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        <title>Cast a Wider Net: Coordinated Pass@K Policy Optimization for Code Reasoning</title>
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    <abstract>While repeated sampling against a verifier is the standard test-time compute strategy for code generation, measured by pass@K, drawing K independent samples from a single distribution often wastes the compute budget on redundant, near-duplicate reasoning paths. This failure is costly in competitive programming, where many problems admit multiple distinct algorithmic strategies and passing pass@K requires only one correct attempt. We propose **Coordinated Pass@K Policy Optimization (CPPO)**, which trains a joint planner–solver policy for pass@K: a planner emits a tuple of K=4 alternative high-level methods, and a shared solver attempts one solution per method. We train it with a multiplicative planner reward, R_plan = J_ψ · R_out assigning credit only to valid strategy tuples that lead to verifier-confirmed pass@K success. Across APPS, CodeContests, and LiveCodeBench-v6, CPPO improves pass@4 over direct sampling, planning baselines, planner-only SFT, and pass@K-oriented RL under the same K=4 solver-attempt budget, with statistically significant gains on six of nine model–benchmark cells. For instance, it improves Qwen3.5-9B on LiveCodeBench-v6 from 0.588 with PKPO, the strongest baseline, to 0.728, an absolute gain of 0.14 under a hierarchical bootstrap test with p&lt;0.05.</abstract>
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%0 Conference Proceedings
%T Cast a Wider Net: Coordinated Pass@K Policy Optimization for Code Reasoning
%A Li, Yilong
%A Banerjee, Suman
%A Che, Tong
%Y Lee, Hung-Yi
%Y Dev, Sunipa
%Y Li, Jessy
%Y Elliott, Desmond
%S Proceedings of the 2026 Conference on Empirical Methods in Natural Language Processing
%D 2026
%8 October
%I Association for Computational Linguistics
%C Budapest, Hungary
%@ 979-8-89176-459-0
%F li-etal-2026-cast
%X While repeated sampling against a verifier is the standard test-time compute strategy for code generation, measured by pass@K, drawing K independent samples from a single distribution often wastes the compute budget on redundant, near-duplicate reasoning paths. This failure is costly in competitive programming, where many problems admit multiple distinct algorithmic strategies and passing pass@K requires only one correct attempt. We propose **Coordinated Pass@K Policy Optimization (CPPO)**, which trains a joint planner–solver policy for pass@K: a planner emits a tuple of K=4 alternative high-level methods, and a shared solver attempts one solution per method. We train it with a multiplicative planner reward, R_plan = J_ψ · R_out assigning credit only to valid strategy tuples that lead to verifier-confirmed pass@K success. Across APPS, CodeContests, and LiveCodeBench-v6, CPPO improves pass@4 over direct sampling, planning baselines, planner-only SFT, and pass@K-oriented RL under the same K=4 solver-attempt budget, with statistically significant gains on six of nine model–benchmark cells. For instance, it improves Qwen3.5-9B on LiveCodeBench-v6 from 0.588 with PKPO, the strongest baseline, to 0.728, an absolute gain of 0.14 under a hierarchical bootstrap test with p<0.05.
%U https://aclanthology.org/2026.emnlp-main.1701/
%P 38736-38761

Markdown (Informal)

[Cast a Wider Net: Coordinated Pass@K Policy Optimization for Code Reasoning](https://aclanthology.org/2026.emnlp-main.1701/) (Li et al., EMNLP 2026)

• Cast a Wider Net: Coordinated Pass@K Policy Optimization for Code Reasoning (Li et al., EMNLP 2026)

ACL

• Yilong Li, Suman Banerjee, and Tong Che. 2026. Cast a Wider Net: Coordinated Pass@K Policy Optimization for Code Reasoning. In Proceedings of the 2026 Conference on Empirical Methods in Natural Language Processing, pages 38736–38761, Budapest, Hungary. Association for Computational Linguistics.