Provable Last-Iterate Convergence for Multi-Objective Safe LLM Alignment via Optimistic Primal-Dual

• URL: http://arxiv.org/abs/2602.22146v1
• Date: Wed, 25 Feb 2026 17:54:52 GMT
• Title: Provable Last-Iterate Convergence for Multi-Objective Safe LLM Alignment via Optimistic Primal-Dual
• Authors: Yining Li, Peizhong Ju, Ness Shroff,
• Abstract summary: We introduce an optimistic primal-dual (OPD) algorithm that incorporates predictive updates for both primal and dual variables to stabilize saddle-point dynamics.<n>Our analysis reveals that optimism plays a crucial role in mitigating oscillations inherent to constrained alignment objectives.
• Score: 26.51548597257528
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Reinforcement Learning from Human Feedback (RLHF) plays a significant role in aligning Large Language Models (LLMs) with human preferences. While RLHF with expected reward constraints can be formulated as a primal-dual optimization problem, standard primal-dual methods only guarantee convergence with a distributional policy where the saddle-point problem is in convex-concave form. Moreover, standard primal-dual methods may exhibit instability or divergence in the last iterate under policy parameterization in practical applications. In this work, we propose a universal primal-dual framework for safe RLHF that unifies a broad class of existing alignment algorithms, including safe-RLHF, one-shot, and multi-shot based methods. Building on this framework, we introduce an optimistic primal-dual (OPD) algorithm that incorporates predictive updates for both primal and dual variables to stabilize saddle-point dynamics. We establish last-iterate convergence guarantees for the proposed method, covering both exact policy optimization in the distributional space and convergence to a neighborhood of the optimal solution whose gap is related to approximation error and bias under parameterized policies. Our analysis reveals that optimism plays a crucial role in mitigating oscillations inherent to constrained alignment objectives, thereby closing a key theoretical gap between constrained RL and practical RLHF.

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