Related papers: Alignment of large language models with constraine…

Planning for both immediate and long-term benefits becomes increasingly important in recommendation. Existing methods apply Reinforcement Learning (RL) to learn planning capacity by maximizing cumulative reward for long-term recommendation.…

The prevailing approach to aligning Large Language Models (LLMs) typically relies on human or AI feedback and assumes access to specific types of preference datasets. In our work, we question the efficacy of such datasets and explore…

We introduce a primal-dual framework for solving linearly constrained nonconvex composite optimization problems. Our approach is based on a newly developed Lagrangian, which incorporates \emph{false penalty} and dual smoothing terms. This…

Many algorithms in verification and automated reasoning leverage some form of duality between proofs and refutations or counterexamples. In most cases, duality is only used as an intuition that helps in understanding the algorithms and is…

Recent advances in Large Language Models (LLMs) highlight the need to align their behaviors with human values. A critical, yet understudied, issue is the potential divergence between an LLM's stated preferences (its reported alignment with…

Recent advances in large language models (LLMs) have demonstrated significant progress in performing complex tasks. While Reinforcement Learning from Human Feedback (RLHF) has been effective in aligning LLMs with human preferences, it is…

In this paper, we propose a unified primal-dual algorithm framework based on the augmented Lagrangian function for composite convex problems with conic inequality constraints. The new framework is highly versatile. First, it not only covers…

In recent years, large language models (LLMs) have achieved remarkable success in natural language processing (NLP). LLMs require an extreme amount of parameters to attain high performance. As models grow into the trillion-parameter range,…

Large Language Models (LLMs) have shown strong promise as rerankers, especially in ``listwise'' settings where an LLM is prompted to rerank several search results at once. However, this ``cascading'' retrieve-and-rerank approach is limited…

We study a class of optimization problems in which the objective function is given by the sum of a differentiable but possibly nonconvex component and a nondifferentiable convex regularization term. We introduce an auxiliary variable to…

Motivated by big data applications, first-order methods have been extremely popular in recent years. However, naive gradient methods generally converge slowly. Hence, much efforts have been made to accelerate various first-order methods.…

In this paper, we employ the concept of quasi-relative interior to analyze the method of Lagrange multipliers and establish strong Lagrangian duality for nonsmooth convex optimization problems in Hilbert spaces. Then, we generalize the…

We present a numerical method for the minimization of constrained optimization problems where the objective is augmented with large quadratic penalties of inconsistent equality constraints. Such objectives arise from quadratic integral…

Alignment of large language models (LLMs) typically involves training a reward model on preference data, followed by policy optimization with respect to the reward model. However, optimizing policies with respect to a single reward model…

The importance of Reinforcement Learning from Human Feedback (RLHF) in aligning large language models (LLMs) with human values cannot be overstated. RLHF is a three-stage process that includes supervised fine-tuning (SFT), reward learning,…

Lagrangian decomposition (LD) is a relaxation method that provides a dual bound for constrained optimization problems by decomposing them into more manageable sub-problems. This bound can be used in branch-and-bound algorithms to prune the…

While Reinforcement Learning from Human Feedback (RLHF) aligns Large Language Models (LLMs) with general, aggregate human preferences, it is suboptimal for learning diverse, individual perspectives. In this work, we study Reinforcement…

Local convergence analysis of the augmented Lagrangian method (ALM) is established for a large class of composite optimization problems with nonunique Lagrange multipliers under a second-order sufficient condition. We present a new…

Recent advances in reasoning with large language models (LLMs) have demonstrated strong performance on complex mathematical tasks, including combinatorial optimization. Techniques such as Chain-of-Thought and In-Context Learning have…

Large language models (LLMs) deliver impressive results but face challenges from increasing model sizes and computational costs. Structured pruning reduces model size and speeds up inference but often causes uneven degradation across…