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This research introduces "progressive point matching," a dense reward formulation that significantly accelerates reinforcement learning for long-horizon tasks by rewarding partial progress on a segment level rather than relying on sparse outcome rewards. The method demonstrates exponential efficiency gains in synthetic environments and successfully enables improvements on extremely difficult math reasoning problems where traditional sparse reward strategies fail to make progress. By utilizing a single reference trajectory per task, this approach offers a scalable solution for training models on complex, multi-step trajectories without introducing the biases found in prior partial-progress methods.
Long-Horizon Language Model Reinforcement Learning via Progressive Point Matching
arXiv:2609.07303v1 Announce Type: new Abstract: Current paradigms for training language models via reinforcement learning rely heavily on sparse outcome rewards. However, as we pursue tasks that require longer and more complicated trajectories, such strategies result in slow learning. Prior work has attempted to address this problem by rewarding partial progress; however, naive formulations are often biased and converge to suboptimal policies. We show that a simple and unbiased dense reward formulation, which we term progressive point matching, scales exponentially more efficiently to long-horizon tasks by rewarding partial progress on a segment level, both theoretically and empirically via synthetic environments. We then show how progressive point matching can be practically instantiated using a single reference trajectory per task. On extremely hard math reasoning problems, sparse outcome rewards cannot make any progress, whereas segment-level rewards enable improvements at larger test-time token budgets when measured by success rate or pass@k.
Abstract:Current paradigms for training language models via reinforcement learning rely heavily on sparse outcome rewards. However, as we pursue tasks that require longer and more complicated trajectories, such strategies result in slow learning. Prior work has attempted to address this problem by rewarding partial progress; however, naive formulations are often biased and converge to suboptimal policies. We show that a simple and unbiased dense reward formulation, which we term progressive point matching, scales exponentially more efficiently to long-horizon tasks by rewarding partial progress on a segment level, both theoretically and empirically via synthetic environments. We then show how progressive point matching can be practically instantiated using a single reference trajectory per task. On extremely hard math reasoning problems, sparse outcome rewards cannot make any progress, whereas segment-level rewards enable improvements at larger test-time token budgets when measured by success rate or pass@k.
Machine Learning (cs.LG)
arXiv:2609.07303 [cs.LG]
(or arXiv:2609.07303v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2609.07303 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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