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We consider simple bilevel optimization problems where the goal is to compute among the optimal solutions of a composite convex optimization problem, one that minimizes a secondary objective function. Our main contribution is threefold. (i)…
Bilevel optimization problems embed the optimality of a subproblem as a constraint of another optimization problem. We introduce the concept of near-optimality robustness for bilevel optimization, protecting the upper-level solution…
A natural optimization model that formulates many online resource allocation and revenue management problems is the online linear program (LP) in which the constraint matrix is revealed column by column along with the corresponding…
Linear programming (LP) relaxations are widely employed in exact solution methods for multilinear programs (MLP). One example is the family of Recursive McCormick Linearization (RML) strategies, where bilinear products are substituted for…
We propose a new randomized algorithm for solving convex optimization problems that have a large number of constraints (with high probability). Existing methods like interior-point or Newton-type algorithms are hard to apply to such…
Bilevel optimization has emerged as a technique for addressing a wide range of machine learning problems that involve an outer objective implicitly determined by the minimizer of an inner problem. While prior works have primarily focused on…
Interest in bilevel optimization has grown in recent years, partially due to its applications to tackle challenging machine-learning problems. Several exciting recent works have been centered around developing efficient gradient-based…
Detectability of failures of linear programming (LP) decoding and the potential for improvement by adding new constraints motivate the use of an adaptive approach in selecting the constraints for the underlying LP problem. In this paper, we…
Pretrained Language Models (PLMs) have advanced Natural Language Processing (NLP) tasks significantly, but finetuning PLMs on low-resource datasets poses significant challenges such as instability and overfitting. Previous methods tackle…
In multi-robot systems, achieving coordinated missions remains a significant challenge due to the coupled nature of coordination behaviors and the lack of global information for individual robots. To mitigate these challenges, this paper…
Large Language Models (LLMs) have revolutionized Natural Language Processing (NLP) but demand massive GPU resources for training. Lowering the threshold for LLMs training would encourage greater participation from researchers, benefiting…
Many key problems in machine learning and data science are routinely modeled as optimization problems and solved via optimization algorithms. With the increase of the volume of data and the size and complexity of the statistical models used…
Meta-learning (a.k.a. learning to learn) has recently emerged as a promising paradigm for a variety of applications. There are now many meta-learning methods, each focusing on different modeling aspects of base and meta learners, but all…
Linear programming (LP) is an extremely useful tool and has been successfully applied to solve various problems in a wide range of areas, including operations research, engineering, economics, or even more abstract mathematical areas such…
Bilevel optimization deals with nested problems in which a leader takes the first decision to minimize their objective function while accounting for a follower's best-response reaction. Constrained bilevel problems with integer variables…
The reformulation-linearization technique (RLT) is a prominent approach to constructing tight linear relaxations of non-convex continuous and mixed-integer optimization problems. The goal of this paper is to extend the applicability and…
Bilevel optimization has been widely applied in many important machine learning applications such as hyperparameter optimization and meta-learning. Recently, several momentum-based algorithms have been proposed to solve bilevel optimization…
Large language models (LLMs) have numerous real-life applications across various domains, such as natural language translation, sentiment analysis, language modeling, chatbots and conversational agents, creative writing, text…
Recently, bi-level optimization (BLO) has taken center stage in some very exciting developments in the area of signal processing (SP) and machine learning (ML). Roughly speaking, BLO is a classical optimization problem that involves two…
We study the feature-based newsvendor problem, in which a decision-maker has access to historical data consisting of demand observations and exogenous features. In this setting, we investigate feature selection, aiming to derive sparse,…