Reinforcement Learning with Verifiable yet Noisy Rewards under Imperfect Verifiers
This work addresses the challenge of training AI models, such as in math reasoning, with automated verifiers that are prone to errors, which is incremental as it builds on existing RLVR frameworks by mitigating verifier noise.
The paper tackled the problem of reinforcement learning with verifiable but noisy rewards, where binary rewards from imperfect verifiers introduce false negatives and false positives, by proposing two correction algorithms to recover unbiased policy gradients. The results showed that both corrections improved training over uncorrected baselines, with the forward variant converging faster and remaining stable under heavy noise, and a practical mechanism using an LLM verifier outperformed other state-of-the-art methods.
Reinforcement Learning with Verifiable Rewards (RLVR) trains policies against automated verifiers to avoid costly human labeling. To reduce vulnerability to verifier hacking, many RLVR systems collapse rewards to binary $\{0,1\}$ during training. This choice carries a cost: it introduces \textit{false negatives} (rejecting correct answers, FNs) and \textit{false positives} (accepting incorrect ones, FPs). For instance, a rule-based checker may mark the correct fraction $\frac{12}{36}$ as wrong when compared against the canonical $\frac{1}{3}$ due to brittle parsing/equivalence rules (FN), while a large language model (LLM) judges can be gamed by superficial cues or even a single adversarial token, yielding inflated correctness for wrong solutions (FP). We formalize verifier unreliability by modeling the verifier as a stochastic reward channel with asymmetric noise rates. From this abstraction, we derive two correction algorithms for verifier errors. The first is a \textit{backward} correction that de-biases the observed binary reward to recover an \textit{unbiased} estimator of the clean policy gradient. The second is a \textit{forward} correction that reweights score-function terms so that the expected update direction aligns with the \textit{clean gradient}; notably, it requires only the FN rate. We implement both as lightweight hooks in a group relative policy optimization (GRPO)-based RLVR pipeline and evaluate them on math-reasoning models and benchmarks. Across models and datasets, both corrections improve over uncorrected training; the forward variant converges faster and remains stable under heavier noise. Finally, we show a practical appeal mechanism in which a lightweight LLM verifier estimates the FN rate online by rechecking rule-based negatives, obtaining outperformance compared with other state-of-the-art contenders.