Analysis of Q-learning with Adaptation and Momentum Restart for Gradient Descent

TL;DR

This paper analyzes the convergence of advanced Q-learning algorithms with adaptive and momentum restart updates, providing theoretical guarantees and demonstrating superior empirical performance over traditional methods.

Contribution

It introduces Q-AMSGrad and Q-AMSGradR algorithms with convergence analysis and shows their improved performance in control and Atari game benchmarks.

Findings

Q-AMSGrad converges with a proven rate.

Q-AMSGradR further improves convergence and performance.

Both algorithms outperform vanilla Q-learning and DQN in experiments.

Abstract

Existing convergence analyses of Q-learning mostly focus on the vanilla stochastic gradient descent (SGD) type of updates. Despite the Adaptive Moment Estimation (Adam) has been commonly used for practical Q-learning algorithms, there has not been any convergence guarantee provided for Q-learning with such type of updates. In this paper, we first characterize the convergence rate for Q-AMSGrad, which is the Q-learning algorithm with AMSGrad update (a commonly adopted alternative of Adam for theoretical analysis). To further improve the performance, we propose to incorporate the momentum restart scheme to Q-AMSGrad, resulting in the so-called Q-AMSGradR algorithm. The convergence rate of Q-AMSGradR is also established. Our experiments on a linear quadratic regulator problem show that the two proposed Q-learning algorithms outperform the vanilla Q-learning with SGD updates. The two algorithms also exhibit significantly better performance than the DQN learning method over a batch of Atari 2600 games.