect to the action maximizing $q$, but find that such updates may lead to a decrease in value. Consequently, we introduce a modified policy update devoid of that flaw, and prove its guarantees of convergence to global optimality in $\mathcal{O}(t^{-1})$ under classic assumptions. Further, we assess standard policy updates and our cross-entropy policy updates along six analytical dimensions. Finally, we empirically validate our theoretical findings.