Beginner Explanation
Imagine you’re trying to learn how to ride a bike. At first, you might wobble a lot and fall over. Each time you fall, you learn something about what not to do. GRPO is like a coach that helps you ride better by giving you tips based on your practice. It looks at how well you did, learns from your mistakes, and helps you adjust your riding technique to improve next time. So, with GRPO, you get better at biking by using what you learned from each ride!Technical Explanation
Generalized Relative Policy Optimization (GRPO) is a reinforcement learning technique that focuses on improving policies based on feedback from the environment. It uses the concept of trust regions to ensure that policy updates do not deviate too much from the previous policy, which helps maintain stability during training. The key idea is to maximize the expected reward while keeping the Kullback-Leibler (KL) divergence between the new and old policies below a certain threshold. This can be formulated as: \[ \max_{\pi} \mathbb{E}_{s \sim \rho_{\pi}}[r(s, a)] \] subject to \[ D_{KL}(\pi || \pi_{old}) \leq \delta \] where \( \pi \) is the new policy, \( \pi_{old} \) is the old policy, and \( \delta \) is the trust region limit. Implementing GRPO typically involves using methods like conjugate gradient for optimization. Here’s a simple pseudo-code example: “`python while not converged: compute_gradient() update_policy_using_conjugate_gradient() “`Academic Context
GRPO is situated within the broader context of policy optimization methods in reinforcement learning. It builds on the foundations of trust region methods, which were first introduced in optimization literature. One of the key papers that laid the groundwork for GRPO is ‘Trust Region Policy Optimization’ by Schulman et al. (2015), which discusses the importance of maintaining a balance between exploration and exploitation in policy updates. The mathematical formulation of GRPO relies on concepts from information theory, particularly the Kullback-Leibler divergence, which measures how one probability distribution diverges from a second, expected probability distribution. Researchers continue to explore variations and improvements of GRPO to enhance stability and performance in complex environments.Code Examples
Example 1:
while not converged:
compute_gradient()
update_policy_using_conjugate_gradient()Example 2:
compute_gradient()
update_policy_using_conjugate_gradient()View Source: https://arxiv.org/abs/2511.16670v1