# A Cheap Verifier is Good Enough: LLM Post-training is Robust to Erroneous Rewards

arXiv: https://arxiv.org/abs/2609.33467 · HTML: https://mlsanity.com/paper/2609.33467/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 29 of its 38 references that are in the map.
- First posted on arXiv 27 Sep 2026.

## Builds on (most cited first, 29 of 29)

- [Judging LLM-as-a-Judge with MT-Bench and Chatbot Arena](https://mlsanity.com/paper/2306.05685/) (2023)
- [Program Synthesis with Large Language Models](https://mlsanity.com/paper/2108.07732/) (2021)
- [A Survey on LLM-as-a-Judge](https://mlsanity.com/paper/2411.15594/) (2024)
- [Scaling Laws for Reward Model Overoptimization](https://mlsanity.com/paper/2210.10760/) (2022)
- [SimpleRL-Zoo: Investigating and Taming Zero Reinforcement Learning for Open Base Models in the Wild](https://mlsanity.com/paper/2503.18892/) (2025)
- [RewardBench: Evaluating Reward Models for Language Modeling](https://mlsanity.com/paper/2403.13787/) (2024)
- [HealthBench: Evaluating Large Language Models Towards Improved Human Health](https://mlsanity.com/paper/2505.08775/) (2025)
- [Rubrics as Rewards: Reinforcement Learning Beyond Verifiable Domains](https://mlsanity.com/paper/2507.17746/) (2025)
- [Replacing Judges with Juries: Evaluating LLM Generations with a Panel of Diverse Models](https://mlsanity.com/paper/2404.18796/) (2024)
- [JudgeBench: A Benchmark for Evaluating LLM-based Judges](https://mlsanity.com/paper/2410.12784/) (2024)
- [Spurious Rewards: Rethinking Training Signals in RLVR](https://mlsanity.com/paper/2506.10947/) (2025)
- [GDPval: Evaluating AI Model Performance on Real-World Economically Valuable Tasks](https://mlsanity.com/paper/2510.04374/) (2025)
- [Crossing the Reward Bridge: Expanding RL with Verifiable Rewards Across Diverse Domains](https://mlsanity.com/paper/2503.23829/) (2025)
- [Checklists Are Better Than Reward Models For Aligning Language Models](https://mlsanity.com/paper/2507.18624/) (2025)
- [DeepSeek-V4.1-Flash: Pushing the Limits of KV Cache Compression](https://mlsanity.com/paper/2609.19969/) (2026)
- [Breaking the Exploration Bottleneck: Rubric-Scaffolded Reinforcement Learning for General LLM Reasoning](https://mlsanity.com/paper/2508.16949/) (2025)
- [Limits to scalable evaluation at the frontier: LLM as Judge won't beat twice the data](https://mlsanity.com/paper/2410.13341/) (2024)
- [AdvancedIF: Rubric-Based Benchmarking and Reinforcement Learning for Advancing LLM Instruction Following](https://mlsanity.com/paper/2511.10507/) (2025)
- [Reinforcement Learning with Verifiable yet Noisy Rewards under Imperfect Verifiers](https://mlsanity.com/paper/2510.00915/) (2025)
- [PRBench: Large-Scale Expert Rubrics for Evaluating High-Stakes Professional Reasoning](https://mlsanity.com/paper/2511.11562/) (2025)
- [Rethinking Reward Model Evaluation: Are We Barking up the Wrong Tree?](https://mlsanity.com/paper/2410.05584/) (2024)
- [Exploration vs Exploitation: Rethinking RLVR through Clipping, Entropy, and Spurious Reward](https://mlsanity.com/paper/2512.16912/) (2025)
- [RubricEval: A Rubric-Level Meta-Evaluation Benchmark for LLM Judges in Instruction Following](https://mlsanity.com/paper/2603.25133/) (2026)
- [Noise-corrected GRPO: From Noisy Rewards to Unbiased Gradients](https://mlsanity.com/paper/2510.18924/) (2025)
- [Examining Reasoning LLMs-as-Judges in Non-Verifiable LLM Post-Training](https://mlsanity.com/paper/2603.12246/) (2026)
- [An Imperfect Verifier is Good Enough: Learning with Noisy Rewards](https://mlsanity.com/paper/2604.07666/) (2026)
- [Tuning LLM Judge Design Decisions for 1/1000 of the Cost](https://mlsanity.com/paper/2501.17178/) (2025)
- [Rethinking Reward Model Evaluation Through the Lens of Reward Overoptimization](https://mlsanity.com/paper/2505.12763/) (2025)
- [BankerToolBench: Evaluating AI Agents in End-to-End Investment Banking Workflows](https://mlsanity.com/paper/2604.11304/) (2026)

## Abstract (arXiv)

When post-training large language models on tasks with semi-verifiable rewards, there are many factors (training steps, base model size, training order, data quality, verifier accuracy, etc.) that practitioners must contend with to maximize model performance. Yet, it remains unclear how well verifier agreement predicts post-training performance on such tasks. In this paper, we explore this question with over 11k H100 GPU-hours, across HealthBench and PRBench tasks in medical, legal, and finance domains. Across the tested domains, Qwen3 trainees (1.7B-8B on HealthBench; 8B on PRBench), evaluation splits, and frontier LLM reference judges (which we call golden verifiers), higher verifier agreement does not consistently identify the best training verifier. Expensive verifiers need not outperform inexpensive ones, and open-weight Gemma verifiers produce strong training outcomes. We compare two low-cost choices retrospectively -- a cost-reducing choice and a balanced choice -- with estimated grading cost reductions of 98.8%-99.7% relative to the golden grading protocols and average post-training score gaps of 1-3 points from the best evaluated training verifier. These averages include larger losses in individual settings; they do not establish that verifier choices are interchangeable.