Alignment of large language models with constrained learning

We study the problem of computing an optimal large language model (LLM) policy for a constrained alignment problem, where the goal is to maximize a primary reward objective while satisfying constraints on secondary utilities. Despite the popularity of Lagrangian-based LLM policy search in constrained alignment, iterative primal-dual methods often fail to converge, and non-iterative dual-based methods do not achieve optimality in the LLM parameter space. To address these challenges, we employ Lagrangian duality to develop an iterative dual-based alignment method that alternates between updating the LLM policy via Lagrangian maximization and updating the dual variable via dual descent. In theory, we characterize the primal-dual gap between the primal value in the distribution space and the dual value in the LLM parameter space. We further quantify the optimality gap of the learned LLM policies at near-optimal dual variables with respect to both the objective and the constraint functions. These results prove that dual-based alignment methods can find an optimal constrained LLM policy, up to an LLM parametrization gap. We demonstrate the effectiveness and merits of our approach through extensive experiments conducted on the PKU-SafeRLHF dataset.

Evaluating the Diversity and Quality of LLM Generated Content

Recent work suggests that preference-tuning techniques--including Reinforcement Learning from Human Preferences (RLHF) methods like PPO and GRPO, as well as alternatives like DPO--reduce diversity, creating a dilemma given that such models are widely deployed in applications requiring diverse outputs. To address this, we introduce a framework for measuring effective semantic diversity--diversity among outputs that meet quality thresholds--which better reflects the practical utility of large language models (LLMs). Using open-ended tasks that require no human intervention, we find counterintuitive results: although preference-tuned models--especially those trained via RL--exhibit reduced lexical and syntactic diversity, they produce greater effective semantic diversity than SFT or base models, not from increasing diversity among high-quality outputs, but from generating more high-quality outputs overall. We discover that preference tuning reduces syntactic diversity while preserving semantic diversity--revealing a distinction between diversity in form and diversity in content that traditional metrics often overlook. Our analysis further shows that smaller models are consistently more parameter-efficient at generating unique content within a fixed sampling budget, offering insights into the relationship between model scaling and diversity. These findings have important implications for applications that require diverse yet high-quality outputs, from creative assistance to synthetic data generation.

Conformal Structured Prediction

Conformal prediction has recently emerged as a promising strategy for quantifying the uncertainty of a predictive model; these algorithms modify the model to output sets of labels that are guaranteed to contain the true label with high probability. However, existing conformal prediction algorithms have largely targeted classification and regression settings, where the structure of the prediction set has a simple form as a level set of the scoring function. However, for complex structured outputs such as text generation, these prediction sets might include a large number of labels and therefore be hard for users to interpret. In this paper, we propose a general framework for conformal prediction in the structured prediction setting, that modifies existing conformal prediction algorithms to output structured prediction sets that implicitly represent sets of labels. In addition, we demonstrate how our approach can be applied in domains where the prediction sets can be represented as a set of nodes in a directed acyclic graph; for instance, for hierarchical labels such as image classification, a prediction set might be a small subset of coarse labels implicitly representing the prediction set of all their more fine-descendants. We demonstrate how our algorithm can be used to construct prediction sets that satisfy a desired coverage guarantee in several domains.