Hybrid Group Relative Policy Optimization: A Multi-Sample Approach to Enhancing Policy Optimization

Hybrid Group Relative Policy Optimization (Hybrid GRPO) is a reinforcement learning framework that extends Proximal Policy Optimization (PPO) and Group Relative Policy Optimization (GRPO) by incorporating empirical multi-sample action evaluation while preserving the stability of value function-based learning. Unlike DeepSeek GRPO, which eliminates the value function in favor of purely empirical reward estimation, Hybrid GRPO introduces a structured advantage computation method that balances empirical action sampling with bootstrapped value estimation. This approach enhances sample efficiency, improves learning stability, and mitigates variance amplification observed in purely empirical methods. A detailed mathematical comparison between PPO, DeepSeek GRPO, and Hybrid GRPO is presented, highlighting key differences in advantage estimation and policy updates. Experimental validation in a controlled reinforcement learning environment demonstrates that Hybrid GRPO achieves superior convergence speed, more stable policy updates, and improved sample efficiency compared to existing methods. Several extensions to Hybrid GRPO are explored, including entropy-regularized sampling, hierarchical multi-step sub-sampling, adaptive reward normalization, and value-based action selection. Beyond reinforcement learning in simulated environments, Hybrid GRPO provides a scalable framework for bridging the gap between large language models (LLMs) and real-world agent-based decision-making. By integrating structured empirical sampling with reinforcement learning stability mechanisms, Hybrid GRPO has potential applications in autonomous robotics, financial modeling, and AI-driven control systems. These findings suggest that Hybrid GRPO serves as a robust and adaptable reinforcement learning methodology, paving the way for further advancements in policy optimization.