GIST: Gibbs-Targeted Hierarchical Data Selection for Offline RLVR

Xuliang Huang, Tianxiang Zhao, Chengwei Qin, Yao Shu

Offline reinforcement learning with verifiable rewards (RLVR) trains on a fixed pool of sampled responses and typically supervises every token of every response, although responses and tokens are not equally informative. We study which ones to supervise through the Gibbs-optimal policy of KL-regularized RLVR, which offline training targets, and measure the mismatch between a policy and this target with a bidirectional KL divergence. At the reference policy, this mismatch factorizes exactly and separates the two outcomes: correct responses contribute mainly through the forward term, concentrated on their low-probability tokens, and incorrect responses through the reverse term, concentrated on the responses the policy generates often and on their high-probability tokens. Based on this analysis, we propose GIST (Gibbs-Targeted Hierarchical Data Selection), a two-level selection method that approximates these principles with signals available before training. GIST uses the sampling temperature to select correct responses on-policy and incorrect responses near the policy's mode, and it uses the initial policy's token probabilities to supervise only the tokens where the mismatch lies.…