Bounded Ratio Reinforcement Learning

2026-04-20

AI Summary

This work addresses the disconnect between trust region theory and the heuristic clipping objective in Proximal Policy Optimization (PPO) by introducing the Bounded Regularized Reinforcement Learning (BRRL) framework. The authors formulate a constrained regularized policy optimization problem, derive its closed-form optimal solution, and design the Bounded Policy Optimization (BPO) algorithm to minimize the advantage-weighted divergence between the parameterized policy and this solution. They further extend BPO to Generalized BPO (GBPO) for large language model (LLM) fine-tuning. This study provides the first theoretical justification for PPO-style methods, unifying trust region optimization with a cross-entropy perspective while guaranteeing monotonic policy improvement. Experiments demonstrate that BPO and GBPO consistently match or outperform PPO and GRPO across MuJoCo, Atari, IsaacLab, and LLM fine-tuning benchmarks in both stability and final performance.

Technology Category

• Machine Learning: Online Learning & Bandits
• Search and Optimization: Learning to Search
• 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: Machine-in-the-loop, human agency and autonomy
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs

Abstract

Proximal Policy Optimization (PPO) has become the predominant algorithm for on-policy reinforcement learning due to its scalability and empirical robustness across domains. However, there is a significant disconnect between the underlying foundations of trust region methods and the heuristic clipped objective used in PPO. In this paper, we bridge this gap by introducing the Bounded Ratio Reinforcement Learning (BRRL) framework. We formulate a novel regularized and constrained policy optimization problem and derive its analytical optimal solution. We prove that this solution ensures monotonic performance improvement. To handle parameterized policy classes, we develop a policy optimization algorithm called Bounded Policy Optimization (BPO) that minimizes an advantage-weighted divergence between the policy and the analytic optimal solution from BRRL. We further establish a lower bound on the expected performance of the resulting policy in terms of the BPO loss function. Notably, our framework also provides a new theoretical lens to interpret the success of the PPO loss, and connects trust region policy optimization and the Cross-Entropy Method (CEM). We additionally extend BPO to Group-relative BPO (GBPO) for LLM fine-tuning. Empirical evaluations of BPO across MuJoCo, Atari, and complex IsaacLab environments (e.g., Humanoid locomotion), and of GBPO for LLM fine-tuning tasks, demonstrate that BPO and GBPO generally match or outperform PPO and GRPO in stability and final performance.

Problem

• Proximal Policy Optimization
• trust region methods
• policy optimization
• reinforcement learning
• clipped objective

Innovation

• Bounded Ratio Reinforcement Learning
• Bounded Policy Optimization
• Trust Region Methods
• Monotonic Performance Improvement
• LLM Fine-tuning