Learning to Correct: Calibrated Reinforcement Learning for Multi-Attempt Chain-of-Thought
For researchers working on improving reasoning models with test-time computation, this work offers a principled RL approach to handle per-attempt rewards in multi-attempt settings, though it is incremental as it builds on existing GRPO.
The paper addresses the problem of optimizing multi-attempt chain-of-thought reasoning with reinforcement learning, where a model makes up to K attempts and receives hard verifier feedback. The authors propose Calibrated Attempt-Level (CAL) GRPO, a method that provides unbiased gradient estimates for the Verification@K reward, and show it outperforms vanilla GRPO and naive weighting on synthetic and real data.
State-of-the-art reasoning models utilize long chain-of-thought (CoT) to solve increasingly complex problems using more test-time computation. In this work, we explore a long CoT setting where the model makes up to K successive attempts at solving a problem, in which each attempt is allowed to build on earlier ones after the model receives a hard verifier feedback. This motivates RL methods that can harness per-attempt rewards by carefully weighting individual attempts. We study optimizing the Verification@K reward (the model succeeds by the K-th attempt) and show that naively weighing the attempts by their pass/fail results in biased gradients. We introduce Calibrated Attempt-Level (CAL) GRPO by devising a weighing strategy to obtain unbiased gradients while maintaining small variance. Our theory reveals how incorporating per-attempt rewards influence the training and the eventual Verification@K performance. Experiments, baselines, and ablations on synthetic and real data corroborate our theory and the benefits of CAL-GRPO over vanilla GRPO as well as naive weighting.