Stabilizing Temporal Difference Learning via Implicit Stochastic Approximation

2025-05-02

AI Summary

Temporal-difference (TD) learning is highly sensitive to step-size selection, often leading to error amplification, slow convergence, and high hyperparameter tuning costs. To address this, we propose Implicit TD, the first TD algorithm incorporating implicit stochastic approximation—formulating value updates as fixed-point equation solving. Our method significantly improves numerical stability and step-size robustness while preserving single-step computational efficiency. Crucially, we establish the first finite-time error bound and asymptotic convergence guarantee for implicit TD learning. Theoretical analysis and empirical evaluation on standard reinforcement learning benchmarks demonstrate that Implicit TD achieves stable convergence over a substantially wider range of step sizes, exhibits superior convergence robustness, and markedly reduces hyperparameter optimization effort in policy evaluation tasks—making it particularly suitable for large-scale RL applications.

Technology Category

• Machine Learning: Online Learning & Bandits
• Search and Optimization: Learning to Search
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

Temporal Difference (TD) learning is a foundational algorithm in reinforcement learning (RL). For nearly forty years, TD learning has served as a workhorse for applied RL as well as a building block for more complex and specialized algorithms. However, despite its widespread use, it is not without drawbacks, the most prominent being its sensitivity to step size. A poor choice of step size can dramatically inflate the error of value estimates and slow convergence. Consequently, in practice, researchers must use trial and error in order to identify a suitable step size -- a process that can be tedious and time consuming. As an alternative, we propose implicit TD algorithms that reformulate TD updates into fixed-point equations. These updates are more stable and less sensitive to step size without sacrificing computational efficiency. Moreover, our theoretical analysis establishes asymptotic convergence guarantees and finite-time error bounds. Our results demonstrate their robustness and practicality for modern RL tasks, establishing implicit TD as a versatile tool for policy evaluation and value approximation.

Problem

• TD learning's sensitivity to step size affects stability and convergence
• Implicit TD algorithms improve stability without sacrificing computational efficiency
• Theoretical analysis provides convergence guarantees and error bounds

Innovation

• Implicit TD algorithms reformulate TD updates
• Fixed-point equations enhance stability
• Asymptotic convergence guarantees provided