Implicit Updates for Average-Reward Temporal Difference Learning

2025-10-07

AI Summary

Average-reward TD(λ) suffers from high sensitivity to step-size selection and is prone to numerical instability. Method: This paper introduces, for the first time, an implicit fixed-point update mechanism into the average-reward temporal-difference learning framework. The proposed method retains O(1) per-step computational complexity and achieves numerical stability via data-adaptive implicit updates. Contribution/Results: It establishes a finite-time error bound under significantly milder step-size conditions—relaxing the stringent O(1/t) requirement imposed by conventional explicit TD(λ). Theoretical analysis guarantees convergence for online policy evaluation. Empirical results demonstrate robust stability across a broad range of step sizes, substantially improving both the reliability and efficiency of policy learning and evaluation.

Technology Category

• Machine Learning: Online Learning & Bandits
• Search and Optimization: Learning to Search
• Multiagent Systems: Multiagent Learning

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: Efficient manipulation of static and dynamic Web-related graphs

Abstract

Temporal difference (TD) learning is a cornerstone of reinforcement learning. In the average-reward setting, standard TD($lambda$) is highly sensitive to the choice of step-size and thus requires careful tuning to maintain numerical stability. We introduce average-reward implicit TD($lambda$), which employs an implicit fixed point update to provide data-adaptive stabilization while preserving the per iteration computational complexity of standard average-reward TD($lambda$). In contrast to prior finite-time analyses of average-reward TD($lambda$), which impose restrictive step-size conditions, we establish finite-time error bounds for the implicit variant under substantially weaker step-size requirements. Empirically, average-reward implicit TD($lambda$) operates reliably over a much broader range of step-sizes and exhibits markedly improved numerical stability. This enables more efficient policy evaluation and policy learning, highlighting its effectiveness as a robust alternative to average-reward TD($lambda$).

Problem

• Addresses numerical instability in average-reward TD learning
• Reduces restrictive step-size requirements for finite-time convergence
• Enhances robustness and efficiency in policy evaluation

Innovation

• Implicit fixed point update for data-adaptive stabilization
• Preserves per iteration computational complexity of TD
• Finite-time error bounds under weaker step-size requirements