# Exploration-Driven Optimization for Test-Time Large Language Model Reasoning

arXiv: https://arxiv.org/abs/2605.09853 · HTML: https://mlsanity.com/paper/2605.09853/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 64 of its 88 references that are in the map.
- First posted on arXiv 11 May 2026.

## Placed in

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

## Builds on (most cited first, 30 of 64)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [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)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [High-Dimensional Continuous Control Using Generalized Advantage Estimation](https://mlsanity.com/paper/1506.02438/) (2015)
- [Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters](https://mlsanity.com/paper/2408.03314/) (2024)
- [Least-to-Most Prompting Enables Complex Reasoning in Large Language Models](https://mlsanity.com/paper/2205.10625/) (2022)
- [s1: Simple test-time scaling](https://mlsanity.com/paper/2501.19393/) (2025)
- [OpenAI o1 System Card](https://mlsanity.com/paper/2412.16720/) (2024)
- [OlympiadBench: A Challenging Benchmark for Promoting AGI with Olympiad-Level Bilingual Multimodal Scientific Problems](https://mlsanity.com/paper/2402.14008/) (2024)
- [Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement](https://mlsanity.com/paper/2409.12122/) (2024)
- [A Diversity-Promoting Objective Function for Neural Conversation Models](https://mlsanity.com/paper/1510.03055/) (2015)
- [Math-Shepherd: Verify and Reinforce LLMs Step-by-step without Human Annotations](https://mlsanity.com/paper/2312.08935/) (2023)
- [Reasoning with Language Model is Planning with World Model](https://mlsanity.com/paper/2305.14992/) (2023)
- [MetaMath: Bootstrap Your Own Mathematical Questions for Large Language Models](https://mlsanity.com/paper/2309.12284/) (2023)
- [WizardMath: Empowering Mathematical Reasoning for Large Language Models via Reinforced Evol-Instruct](https://mlsanity.com/paper/2308.09583/) (2023)
- [Language Agent Tree Search Unifies Reasoning Acting and Planning in Language Models](https://mlsanity.com/paper/2310.04406/) (2023)
- [Smarter, Better, Faster, Longer: A Modern Bidirectional Encoder for Fast, Memory Efficient, and Long Context Finetuning and Inference](https://mlsanity.com/paper/2412.13663/) (2024)
- [Reinforced Self-Training (ReST) for Language Modeling](https://mlsanity.com/paper/2308.08998/) (2023)
- [MAmmoTH: Building Math Generalist Models through Hybrid Instruction Tuning](https://mlsanity.com/paper/2309.05653/) (2023)
- [The Entropy Mechanism of Reinforcement Learning for Reasoning Language Models](https://mlsanity.com/paper/2505.22617/) (2025)
- [Scaling Relationship on Learning Mathematical Reasoning with Large Language Models](https://mlsanity.com/paper/2308.01825/) (2023)
- [The Lessons of Developing Process Reward Models in Mathematical Reasoning](https://mlsanity.com/paper/2501.07301/) (2025)
- [Understanding the Effects of RLHF on LLM Generalisation and Diversity](https://mlsanity.com/paper/2310.06452/) (2023)
- [Large Language Models are Better Reasoners with Self-Verification](https://mlsanity.com/paper/2212.09561/) (2022)
- [Alphazero-like Tree-Search can Guide Large Language Model Decoding and Training](https://mlsanity.com/paper/2309.17179/) (2023)

## Abstract (arXiv)

Post-training techniques combined with inference-time scaling significantly enhance the reasoning and alignment capabilities of large language models (LLMs). However, a fundamental tension arises: inference-time methods benefit from diverse sampling from a relatively flattened probability distribution, whereas reinforcement learning (RL)-based post-training inherently sharpens these distributions. To address this, we propose Exploration-Driven Optimization (EDO), which extends reward-biasing style exploration objectives to iterative post-training and integrates them into standard RL objectives, encouraging greater diversity in sampled solutions while facilitating more effective inference-time computation. We incorporate EDO into iterative Direct Preference Optimization (iDPO) and Group Relative Policy Optimization (GRPO), resulting in two variants: ED-iDPO and ED-GRPO. Extensive experiments demonstrate that both ED-iDPO and ED-GRPO exhibit greater solution diversity and improved reasoning abilities, particularly when combined with test-time computation techniques like self-consistency. Across three in-distribution reasoning benchmarks, EDO achieves a 1.0-1.3% improvement over the strongest baselines, and delivers an additional 1.5% average gain on five out-of-distribution tasks. Beyond accuracy, EDO preserves model entropy and stabilizes RL training dynamics, highlighting its effectiveness in preventing over-optimization collapse. Taken together, these results establish EDO as a practical framework for balancing exploration and exploitation in LLM reasoning, especially in settings that rely on test-time scaling.