Random Policy Valuation is Enough for LLM Reasoning with Verifiable Rewards

• URL: http://arxiv.org/abs/2509.24981v1
• Date: Mon, 29 Sep 2025 16:09:07 GMT
• Title: Random Policy Valuation is Enough for LLM Reasoning with Verifiable Rewards
• Authors: Haoran He, Yuxiao Ye, Qingpeng Cai, Chen Hu, Binxing Jiao, Daxin Jiang, Ling Pan,
• Abstract summary: We introduce Random Policy Valuation for Diverse Reasoning (ROVER)<n>ROVER is a minimalist yet highly effective RL method that samples actions from a softmax over uniform-policy Q-values.<n>It demonstrates superior performance in both textbfquality (textbf+8.2 on pass@1, textbf+16.8 on pass@256) and textbfdiversity (textbf+17.6%)
• Score: 47.557539197058496
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: RL with Verifiable Rewards (RLVR) has emerged as a promising paradigm for improving the reasoning abilities of large language models (LLMs). Current methods rely primarily on policy optimization frameworks like PPO and GRPO, which follow generalized policy iteration that alternates between evaluating the current policy's value and improving the policy based on evaluation. While effective, they often suffer from training instability and diversity collapse, requiring complex heuristic tricks and careful tuning. We observe that standard RLVR in math reasoning can be formalized as a specialized finite-horizon Markov Decision Process with deterministic state transitions, tree-structured dynamics, and binary terminal rewards. Though large in scale, the underlying structure is simpler than general-purpose control settings for which popular RL algorithms (e.g., PPO) were developed, suggesting that several sophisticated techniques in existing methods may be reduced or even omitted. Based on this insight, we prove a surprising result: the optimal action can be recovered from the Q-function of a fixed uniformly random policy, thereby bypassing the generalized policy iteration loop and its associated heuristics. We introduce Random Policy Valuation for Diverse Reasoning (ROVER) to translate this principle into a practical and scalable algorithm for LLM math reasoning, a minimalist yet highly effective RL method that samples actions from a softmax over these uniform-policy Q-values. ROVER preserves diversity throughout training, allowing sustained exploration of multiple valid pathways. Across multiple base models and standard math reasoning benchmarks, ROVER demonstrates superior performance in both \textbf{quality} (\textbf{+8.2} on pass@1, \textbf{+16.8} on pass@256) and \textbf{diversity} (\textbf{+17.6\%}), despite its radical simplification compared to strong, complicated existing methods.

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