Target Networks and Over-parameterization Stabilize Off-policy Bootstrapping with Function Approximation

TL;DR

This paper demonstrates that combining target networks with over-parameterized linear function approximation improves convergence guarantees for off-policy value estimation, supported by theoretical proofs and empirical evaluations.

Contribution

It introduces a novel convergence condition for bootstrapped value estimation using both target networks and over-parameterization, extending to control tasks and truncated trajectories.

Findings

We establish weaker convergence conditions for off-policy learning.

Empirical results show improved stability on Baird's counterexample and Four-room task.

Theoretical bounds confirm high-probability error guarantees.

Abstract

We prove that the combination of a target network and over-parameterized linear function approximation establishes a weaker convergence condition for bootstrapped value estimation in certain cases, even with off-policy data. Our condition is naturally satisfied for expected updates over the entire state-action space or learning with a batch of complete trajectories from episodic Markov decision processes. Notably, using only a target network or an over-parameterized model does not provide such a convergence guarantee. Additionally, we extend our results to learning with truncated trajectories, showing that convergence is achievable for all tasks with minor modifications, akin to value truncation for the final states in trajectories. Our primary result focuses on temporal difference estimation for prediction, providing high-probability value estimation error bounds and empirical analysis on Baird's counterexample and a Four-room task. Furthermore, we explore the control setting, demonstrating that similar convergence conditions apply to Q-learning.