# Exploration vs Exploitation: Rethinking RLVR through Clipping, Entropy, and Spurious Reward

arXiv: https://arxiv.org/abs/2512.16912 · HTML: https://mlsanity.com/paper/2512.16912/

## Key facts

- Cited by 27 papers in the map (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 74 of its 93 references that are in the map.
- First posted on arXiv 18 Dec 2025.

## Placed in

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

## Builds on (most cited first, 30 of 74)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [HybridFlow: A Flexible and Efficient RLHF Framework](https://mlsanity.com/paper/2409.19256/) (2024)
- [Understanding R1-Zero-Like Training: A Critical Perspective](https://mlsanity.com/paper/2503.20783/) (2025)
- [Curiosity-driven Exploration by Self-supervised Prediction](https://mlsanity.com/paper/1705.05363/) (2017)
- [Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement](https://mlsanity.com/paper/2409.12122/) (2024)
- [Exploration by Random Network Distillation](https://mlsanity.com/paper/1810.12894/) (2018)
- [SimPO: Simple Preference Optimization with a Reference-Free Reward](https://mlsanity.com/paper/2405.14734/) (2024)
- [Math-Shepherd: Verify and Reinforce LLMs Step-by-step without Human Annotations](https://mlsanity.com/paper/2312.08935/) (2023)
- [A General Theoretical Paradigm to Understand Learning from Human Preferences](https://mlsanity.com/paper/2310.12036/) (2023)
- [Solving math word problems with process- and outcome-based feedback](https://mlsanity.com/paper/2211.14275/) (2022)
- [RAFT: Reward rAnked FineTuning for Generative Foundation Model Alignment](https://mlsanity.com/paper/2304.06767/) (2023)
- [ProgPrompt: Generating Situated Robot Task Plans using Large Language Models](https://mlsanity.com/paper/2209.11302/) (2022)
- [ORPO: Monolithic Preference Optimization without Reference Model](https://mlsanity.com/paper/2403.07691/) (2024)
- [Beyond the 80/20 Rule: High-Entropy Minority Tokens Drive Effective Reinforcement Learning for LLM Reasoning](https://mlsanity.com/paper/2506.01939/) (2025)
- [The Entropy Mechanism of Reinforcement Learning for Reasoning Language Models](https://mlsanity.com/paper/2505.22617/) (2025)
- [RRHF: Rank Responses to Align Language Models with Human Feedback without tears](https://mlsanity.com/paper/2304.05302/) (2023)
- [Improve Mathematical Reasoning in Language Models by Automated Process Supervision](https://mlsanity.com/paper/2406.06592/) (2024)
- [The Lessons of Developing Process Reward Models in Mathematical Reasoning](https://mlsanity.com/paper/2501.07301/) (2025)
- [SLiC-HF: Sequence Likelihood Calibration with Human Feedback](https://mlsanity.com/paper/2305.10425/) (2023)
- [Iterative Preference Learning from Human Feedback: Bridging Theory and Practice for RLHF under KL-Constraint](https://mlsanity.com/paper/2312.11456/) (2023)
- [The Effects of Reward Misspecification: Mapping and Mitigating Misaligned Models](https://mlsanity.com/paper/2201.03544/) (2022)
- [Statistical Rejection Sampling Improves Preference Optimization](https://mlsanity.com/paper/2309.06657/) (2023)
- [Preference Ranking Optimization for Human Alignment](https://mlsanity.com/paper/2306.17492/) (2023)

## Built on by (most cited first, 27 of 27)

- [GenEnv: Difficulty-Aligned Co-Evolution Between LLM Agents and Environment Simulators](https://mlsanity.com/paper/2512.19682/) (2025)
- [Maximum Likelihood Reinforcement Learning](https://mlsanity.com/paper/2602.02710/) (2026)
- [Spurious Rewards Paradox: Mechanistically Understanding How RLVR Activates Memorization Shortcuts in LLMs](https://mlsanity.com/paper/2601.11061/) (2026)
- [An Imperfect Verifier is Good Enough: Learning with Noisy Rewards](https://mlsanity.com/paper/2604.07666/) (2026)
- [Reward-free Alignment for Conflicting Objectives](https://mlsanity.com/paper/2602.02495/) (2026)
- [LaDi-RL: Latent Diffusion Reasoning Prevents Entropy Collapse in Reinforcement Learning](https://mlsanity.com/paper/2602.01705/) (2026)
- [OmniOPD: Logit-Free On-Policy Distillation via Speculative Verification](https://mlsanity.com/paper/2606.01476/) (2026)
- [Thinking by Subtraction: Confidence-Driven Contrastive Decoding for LLM Reasoning](https://mlsanity.com/paper/2602.18232/) (2026)
- [CLIPO: Contrastive Learning in Policy Optimization Generalizes RLVR](https://mlsanity.com/paper/2603.10101/) (2026)
- [StaRPO: Stability-Augmented Reinforcement Policy Optimization](https://mlsanity.com/paper/2604.08905/) (2026)
- [VeriGate: Verifier-Gated Step-Level Supervision for GRPO](https://mlsanity.com/paper/2605.30451/) (2026)
- [Self-Improvement Can Self-Regress: The Rise-and-Collapse Failure Mode of LLM Self-Training](https://mlsanity.com/paper/2606.21090/) (2026)
- [Entropy Polarity in Reinforcement Fine-Tuning: Direction, Asymmetry, and Control](https://mlsanity.com/paper/2605.11775/) (2026)
- [Policy Improvement Reinforcement Learning](https://mlsanity.com/paper/2604.00860/) (2026)
- [When Can LLMs Learn to Reason with Weak Supervision?](https://mlsanity.com/paper/2604.18574/) (2026)
- [PAEC: Position-Aware Entropy Calibration for LLM Reasoning in RLVR](https://mlsanity.com/paper/2606.08543/) (2026)
- [Two-Fidelity Best-Action Identification for Stochastic Minimax Tree](https://mlsanity.com/paper/2606.01708/) (2026)
- [Parameter Exploration for RLVR via Variational Learning](https://mlsanity.com/paper/2608.09805/) (2026)
- [Rethinking Reinforcement fine-tuning of LLMs: A Multi-armed Bandit Learning Perspective](https://mlsanity.com/paper/2601.14599/) (2026)
- [Two is better than one: A Collapse-free Multi-Reward RLIF Training Framework](https://mlsanity.com/paper/2605.22620/) (2026)
- [EAPO: Entropy-Driven Adaptive Positive-Negative Sample Weighting for Policy Optimization in Open-Ended QA](https://mlsanity.com/paper/2605.27846/) (2026)
- [A Zeroth-Order Paradigm for LLM Preference Alignment](https://mlsanity.com/paper/2609.19144/) (2026)
- [Towards Full Pipeline FP8 Reinforcement Learning for LLMs](https://mlsanity.com/paper/2609.22870/) (2026)
- [A Cheap Verifier is Good Enough: LLM Post-training is Robust to Erroneous Rewards](https://mlsanity.com/paper/2609.33467/) (2026)
- [Learned Reporting Preferences in RLVR Can Conflict with the Current Request](https://mlsanity.com/paper/2609.36587/) (2026)
- [Training Numerical Intelligence via Auto-Diagnosis and Skill Discovery](https://mlsanity.com/paper/2610.03872/) (2026)
- [Checking the Checkers: A Synthesis of Verifier Noise and Robustness in RLVR](https://mlsanity.com/paper/2610.17824/) (2026)

## Abstract (arXiv)

This paper examines the exploration-exploitation trade-off in reinforcement learning with verifiable rewards (RLVR), a framework for improving the reasoning of Large Language Models (LLMs). Recent studies suggest that RLVR can elicit strong mathematical reasoning in LLMs through two seemingly paradoxical mechanisms: spurious rewards, which suppress exploitation by rewarding outcomes unrelated to the ground truth, and entropy minimization, which suppresses exploration by pushing the model toward more confident and deterministic outputs, highlighting a puzzling dynamic: both discouraging exploitation and discouraging exploration improve reasoning performance, yet the underlying principles that reconcile these effects remain poorly understood. We focus on two fundamental questions: (i) how policy entropy relates to performance, and (ii) whether spurious rewards yield gains, potentially through the interplay of clipping bias and model contamination. Our results show that clipping bias under spurious rewards reduces policy entropy, leading to more confident and deterministic outputs, while entropy minimization alone is insufficient for improvement. We further propose a reward-misalignment model explaining why spurious rewards can enhance performance beyond contaminated settings. Our findings clarify the mechanisms behind spurious-reward benefits and provide principles for more effective RLVR training.