aiqbench analysis
This research addresses a critical instability in verifier-free reinforcement learning for LLMs, specifically the "Posterior Concentration Phenomenon" where long reasoning traces yield indistinguishable probability rewards. The proposed RLCPR framework mitigates this by incorporating uncertainty-aware sampling and regularization, resulting in improved optimization stability and token efficiency across mathematical and general reasoning benchmarks. For practitioners training models without external verifiers, this work offers a necessary correction to current GRPO-based strategies that often fail on long-horizon tasks.
Rethinking Probability-Based Reinforcement Learning From Posterior Concentration
arXiv:2610.01458v1 Announce Type: new Abstract: Verifier-free reinforcement learning with probability-based rewards offers a promising way to train LLMs on general reasoning tasks where external verifiers are unavailable. Yet the reliability of these rewards, especially in long-horizon reasoning, remains underexplored. This work identifies a length-dependent failure mode of probability rewards, which we call the Posterior Concentration Phenomenon (PCP). We show that the probability of a reference answer conditioned on a reasoning trace often collapses to a low-variance interval as the trace becomes lengthy. This phenomenon results in nearly indistinguishable rewards, which, under GRPO-based settings, makes probability-based policy optimization unstable and inefficient. Motivated by this, we propose Reinforcement Learning with Concentration-aware Posterior Rewards (RLCPR), a verifier-free RL framework to explicitly account for PCP for better optimization stability and token efficiency. It has two components: uncertainty-aware data sampling, which reduces concentration-prone rollouts before generation, and concentration-aware regularization, which penalizes unnecessarily long traces when posterior rewards collapse. Extensive experiments show that, alongside higher token efficiency, RLCPR outperforms the state-of-the-art verifier-free RL baseline by up to 4.0% on six of seven benchmarks, including general-domain and mathematical reasoning challenges.
Abstract:Verifier-free reinforcement learning with probability-based rewards offers a promising way to train LLMs on general reasoning tasks where external verifiers are unavailable. Yet the reliability of these rewards, especially in long-horizon reasoning, remains underexplored. This work identifies a length-dependent failure mode of probability rewards, which we call the Posterior Concentration Phenomenon (PCP). We show that the probability of a reference answer conditioned on a reasoning trace often collapses to a low-variance interval as the trace becomes lengthy. This phenomenon results in nearly indistinguishable rewards, which, under GRPO-based settings, makes probability-based policy optimization unstable and inefficient. Motivated by this, we propose Reinforcement Learning with Concentration-aware Posterior Rewards (RLCPR), a verifier-free RL framework to explicitly account for PCP for better optimization stability and token efficiency. It has two components: uncertainty-aware data sampling, which reduces concentration-prone rollouts before generation, and concentration-aware regularization, which penalizes unnecessarily long traces when posterior rewards collapse. Extensive experiments show that, alongside higher token efficiency, RLCPR outperforms the state-of-the-art verifier-free RL baseline by up to 4.0% on six of seven benchmarks, including general-domain and mathematical reasoning challenges.
Artificial Intelligence (cs.AI)
arXiv:2610.01458 [cs.AI]
(or arXiv:2610.01458v1 [cs.AI] for this version)
https://doi.org/10.48550/arXiv.2610.01458 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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