Efficient RLVR Training via Weighted Mutual Information Data Selection

TL;DR

This paper introduces InSight, a novel data selection method for reinforcement learning with verifiable rewards, that improves training efficiency and performance by using a Bayesian mutual information approach to better select informative data.

Contribution

InSight is a new data sampling method based on weighted mutual information, addressing limitations of difficulty-based heuristics in RL training for language models.

Findings

Achieves state-of-the-art performance on multiple benchmarks.

Improves training efficiency by up to 2.2x.

Demonstrates consistent gains across diverse reasoning tasks.

Abstract

Reinforcement learning (RL) plays a central role in improving the reasoning and alignment of large language models, yet its efficiency critically depends on how training data are selected. Existing online selection strategies predominantly rely on difficulty-based heuristics, favouring datapoints with intermediate success rates, implicitly equating difficulty with informativeness and neglecting epistemic uncertainty arising from limited evidence. We introduce InSight, an INformation-guided data SamplInG metHod for RL Training, grounded in a weighted mutual information objective. By modeling data outcomes with Bayesian latent success rates, we show that expected uncertainty reduction decomposes into complementary difficulty- and evidence-dependent components, revealing a fundamental limitation of difficulty-only selection. Leveraging this observation, InSight constructs a stable acquisition score based on the mean belief of datapoints' success rather than noisy sampled outcomes, and naturally extends to multi-rollout settings common in reinforcement learning with verifiable rewards (RLVR). Extensive experiments demonstrate that InSight consistently achieves state-of-the-art performance and improves training efficiency, including a +1.41 average gain on Planning & Mathmatics benchmarks, +1.01 improvement on general reasoning, and up to ~2.2x acceleration, with negligible additional computational overhead.