HISPO: Hierarchical Importance-Sampling Policy Optimization with Entropy-Derived Segments

• URL: http://arxiv.org/abs/2609.15471v1
• Date: Mon, 14 Sep 2026 12:29:00 GMT
• Title: HISPO: Hierarchical Importance-Sampling Policy Optimization with Entropy-Derived Segments
• Abstract summary: Reinforcement learning with verifiable rewards (RLVR) has become a central approach for improving mathematical reasoning in language models.<n>Long-form completions introduce a difficult credit-assignment problem: different parts of a solution trace may contribute unevenly to final correctness.<n>We introduce Hierarchical Importance-Sampling Policy Optimization (HISPO), a segment-level policy-optimization method that constructs rollout-time entropy-derived contiguous segments.
• Score: 3.6883184884620004
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Reinforcement learning with verifiable rewards (RLVR) has become a central approach for improving mathematical reasoning in language models, but long-form completions introduce a difficult credit-assignment problem: different parts of a solution trace may contribute unevenly to final correctness. Existing policyoptimization objectives for RLVR commonly apply importance-sampling correction at either the token level (GRPO, DAPO) or the sequence level (GSPO), imposing different granularities for assigning credit across a response. We introduce Hierarchical Importance-Sampling Policy Optimization (HISPO), a segment-level policy-optimization method that constructs rollout-time entropy-derived contiguous segments, assigns soft entropy-based saliency weights, and applies clipped importance-sampling correction at the segment granularity. This provides an intermediate correction unit between token-level GRPO/DAPO and sequence-level GSPO. We evaluate HISPO by fine-tuning Qwen3-1.7B-Base on mathematical reasoning tasks. Across six benchmarks, HISPO improves Pass@8 over the strongest baseline on all benchmarks and matches or exceeds the strongest baseline in Acc@8 on five of them. On AIME25, HISPO improves over GRPO by +3.75 Acc@8 and +3.78 Pass@8, and over GSPO by +2.50 Acc@8 and +1.27 Pass@8. These results suggest that segment-level correction is a promising granularity for RLVR in long-form mathematical reasoning.

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