GRPO and Reflection Reward for Mathematical Reasoning in Large Language Models

Recent advances in large language models (LLMs) highlight the importance of post training techniques for improving reasoning and mathematical ability. Group Relative Policy Optimization (GRPO) has shown promise in this domain by combining group relative advantage estimation, PPO style clipping, and KL regularization. However, its complexity raises the question of whether all components are necessary for fostering reasoning behaviors. We conduct a systematic analysis of GRPO and identify two key findings: (1) incorporating negative feedback is essential training solely on actions above a baseline limits learning; and (2) PPO style constraints, such as policy ratio clipping, are not required to improve mathematical reasoning or performance. Building on these insights, we propose REINFORCE with Group Relative Advantage (RGRA), a simplified variant that retains group relative advantage estimation but removes PPO style clipping and policy ratio terms. Experiments across standard mathematical benchmarks indicate that RGRA has the potential to achieve stronger performance than GRPO. Our results suggest that simpler REINFORCE based approaches can effectively enhance reasoning in LLMs, offering a more transparent and efficient alternative to GRPO.

Self-reflection is a powerful mechanism for credit assignment in human learning, converting sparse outcome feedback into actionable guidance. However, its potential for post-training Large Language Models (LLMs) remains underexplored. We propose Self-Reflective Policy Optimization (SRPO), a framework that internalizes this capability. SRPO enables LLMs to analyze their own completed trajectories, synthesize errors into concise "reflection patches," and use reflection-conditioned teacher scores on student on-policy rollouts as dense token-level training signals. This process effectively transforms sparse terminal supervision into dense, token-level learning signals without requiring external critics, separate reward models, or larger teacher models. We demonstrate that SRPO achieves state-of-the-art performance across mathematical reasoning and long-horizon agentic benchmarks with exceptional data efficiency. Using a Qwen3-8B base model, SRPO attains 73.3% on AIME'24 using only 8% (0.08x) of the training FLOPs required by scaled supervised fine-tuning, while significantly improving success rates on WebShop (64.7%), ALFWorld (76.8%), and SWE-Bench-Lite (31.2%). Code is available at https://github.com/Galleons2029/SRPO

Mathematical reasoning is a key benchmark for large language models. Reinforcement learning is a standard post-training mechanism for improving the reasoning capabilities of large language models, yet performance remains sensitive to the design of the reward function that drives policy optimization. This paper introduces a search-driven framework that treats the reward specification itself as an object of optimization. The setting of interest is one in which the base model is held fixed and the reward specification is the primary remaining design lever. Candidate reward functions are generated by a frontier language model, validated automatically, screened through 500-step Group Relative Policy Optimization (GRPO) training runs on a Llama-3.2-3B-Instruct base model with Low-Rank Adaptation (LoRA), and ranked by F1 on the GSM8K test set. Ranked summaries from prior rounds are then fed back into the next round of generation. Over five rounds, the search produces 50 candidate rewards. The mean F1 rises from 0.596 in Round 1 to 0.632 in Round 5, and the top individual reward reaches F1 = 0.787. Seven ensemble configurations of top-ranked rewards are evaluated. The best ensemble achieves F1 = 0.795 (95% bootstrap CI [0.756, 0.832]) and accuracy 0.660 [0.635, 0.686], a 0.19 absolute F1 gain over a base-rewards-only GRPO baseline (F1 = 0.609). Pairwise McNemar tests with Bonferroni correction show all five-or-more-reward configurations are statistically indistinguishable at α = 0.05/21. A three-seed re-training of the best ensemble yields F1 of 0.785. A randomly drawn 5-reward control collapses to F1 = 0.047, which shows that the ranked-feedback loop, not the additive signal of having more rewards, drives the gain.