# Risk-Sensitive RL for Alleviating Exploration Dilemmas in Large Language Models

arXiv: https://arxiv.org/abs/2509.24261 · HTML: https://mlsanity.com/paper/2509.24261/

## 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 51 of its 63 references that are in the map.
- First posted on arXiv 29 Sep 2025.

## Placed in

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

## Builds on (most cited first, 30 of 51)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [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)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Efficient Memory Management for Large Language Model Serving with PagedAttention](https://mlsanity.com/paper/2309.06180/) (2023)
- [Gemini 2.5: Pushing the Frontier with Advanced Reasoning, Multimodality, Long Context, and Next Generation Agentic Capabilities](https://mlsanity.com/paper/2507.06261/) (2025)
- [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)
- [Kimi k1.5: Scaling Reinforcement Learning with LLMs](https://mlsanity.com/paper/2501.12599/) (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)
- [Does Reinforcement Learning Really Incentivize Reasoning Capacity in LLMs Beyond the Base Model?](https://mlsanity.com/paper/2504.13837/) (2025)
- [A Distributional Perspective on Reinforcement Learning](https://mlsanity.com/paper/1707.06887/) (2017)
- [Mastering Chess and Shogi by Self-Play with a General Reinforcement Learning Algorithm](https://mlsanity.com/paper/1712.01815/) (2017)
- [Unifying Count-Based Exploration and Intrinsic Motivation](https://mlsanity.com/paper/1606.01868/) (2016)
- [The Entropy Mechanism of Reinforcement Learning for Reasoning Language Models](https://mlsanity.com/paper/2505.22617/) (2025)
- [Training Language Models to Self-Correct via Reinforcement Learning](https://mlsanity.com/paper/2409.12917/) (2024)
- [Demystifying Long Chain-of-Thought Reasoning in LLMs](https://mlsanity.com/paper/2502.03373/) (2025)
- [Reasoning with Exploration: An Entropy Perspective](https://mlsanity.com/paper/2506.14758/) (2025)
- [DeepMath-103K: A Large-Scale, Challenging, Decontaminated, and Verifiable Mathematical Dataset for Advancing Reasoning](https://mlsanity.com/paper/2504.11456/) (2025)
- [On the Global Convergence Rates of Softmax Policy Gradient Methods](https://mlsanity.com/paper/2005.06392/) (2020)
- [ProRL: Prolonged Reinforcement Learning Expands Reasoning Boundaries in Large Language Models](https://mlsanity.com/paper/2505.24864/) (2025)
- [SPoC: Search-based Pseudocode to Code](https://mlsanity.com/paper/1906.04908/) (2019)
- [The Surprising Effectiveness of Negative Reinforcement in LLM Reasoning](https://mlsanity.com/paper/2506.01347/) (2025)
- [Seed1.5-Thinking: Advancing Superb Reasoning Models with Reinforcement Learning](https://mlsanity.com/paper/2504.13914/) (2025)
- [Pass@k Training for Adaptively Balancing Exploration and Exploitation of Large Reasoning Models](https://mlsanity.com/paper/2508.10751/) (2025)

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

- [DSDR: Dual-Scale Diversity Regularization for Exploration in LLM Reasoning](https://mlsanity.com/paper/2602.19895/) (2026)
- [Why Pass@k Optimization Can Degrade Pass@1: Prompt Interference in LLM Post-training](https://mlsanity.com/paper/2602.21189/) (2026)
- [PACEvolve++: Improving Test-time Learning for Evolutionary Search Agents](https://mlsanity.com/paper/2605.07039/) (2026)
- [Inference-Aware Meta-Alignment of LLMs via Non-Linear GRPO](https://mlsanity.com/paper/2602.01603/) (2026)
- [Boosting LLM Reasoning via Human-Inspired Reward Shaping](https://mlsanity.com/paper/2602.04265/) (2026)
- [All Roads Lead to Rome: Incentivizing Divergent Thinking in Vision-Language Models](https://mlsanity.com/paper/2604.00479/) (2026)
- [Reinforcement Learning for Exponential Utility: Algorithms and Convergence in Discounted MDPs](https://mlsanity.com/paper/2605.08053/) (2026)
- [Breaking textitWinner-Takes-All: Cooperative Policy Optimization Improves Diverse LLM Reasoning](https://mlsanity.com/paper/2605.11461/) (2026)
- [Reinforcement Learning without Ground-Truth Solutions can Improve LLMs](https://mlsanity.com/paper/2606.27369/) (2026)
- [Don't Let Gains FADE: Breaking Down Policy Gradient Weights in RL](https://mlsanity.com/paper/2607.01490/) (2026)
- [Planned Test-Time Scaling with Coordinated Reasoning Paths](https://mlsanity.com/paper/2609.27374/) (2026)
- [Exploring More, Reasoning Better: Stepwise Risk-Sensitive GRPO for Diffusion Language Models](https://mlsanity.com/paper/2610.00661/) (2026)
- [Distribution Matching Evolutionary Algorithms for Rare Event Sampling](https://mlsanity.com/paper/2610.03833/) (2026)
- [Improving Neural Symbolic Regression with a Diverse Prior and Post-training Alignment](https://mlsanity.com/paper/2610.17994/) (2026)

## Abstract (arXiv)

Reinforcement Learning with Verifiable Rewards (RLVR) has proven effective for enhancing Large Language Models (LLMs) on complex reasoning tasks. However, existing methods suffer from an exploration dilemma: the sharply peaked initial policies of pre-trained LLMs confine standard RL algorithms to a narrow set of solutions, boosting single-solution accuracy (pass@1) but suppressing solution diversity and multi-solution performance (pass@k). As a result, RLVR often distills existing capabilities rather than discovering new reasoning strategies. To overcome this, we introduce a Risk-Sensitive Reinforcement Learning framework. Our approach employs a risk-seeking objective that interpolates between mean and maximum rewards, leading to a novel algorithm, Risk-Sensitive GRPO (RS-GRPO), which drives deeper exploration by amplifying learning from challenging prompts. Remarkably, RS-GRPO is simple to implement, requiring only minor code modifications. On six mathematical reasoning benchmarks and with five different LLMs, RS-GRPO consistently improves pass@k performance while maintaining or enhancing pass@1 accuracy.