Breaking the Deadly Triad with a Target Network

TL;DR

This paper demonstrates how a novel target network update rule can stabilize off-policy reinforcement learning algorithms employing function approximation and bootstrapping, effectively addressing the deadly triad problem.

Contribution

It introduces a new target network update method with projections, providing theoretical convergence guarantees for off-policy RL algorithms without bi-level optimization.

Findings

Proposes a novel target network update rule with projections.

Shows convergence of off-policy algorithms to regularized TD fixed points.

First to establish convergent linear Q-learning under nonrestrictive policies.

Abstract

The deadly triad refers to the instability of a reinforcement learning algorithm when it employs off-policy learning, function approximation, and bootstrapping simultaneously. In this paper, we investigate the target network as a tool for breaking the deadly triad, providing theoretical support for the conventional wisdom that a target network stabilizes training. We first propose and analyze a novel target network update rule which augments the commonly used Polyak-averaging style update with two projections. We then apply the target network and ridge regularization in several divergent algorithms and show their convergence to regularized TD fixed points. Those algorithms are off-policy with linear function approximation and bootstrapping, spanning both policy evaluation and control, as well as both discounted and average-reward settings. In particular, we provide the first convergent linear $Q$-learning algorithms under nonrestrictive and changing behavior policies without bi-level optimization.