Rate or Fate? RLV$^\varepsilon$R: Reinforcement Learning with Verifiable Noisy Rewards

Fuente: arXiv
Guardado en:
Detalles Bibliográficos
Autores principales: Rad, Ali, Filom, Khashayar, Keivan, Darioush, Esfahani, Peyman Mohajerin, Kamalinejad, Ehsan
Formato: Preprint
Publicado: 2026
Materias:
Acceso en línea:
Etiquetas: Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
_version_ 1866912809591242752
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