Pass@k Metric for RLVR: A Diagnostic Tool of Exploration, But Not an Objective

• URL: http://arxiv.org/abs/2511.16231v1
• Date: Thu, 20 Nov 2025 10:58:21 GMT
• Title: Pass@k Metric for RLVR: A Diagnostic Tool of Exploration, But Not an Objective
• Authors: Yang Yu,
• Abstract summary: We analyze the pass@k metric, which measures the probability of obtaining at least one correct solution in k independent samples.<n>Our analysis reveals that the pass@k objective provides a vanishing learning signal in regimes where exploration is most critical.<n>We conclude that while pass@k is a useful diagnostic tool, it may be an unsuitable direct objective for optimization.
• Score: 3.79187263097166
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: The ability of Large Language Models (LLMs) to perform complex, multi-step reasoning is a central focus of modern AI research. To evaluate and enhance this capability, the pass@k metric, which measures the probability of obtaining at least one correct solution in k independent samples, has received significant attention. Its intuitive appeal has led to its adoption not only as an evaluation standard but also as a direct optimization objective in reinforcement learning. In this paper, we analyze the pass@k objective, derive its gradient, and demonstrate that it is fundamentally a per-example positive reweighting of the simpler pass@1 objective. Our analysis reveals that the pass@k objective provides a vanishing learning signal in regimes where exploration is most critical. We further analyze the dynamics of "exploration collapse", showing that as the policy concentrates probability mass, the gap between pass@k and pass@1 diminishes. We conclude that while pass@k is a useful diagnostic tool, it may be an unsuitable direct objective for optimization. Instead, mechanisms explicitly encouraging efficient exploration could offer a more effective path forward for reinforcement learning in reasoning tasks.

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