# Cast a Wider Net: Coordinated Pass@K Policy Optimization for Code Reasoning

arXiv: https://arxiv.org/abs/2605.27000 · HTML: https://mlsanity.com/paper/2605.27000/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 13 of its 26 references that are in the map.
- First posted on arXiv 26 May 2026.

## Placed in

- LLM reasoning / [Reinforcement learning for reasoning](https://mlsanity.com/lr/reinforcement-learning-for-reasoning/)

## Builds on (most cited first, 13 of 13)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Judging LLM-as-a-Judge with MT-Bench and Chatbot Arena](https://mlsanity.com/paper/2306.05685/) (2023)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [LiveCodeBench: Holistic and Contamination Free Evaluation of Large Language Models for Code](https://mlsanity.com/paper/2403.07974/) (2024)
- [Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters](https://mlsanity.com/paper/2408.03314/) (2024)
- [Large Language Monkeys: Scaling Inference Compute with Repeated Sampling](https://mlsanity.com/paper/2407.21787/) (2024)
- [Measuring Coding Challenge Competence With APPS](https://mlsanity.com/paper/2105.09938/) (2021)
- [Texygen: A Benchmarking Platform for Text Generation Models](https://mlsanity.com/paper/1802.01886/) (2018)
- [Pass@k Training for Adaptively Balancing Exploration and Exploitation of Large Reasoning Models](https://mlsanity.com/paper/2508.10751/) (2025)
- [Jointly Reinforcing Diversity and Quality in Language Model Generations](https://mlsanity.com/paper/2509.02534/) (2025)
- [Diversity-Incentivized Exploration for Versatile Reasoning](https://mlsanity.com/paper/2509.26209/) (2025)

## Built on by (most cited first, 2 of 2)

- [Rank-Conditioned Sample Reuse for the Plackett--Luce Best-of-K Objective](https://mlsanity.com/paper/2607.11146/) (2026)
- [Planned Test-Time Scaling with Coordinated Reasoning Paths](https://mlsanity.com/paper/2609.27374/) (2026)

## Abstract (arXiv)

Repeated sampling with a verifier is the standard way to allocate test-time compute for code generation, with pass@K as the canonical metric. Yet the standard policy class draws K independent samples from a single answer distribution, so attempts often collapse onto near-duplicate reasoning paths and waste the budget on redundant rollouts. This failure is costly in competitive programming, where many problems admit multiple distinct algorithmic strategies and pass@K requires only one correct attempt. We propose Coordinated Pass@K Policy Optimization (CPPO), which turns pass@K generation into joint exploration over strategies: a planner emits a tuple of K=4 alternative high-level methods, and a shared solver attempts one solution per method. CPPO trains this joint policy with a multiplicative planner reward, Rplan = J_psi · Rout, 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. The largest single gain is +0.16 on Qwen3.5-9B LiveCodeBench-v6 over the strongest baseline, PKPO (0.588 rightarrow 0.748; paired bootstrap, p < 0.05).