Maximum Likelihood Reinforcement Learning

• URL: http://arxiv.org/abs/2602.02710v1
• Date: Mon, 02 Feb 2026 19:23:42 GMT
• Title: Maximum Likelihood Reinforcement Learning
• Authors: Fahim Tajwar, Guanning Zeng, Yueer Zhou, Yuda Song, Daman Arora, Yiding Jiang, Jeff Schneider, Ruslan Salakhutdinov, Haiwen Feng, Andrea Zanette,
• Abstract summary: MaxRL is a sampling-based framework to approximate maximum likelihood using reinforcement learning techniques.<n>We show that MaxRL achieves up to 20x test-time scaling efficiency gains compared to its GRPO-trained counterpart.
• Score: 51.83034817019976
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Reinforcement learning is the method of choice to train models in sampling-based setups with binary outcome feedback, such as navigation, code generation, and mathematical problem solving. In such settings, models implicitly induce a likelihood over correct rollouts. However, we observe that reinforcement learning does not maximize this likelihood, and instead optimizes only a lower-order approximation. Inspired by this observation, we introduce Maximum Likelihood Reinforcement Learning (MaxRL), a sampling-based framework to approximate maximum likelihood using reinforcement learning techniques. MaxRL addresses the challenges of non-differentiable sampling by defining a compute-indexed family of sample-based objectives that interpolate between standard reinforcement learning and exact maximum likelihood as additional sampling compute is allocated. The resulting objectives admit a simple, unbiased policy-gradient estimator and converge to maximum likelihood optimization in the infinite-compute limit. Empirically, we show that MaxRL Pareto-dominates existing methods in all models and tasks we tested, achieving up to 20x test-time scaling efficiency gains compared to its GRPO-trained counterpart. We also observe MaxRL to scale better with additional data and compute. Our results suggest MaxRL is a promising framework for scaling RL training in correctness based settings.

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