# VerifierQ: Enhancing LLM Test Time Compute with Q-Learning-based Verifiers

arXiv: https://arxiv.org/abs/2410.08048 · HTML: https://mlsanity.com/paper/2410.08048/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 9 of its 21 references that are in the map.
- First posted on arXiv 10 Oct 2024.

## Placed in

- LLM reasoning / [Reinforcement learning for reasoning](https://mlsanity.com/lr/reinforcement-learning-for-reasoning/)

## Builds on (most cited first, 9 of 9)

- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters](https://mlsanity.com/paper/2408.03314/) (2024)
- [Conservative Q-Learning for Offline Reinforcement Learning](https://mlsanity.com/paper/2006.04779/) (2020)
- [MetaMath: Bootstrap Your Own Mathematical Questions for Large Language Models](https://mlsanity.com/paper/2309.12284/) (2023)
- [TinyLlama: An Open-Source Small Language Model](https://mlsanity.com/paper/2401.02385/) (2024)
- [Accessing GPT-4 level Mathematical Olympiad Solutions via Monte Carlo Tree Self-refine with LLaMa-3 8B](https://mlsanity.com/paper/2406.07394/) (2024)
- [Q*: Improving Multi-step Reasoning for LLMs with Deliberative Planning](https://mlsanity.com/paper/2406.14283/) (2024)
- [When Should We Prefer Offline Reinforcement Learning Over Behavioral Cloning?](https://mlsanity.com/paper/2204.05618/) (2022)
- [CHAI: A CHatbot AI for Task-Oriented Dialogue with Offline Reinforcement Learning](https://mlsanity.com/paper/2204.08426/) (2022)

## Built on by (most cited first, 14 of 14)

- [Why Do Multi-Agent LLM Systems Fail?](https://mlsanity.com/paper/2503.13657/) (2025)
- [LLM Post-Training: A Deep Dive into Reasoning Large Language Models](https://mlsanity.com/paper/2502.21321/) (2025)
- [A Survey of Test-Time Compute: From Intuitive Inference to Deliberate Reasoning](https://mlsanity.com/paper/2501.02497/) (2025)
- [LLaVA-Critic-R1: Your Critic Model is Secretly a Strong Policy Model](https://mlsanity.com/paper/2509.00676/) (2025)
- [From Passive to Active Reasoning: Can Large Language Models Ask the Right Questions under Incomplete Information?](https://mlsanity.com/paper/2506.08295/) (2025)
- [A Technical Survey of Reinforcement Learning Techniques for Large Language Models](https://mlsanity.com/paper/2507.04136/) (2025)
- [A Survey on Feedback-based Multi-step Reasoning for Large Language Models on Mathematics](https://mlsanity.com/paper/2502.14333/) (2025)
- [Trust but Verify! A Survey on Verification Design for Test-time Scaling](https://mlsanity.com/paper/2508.16665/) (2025)
- [Enhancing Large Language Model Reasoning with Reward Models: An Analytical Survey](https://mlsanity.com/paper/2510.01925/) (2025)
- [Accelerating LLM Reasoning via Early Rejection with Partial Reward Modeling](https://mlsanity.com/paper/2508.01969/) (2025)
- [The 4/δ Bound: Designing Predictable LLM-Verifier Systems for Formal Method Guarantee](https://mlsanity.com/paper/2512.02080/) (2025)
- [Online Finetuning Decision Transformers with Pure RL Gradients](https://mlsanity.com/paper/2601.00167/) (2026)
- [MAVIS: Multi-Objective Alignment via Inference-Time Value-Guided Selection](https://mlsanity.com/paper/2508.13415/) (2025)
- [TensorCommitments: A Lightweight Verifiable Inference for Language Models](https://mlsanity.com/paper/2602.12630/) (2026)

## Abstract (arXiv)

Recent advancements in test time compute, particularly through the use of verifier models, have significantly enhanced the reasoning capabilities of Large Language Models (LLMs). This generator-verifier approach closely resembles the actor-critic framework in reinforcement learning (RL). However, current verifier models in LLMs often rely on supervised fine-tuning without temporal difference learning such as Q-learning. This paper introduces VerifierQ, a novel approach that integrates Offline Q-learning into LLM verifier models. We address three key challenges in applying Q-learning to LLMs: (1) handling utterance-level Markov Decision Processes (MDPs), (2) managing large action spaces, and (3) mitigating overestimation bias. VerifierQ introduces a modified Bellman update for bounded Q-values, incorporates Implicit Q-learning (IQL) for efficient action space management, and integrates a novel Conservative Q-learning (CQL) formulation for balanced Q-value estimation. Our method enables parallel Q-value computation and improving training efficiency. While recent work has explored RL techniques like MCTS for generators, VerifierQ is among the first to investigate the verifier (critic) aspect in LLMs through Q-learning. This integration of RL principles into verifier models complements existing advancements in generator techniques, potentially enabling more robust and adaptive reasoning in LLMs. Experimental results on mathematical reasoning tasks demonstrate VerifierQ's superior performance compared to traditional supervised fine-tuning approaches, with improvements in efficiency, accuracy and robustness. By enhancing the synergy between generation and evaluation capabilities, VerifierQ contributes to the ongoing evolution of AI systems in addressing complex cognitive tasks across various domains.