ReAPO: Retry-Aware Policy Optimization for Efficient Exploration in LLM Reasoning

RLVR improves language-model reasoning, but commonly relies on independent stochastic rollouts for exploration, which can repeatedly sample similar failed strategies. Prior work has seen success with approaches that guide exploration by introducing dependence into the sampling process by including incorrect solutions in the context for subsequent attempts. Still, these methods introduce the additional question of how to assign credit to each attempt. We propose to view the credit assignment through the lens of *Stochastic Shortest Paths*, a framework in classical reinforcement learning that seeks to minimize the expected cumulative cost to reach a terminal state (in our case, a verified successful response). We show that, under suitable simplifying assumptions, this perspective naturally leads to a simple modification to GRPO, which we call **Retry-Aware Policy Optimization (ReAPO)**. ReAPO allocates additional generation to failed trajectories, allowing successful retries to be reinforced without rewarding preceding failures, and assigns credit in a theoretically principled way to each attempt. Across Qwen3 models from 0.6B to 4B and eight mathematical and scientific reasoning benchmarks, ReAPO improves first-attempt performance over GRPO as well as natural recent baseline algorithms, while additional ablations demonstrate the utility of both serial sampling and ReAPO's credit assignment. ReAPO also outperforms GRPO with larger group size, with gains preserved under token- and wall-clock-normalized comparisons. Taken together, our results suggest that ReAPO is a simple yet effective approach for improving LM reasoning performance through improved exploration and retry-aware credit assignment.