Implicit Q-Learning and SARSA: Liberating Policy Control from Step-Size Calibration

2026-01-26

AI Summary

This work addresses the high sensitivity of traditional Q-learning and SARSA to step size, which typically requires meticulous hyperparameter tuning to ensure stability and convergence speed. The authors reformulate the update rules of both algorithms as fixed-point equations and propose an implicit reinforcement learning update mechanism that leverages implicit optimization to achieve adaptive step-size adjustment. This approach automatically regularizes learning without manual parameter tuning. Theoretical analysis demonstrates that the method substantially expands the allowable range of stable step sizes—even supporting arbitrarily large step sizes—while maintaining convergence guarantees. Empirical evaluations on benchmark tasks with both discrete and continuous state spaces confirm the robustness of the proposed method to step-size selection, consistently delivering stable and efficient performance where standard algorithms fail due to overly large step sizes.

Technology Category

• Search and Optimization: Learning to Search
• Machine Learning: Online Learning & Bandits
• Intelligent Robots: Learning & Optimization for ROB

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
• Economics, Online Markets and Human Computation: Social networks and social learning

Abstract

Q-learning and SARSA are foundational reinforcement learning algorithms whose practical success depends critically on step-size calibration. Step-sizes that are too large can cause numerical instability, while step-sizes that are too small can lead to slow progress. We propose implicit variants of Q-learning and SARSA that reformulate their iterative updates as fixed-point equations. This yields an adaptive step-size adjustment that scales inversely with feature norms, providing automatic regularization without manual tuning. Our non-asymptotic analyses demonstrate that implicit methods maintain stability over significantly broader step-size ranges. Under favorable conditions, it permits arbitrarily large step-sizes while achieving comparable convergence rates. Empirical validation across benchmark environments spanning discrete and continuous state spaces shows that implicit Q-learning and SARSA exhibit substantially reduced sensitivity to step-size selection, achieving stable performance with step-sizes that would cause standard methods to fail.

Problem

• Q-learning
• SARSA
• step-size calibration
• reinforcement learning
• numerical stability

Innovation

• Implicit Q-Learning
• Implicit SARSA
• Adaptive Step-Size
• Fixed-Point Update
• Automatic Regularization