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To solve unmodeled optimization problems with hard constraints, this paper proposes a novel zeroth-order approach called Safe Zeroth-order Optimization using Linear Programs (SZO-LP). The SZO-LP method solves a linear program in each…
Direct Preference Optimization (DPO) is an effective framework for aligning large language models with human preferences, but it struggles with complex reasoning tasks. DPO optimizes for the likelihood of generating preferred over…
In this paper, we propose a distributed stochastic second-order proximal method that enables agents in a network to cooperatively minimize the sum of their local loss functions without any centralized coordination. The proposed algorithm,…
Reinforcement Learning with Human Feedback (RLHF) enhances the alignment of Large Language Models (LLMs). However, its limitations have led to the development of Direct Preference Optimization (DPO), an RL-free approach designed to overcome…
Online linear programming (OLP) has gained significant attention from both researchers and practitioners due to its extensive applications, such as online auction, network revenue management, order fulfillment and advertising. Existing OLP…
Reinforcement learning from human feedback (RLHF) has proven effectiveness for aligning text-to-image (T2I) diffusion models with human preferences. Although Direct Preference Optimization (DPO) is widely adopted for its computational…
We consider the facility location problem in the one-dimensional setting where each facility can serve a limited number of agents from the algorithmic and mechanism design perspectives. From the algorithmic perspective, we prove that the…
The recent success in using human preferences to align large language models (LLMs) has significantly improved their performance in various downstream tasks, such as question answering, mathematical reasoning, and code generation. However,…
Effective personalization of LLMs is critical for a broad range of user-interfacing applications such as virtual assistants and content curation. Inspired by the strong in-context capabilities of LLMs, we propose few-shot preference…
In the Seat Arrangement problem the goal is to allocate agents to vertices in a graph such that the resulting arrangement is optimal or fair in some way. Examples include an arrangement that maximises utility or one where no agent envies…
We give a new randomized LP-rounding 1.725-approximation algorithm for the metric Fault-Tolerant Uncapacitated Facility Location problem. This improves on the previously best known 2.076-approximation algorithm of Swamy & Shmoys. To the…
The reliability redundancy allocation problem (RRAP) is a well-known tool in system design, development, and management. The RRAP is always modeled as a nonlinear mixed-integer non-deterministic polynomial-time hardness (NP-hard) problem.…
Improving the alignment of language models with human preferences remains an active research challenge. Previous approaches have primarily utilized Reinforcement Learning from Human Feedback (RLHF) via online RL methods such as Proximal…
We investigate the sequential competitive facility location problem (SCFLP) under partially binary rule where two companies sequentially open a limited number of facilities to maximize their market shares, requiring customers to patronize,…
Group Relative Policy Optimization(GRPO) has become a cornerstone of modern reinforcement learning alignment, prized for its efficacy in foregoing an explicit value-critic by leveraging reward normalization across sampled trajectory…
In this paper, we consider the Online Traveling Salesperson Problem (OLTSP) where the locations of the requests are known in advance, but not their arrival times. We study both the open variant, in which the algorithm is not required to…
Graphical models with High Order Potentials (HOPs) have received considerable interest in recent years. While there are a variety of approaches to inference in these models, nearly all of them amount to solving a linear program (LP)…
The combining of a General-Purpose Particle Swarm Optimizer (GP-PSO) with Sequential Quadratic Programming (SQP) algorithm for constrained optimization problems has been shown to be highly beneficial to the refinement, and in some cases,…
The Container Relocation Problem (CRP) is concerned with finding a sequence of moves of containers that minimizes the number of relocations needed to retrieve all containers, while respecting a given order of retrieval. However, the…
The Discrete Ordered Median Problem (DOMP) is formulated as a set partitioning problem using an exponential number of variables. Each variable corresponds to a set of demand points allocated to the same facility with the information of the…