Bounded Ratio Reinforcement Learning

Reinforcement Learning (RL) has made significant strides in recent years across various domains, particularly in applications such as robotic control, game AI, and autonomous driving. Proximal Policy Optimization (PPO) is a widely adopted policy optimization algorithm known for its stability and scalability. However, the objective function of PPO primarily relies on heuristic design driven by experimentation rather than rigorous theoretical derivation. This has led to a significant gap between the theoretical foundations and practical applications of PPO. Although numerous PPO variants have been proposed to improve its performance, these variants mostly rely on existing trust region policy optimization (TRPO) theory, failing to provide new theoretical frameworks or performance guarantees. Consequently, researchers have been seeking a framework that can theoretically explain the success of PPO.

The core problem with PPO lies in its objective function design, which primarily relies on heuristic methods rather than rigorous theoretical derivation. This has resulted in a significant gap between the theoretical foundations and practical applications of PPO. Specifically, the PPO objective function is not directly derived from the trust region formulation it was intended to approximate but rather through experimentation-driven heuristic design. While this design method performs well in practice, it lacks theoretical explanation and guarantees. Additionally, existing PPO variants mostly rely on existing trust region policy optimization (TRPO) theory, failing to provide new theoretical frameworks or performance guarantees.

The core innovation of this paper lies in the introduction of the Bounded Ratio Reinforcement Learning (BRRL) framework, which replaces traditional KL divergence constraints with bounded ratio constraints. Specifically, the BRRL framework provides a new structure for policy updates by constraining the range of policy likelihood ratios. The authors derive the analytical optimal solution of BRRL and prove that it ensures monotonic performance improvement. Additionally, to handle parameterized policy classes, they develop a Bounded Policy Optimization (BPO) algorithm that minimizes an advantage-weighted divergence between the policy and the BRRL analytical optimal solution. They also extend BPO to Group-relative BPO (GBPO) for fine-tuning large language models (LLMs).

• �� Introduce the Bounded Ratio Reinforcement Learning (BRRL) framework, replacing traditional KL divergence constraints with bounded ratio constraints.
• �� Derive the analytical optimal solution of BRRL and prove its monotonic performance improvement.
• �� Develop the Bounded Policy Optimization (BPO) algorithm, minimizing an advantage-weighted divergence between the policy and the BRRL analytical optimal solution.
• �� Extend BPO to Group-relative BPO (GBPO) for fine-tuning large language models (LLMs).
• �� Conduct experiments in MuJoCo, Atari, and complex IsaacLab environments to evaluate the performance of BPO and GBPO.

The experimental design includes evaluating the performance of BPO and GBPO in MuJoCo, Atari, and IsaacLab environments. In the MuJoCo environment, Ant-v4, Hopper-v4, and Humanoid-v4 were chosen as test benchmarks. In the Atari environment, Asterix and Breakout were selected as test benchmarks. Additionally, complex quadruped and humanoid tasks were tested in IsaacLab. Baseline algorithms used in the experiments include PPO and GRPO. Standard performance metrics, such as total reward and stability, were used to evaluate the algorithms' performance.

The experimental results show that BPO achieved a total reward of 4871.4 in the Ant-v4 task in the MuJoCo environment, significantly outperforming PPO's 4230.1. In the Atari game Asterix, BPO scored 9471.5, surpassing PPO's 7122.8, demonstrating superior stability and final performance. Additionally, GBPO performed excellently in LLM fine-tuning tasks, providing better stability and performance compared to GRPO. The experimental results validate the effectiveness of the BRRL framework and demonstrate its superior performance across various complex environments.

The BRRL framework and BPO algorithm can be directly applied to domains such as robotic control, game AI, and large language model fine-tuning. In robotic control, BPO can be used to optimize the motion strategies of robots, improving their stability and performance in complex environments. In game AI, BPO can be used to train smarter game agents, enhancing their performance across various games. In large language model fine-tuning, GBPO can be used to optimize the model's generative capabilities, improving its performance in natural language processing tasks.

Despite the excellent performance of the BRRL framework in multiple experiments, the parameterization of policies in high-dimensional continuous action spaces may lead to increased computational complexity. Additionally, in certain extreme environments, the performance improvement of BPO may not meet expectations. Future research could explore the application of the BRRL framework in more complex environments, especially tasks with high-dimensional continuous action spaces. Additionally, integrating the BRRL framework with other reinforcement learning methods to enhance adaptability and performance across different tasks could be investigated.