Paper
Provable Last-Iterate Convergence for Multi-Objective Safe LLM Alignment via Optimistic Primal-Dual
Authors
Yining Li, Peizhong Ju, Ness Shroff
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.
Metadata
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Raw Data (Debug)
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"raw_xml": "<entry>\n <id>http://arxiv.org/abs/2602.22146v1</id>\n <title>Provable Last-Iterate Convergence for Multi-Objective Safe LLM Alignment via Optimistic Primal-Dual</title>\n <updated>2026-02-25T17:54:52Z</updated>\n <link href='https://arxiv.org/abs/2602.22146v1' rel='alternate' type='text/html'/>\n <link href='https://arxiv.org/pdf/2602.22146v1' rel='related' title='pdf' type='application/pdf'/>\n <summary>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.</summary>\n <category scheme='http://arxiv.org/schemas/atom' term='cs.LG'/>\n <category scheme='http://arxiv.org/schemas/atom' term='cs.AI'/>\n <published>2026-02-25T17:54:52Z</published>\n <arxiv:primary_category term='cs.LG'/>\n <author>\n <name>Yining Li</name>\n </author>\n <author>\n <name>Peizhong Ju</name>\n </author>\n <author>\n <name>Ness Shroff</name>\n </author>\n </entry>"
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