Risk-Sensitive Reinforcement Learning for Alleviating Exploration Dilemmas in Large Language Models

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.