Not yet reviewed by Pith; the record is open.

In many large language model (LLM) alignment applications, users expect not only high-quality outputs but also substantial diversity. However, existing methods often face a fundamental trade-off between these objectives: approaches that improve output quality tend to reduce diversity, while methods that increase diversity often do so at the expense of quality. In this work, we propose Quality-constrained Entropy Maximization Policy Optimization (QEMPO), a novel framework that enhances the diversity of LLM outputs while explicitly preserving output quality. QEMPO is grounded in a strong theoretical foundation: we derive a closed-form analytical solution that provably maximizes entropy-a principled measure of diversity-subject to a quality constraint, with guarantees on optimality under the defined objective. Leveraging this solution, QEMPO naturally supports both online and offline training settings. Empirical results demonstrate that QEMPO consistently improves output diversity without sacrificing quality, and in many cases yields gains in both dimensions compared to existing baselines, aligning with our theoretical guarantees.