Holder Policy Optimisation

• URL: http://arxiv.org/abs/2605.12058v2
• Date: Thu, 21 May 2026 13:10:04 GMT
• Title: Holder Policy Optimisation
• Abstract summary: textbfHlderPO is a generalised policy optimisation framework.<n>It unifies token-level probability aggregation via the Hlder mean.<n>It achieves a state-of-the-art average accuracy of $54.9%$ across multiple mathematical benchmarks.
• Score: 26.521180498291717
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Group Relative Policy Optimisation (GRPO) enhances large language models by estimating advantages across a group of sampled trajectories. However, mapping these trajectory-level advantages to policy updates requires aggregating token-level probabilities within each sequence. Relying on a fixed aggregation mechanism for this step fundamentally limits the algorithm's adaptability. Empirically, we observe a critical trade-off: certain fixed aggregations frequently suffer from training collapse, while others fail to yield satisfactory performance. To resolve this, we propose \textbf{HölderPO}, a generalised policy optimisation framework unifying token-level probability aggregation via the Hölder mean. By explicitly modulating the parameter $p$, our framework provides continuous control over the trade-off between gradient concentration and variance bounds. Theoretically, we prove that a larger $p$ concentrates the gradient to amplify sparse learning signals, whereas a smaller $p$ strictly bounds gradient variance. Because no static configuration can universally resolve this concentration-stability trade-off, we instantiate the framework with a dynamic annealing algorithm that progressively schedules $p$ across the training lifecycle. Extensive evaluations demonstrate superior stability and convergence over existing baselines. Specifically, our approach achieves a state-of-the-art average accuracy of $54.9\%$ across multiple mathematical benchmarks, yielding a substantial $7.2\%$ relative gain over standard GRPO and secures an exceptional $93.8\%$ success rate on ALFWorld.

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