Towards Optimal Policy Improvement

2026-10-01

AI Summary

This study addresses the fundamental limitation that policy improvement based on approximate value estimation in reinforcement learning typically lacks optimality guarantees. By revisiting optimal policy improvement from first principles, this work reformulates the improvement problem over restricted state spaces as solving an induced Markov Decision Process (MDP). Integrating probabilistic decision theory, it introduces an optimal greedification operator framework and derives novel operators along with their gradient approximation algorithms under constrained conditions. The proposed approach yields significant performance improvements across discrete and continuous action spaces, as well as online and offline reinforcement learning settings, as demonstrated on benchmarks including Gumbel AlphaZero and SAC. Ultimately, this research establishes a rigorous theoretical foundation alongside an efficient practical methodology for principled policy improvement.

Abstract

Practical Reinforcement Learning (RL) algorithms learn to solve Markov Decision Processes (MDPs) through iterative policy improvement in the presence of approximate evaluation. We study policy improvement from first principles, defining optimal policy improvement as producing the best policy attainable in a single update under specified constraints. We show that optimal improvement restricted to a set of states is equivalent to solving an induced MDP, characterizing planning with an explicit or implicit model as a path towards optimal policy improvement. Because practical methods commonly solve such induced problems through iterative improvement in the form of greedification, we take steps towards optimal greedification under the central practical constraint of approximate evaluation. We formulate greedification under this constraint as probabilistic decision-making under uncertainty and derive a novel operator that is optimal with respect to the resulting objective. Empirically, the operator and its practical gradient-based approximations improve aggregate performance across GumbelAlphaZero, SAC, ReBRAC and Generalized Policy Iteration, in experiments spanning discrete and continuous actions, model-based and model-free, online and offline RL.

Problem

• Reinforcement Learning
• Policy Improvement
• Approximate Evaluation
• Greedification
• Markov Decision Processes

Innovation

• Optimal Policy Improvement
• Induced MDP
• Greedification
• Approximate Evaluation
• Probabilistic Decision-Making