Related papers: Neighborhood persistency of the linear optimizatio…
The Nemhauser-Trotter theorem states that the standard linear programming (LP) formulation for the stable set problem has a remarkable property, also known as (weak) persistency: for every optimal LP solution that assigns integer values to…
We address combinatorial problems that can be formulated as minimization of a partially separable function of discrete variables (energy minimization in graphical models, weighted constraint satisfaction, pseudo-Boolean optimization, 0-1…
We consider the stability of Robust Optimization problems with respect to perturbations in their uncertainty sets. We focus on Linear Optimization problems, including those with a possibly infinite number of constraints, also known as…
While recent state-of-the-art results for adversarial imitation-learning algorithms are encouraging, recent works exploring the imitation learning from observation (ILO) setting, where trajectories \textit{only} contain expert observations,…
We consider solving linear optimization (LO) problems with uncertain objective coefficients. For such problems, we often employ robust optimization (RO) approaches by introducing an uncertainty set for the unknown coefficients. Typical RO…
While reinforcement learning (RL) has been central to the recent success of large language models (LLMs), RL optimization is notoriously unstable, especially when compared to supervised fine-tuning (SFT). In this work, we investigate the…
Preference alignment is pivotal for empowering large language models (LLMs) to generate helpful and harmless responses. However, the performance of preference alignment is highly sensitive to the prevalent noise in the preference data.…
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)…
In present paper, an analysis of the stability behaviour of ideal efficient solutions to parametric vector optimization problems is conducted. A sufficient condition for the existence of ideal efficient solutions to locally perturbed…
Integrated learning and optimization (ILO) is a framework in contextual optimization which aims to train a predictive model for the probability distribution of the underlying problem data uncertainty, with the goal of enhancing the quality…
Policy optimization (PO) is a key ingredient for reinforcement learning (RL). For control design, certain constraints are usually enforced on the policies to optimize, accounting for either the stability, robustness, or safety concerns on…
Typical behavior of the linear programming (LP) problem is studied as a relaxation of the minimum vertex cover, a type of integer programming (IP) problem. A lattice-gas model on the Erd\"os-R\'enyi random graphs of $\alpha$-uniform…
We study inverse optimization (IO), where the goal is to use a parametric optimization program as the hypothesis class to infer relationships between input-decision pairs. Most of the literature focuses on learning only the objective…
DPO (Direct Preference Optimization) has become a widely used offline preference optimization algorithm due to its simplicity and training stability. However, DPO is prone to overfitting and collapse. To address these challenges, we propose…
The linear programming (LP) approach has a long history in the theory of approximate dynamic programming. When it comes to computation, however, the LP approach often suffers from poor scalability. In this work, we introduce a relaxed…
Linear programming has played a key role in the study of algorithms for combinatorial optimization problems. In the field of approximation algorithms, this is well illustrated by the uncapacitated facility location problem. A variety of…
Robust optimization(RO) is an important tool for handling optimization problem with uncertainty. The main objective of RO is to solve optimization problems due to uncertainty associated with constraints satisfying all realizations of…
Robust topology optimization (RTO), as a class of topology optimization problems, identifies a design with the best average performance while reducing the response sensitivity to input uncertainties, e.g. load uncertainty. Solving RTO is…
This paper investigates two issues on identification of switched linear systems: persistence of excitation and numerical algorithms. The main contribution is a much weaker condition on the regressor to be persistently exciting that…
This paper studies stabilization of linear time-invariant (LTI) systems when control actions can only be realized in finitely many directions where it is possible to actuate uniformly or logarithmically extended positive scaling factors in…