Rate or Fate? RLV$^\varepsilon$R: Reinforcement Learning with Verifiable Noisy Rewards
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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866912809591242752 |
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| author | Rad, Ali Filom, Khashayar Keivan, Darioush Esfahani, Peyman Mohajerin Kamalinejad, Ehsan |
| author_facet | Rad, Ali Filom, Khashayar Keivan, Darioush Esfahani, Peyman Mohajerin Kamalinejad, Ehsan |
| contents | Reinforcement learning with verifiable rewards (RLVR) is a simple but powerful paradigm for training LLMs: sample a completion, verify it, and update. In practice, however, the verifier is almost never clean--unit tests probe only limited corner cases; human and synthetic labels are imperfect; and LLM judges (e.g., RLAIF) are noisy and can be exploited--and this problem worsens on harder domains (especially coding) where tests are sparse and increasingly model-generated. We ask a pragmatic question: does the verification noise merely slow down the learning (rate), or can it flip the outcome (fate)?
To address this, we develop an analytically tractable multi-armed bandit view of RLVR dynamics, instantiated with GRPO and validated in controlled experiments. Modeling false positives and false negatives and grouping completions into recurring reasoning modes yields a replicator-style (natural-selection) flow on the probability simplex. The dynamics decouples into within-correct-mode competition and a one-dimensional evolution for the mass on incorrect modes, whose drift is determined solely by Youden's index J=TPR-FPR. This yields a sharp phase transition: when J>0, the incorrect mass is driven toward extinction (learning); when J=0, the process is neutral; and when J<0, incorrect modes amplify until they dominate (anti-learning and collapse). In the learning regime J>0, noise primarily rescales convergence time ("rate, not fate"). Experiments on verifiable programming tasks under synthetic noise reproduce the predicted J=0 boundary. Beyond noise, the framework offers a general lens for analyzing RLVR stability, convergence, and algorithmic interventions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_04411 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Rate or Fate? RLV$^\varepsilon$R: Reinforcement Learning with Verifiable Noisy Rewards Rad, Ali Filom, Khashayar Keivan, Darioush Esfahani, Peyman Mohajerin Kamalinejad, Ehsan Machine Learning Artificial Intelligence Computation and Language Reinforcement learning with verifiable rewards (RLVR) is a simple but powerful paradigm for training LLMs: sample a completion, verify it, and update. In practice, however, the verifier is almost never clean--unit tests probe only limited corner cases; human and synthetic labels are imperfect; and LLM judges (e.g., RLAIF) are noisy and can be exploited--and this problem worsens on harder domains (especially coding) where tests are sparse and increasingly model-generated. We ask a pragmatic question: does the verification noise merely slow down the learning (rate), or can it flip the outcome (fate)? To address this, we develop an analytically tractable multi-armed bandit view of RLVR dynamics, instantiated with GRPO and validated in controlled experiments. Modeling false positives and false negatives and grouping completions into recurring reasoning modes yields a replicator-style (natural-selection) flow on the probability simplex. The dynamics decouples into within-correct-mode competition and a one-dimensional evolution for the mass on incorrect modes, whose drift is determined solely by Youden's index J=TPR-FPR. This yields a sharp phase transition: when J>0, the incorrect mass is driven toward extinction (learning); when J=0, the process is neutral; and when J<0, incorrect modes amplify until they dominate (anti-learning and collapse). In the learning regime J>0, noise primarily rescales convergence time ("rate, not fate"). Experiments on verifiable programming tasks under synthetic noise reproduce the predicted J=0 boundary. Beyond noise, the framework offers a general lens for analyzing RLVR stability, convergence, and algorithmic interventions. |
| title | Rate or Fate? RLV$^\varepsilon$R: Reinforcement Learning with Verifiable Noisy Rewards |
| topic | Machine Learning Artificial Intelligence Computation and Language |
| url | https://arxiv.org/abs/2601.04411 |