Related papers: Beyond Value Functions: Single-Loop Bilevel Optimi…
We study a class of bilevel optimization problems in which both the upper- and lower-level problems have minimax structures. This setting captures a broad range of emerging applications. Despite the extensive literature on bilevel…
Bilevel optimization has garnered significant attention in the machine learning community recently, particularly regarding the development of efficient numerical methods. While substantial progress has been made in developing efficient…
Bilevel optimization problems consist of minimizing a value function whose evaluation depends on the solution of an inner optimization problem. These problems are typically tackled using first-order methods that require computing the…
We propose a new class of rigorous methods for derivative-free optimization with the aim of delivering efficient and robust numerical performance for functions of all types, from smooth to non-smooth, and under different noise regimes. To…
Bilevel optimization is a central tool in machine learning for high-dimensional hyperparameter tuning. Its applications are vast; for instance, in imaging it can be used for learning data-adaptive regularizers and optimizing forward…
A large number of application problems involve two levels of optimization, where one optimization task is nested inside the other. These problems are known as bilevel optimization problems and have been studied by both classical…
Strongly motivated from use in various fields including machine learning, the methodology of sparse optimization has been developed intensively so far. Especially, the recent advance of algorithms for solving problems with nonsmooth…
Bilevel programs (BPs) find a wide range of applications in fields such as energy, transportation, and machine learning. As compared to BPs with continuous (linear/convex) optimization problems in both levels, the BPs with discrete decision…
In this paper, we propose the Bi-Sub-Gradient (Bi-SG) method, which is a generalization of the classical sub-gradient method to the setting of convex bi-level optimization problems. This is a first-order method that is very easy to…
Simple bilevel problems are optimization problems in which we want to find an optimal solution to an inner problem that minimizes an outer objective function. Such problems appear in many machine learning and signal processing applications…
This work presents the first projection-free algorithm to solve stochastic bi-level optimization problems, where the objective function depends on the solution of another stochastic optimization problem. The proposed $\textbf{S}$tochastic…
Multilevel optimization has gained renewed interest in machine learning due to its promise in applications such as hyperparameter tuning and continual learning. However, existing methods struggle with the inherent difficulty of efficiently…
Gradient-based optimization has been critical to the success of machine learning, updating a single set of parameters to minimize a single loss. A growing number of applications rely on a generalization of this, where we have a bilevel or…
We study a class of bilevel convex optimization problems where the goal is to find the minimizer of an objective function in the upper level, among the set of all optimal solutions of an optimization problem in the lower level. A wide range…
Fine-tuning large-scale pre-trained models is prohibitively expensive in terms of computation and memory costs. Low-Rank Adaptation (LoRA), a popular Parameter-Efficient Fine-Tuning (PEFT) method, offers an efficient solution by optimizing…
This paper presents a novel method for utilizing fine-tuned Large Language Models (LLMs) to minimize data requirements in load profile analysis, demonstrated through the restoration of missing data in power system load profiles. A two-stage…
Reinforcement learning (RL) often has a hierarchical structure, where an upper-level (UL) learner selects model parameters and a lower-level (LL) decision-making process responds, naturally leading to a bilevel optimization problem. Most…
Generative models form the backbone of modern machine learning, underpinning state-of-the-art systems in text, vision, and multimodal applications. While Maximum Likelihood Estimation has traditionally served as the dominant training…
This paper investigates projection-free algorithms for stochastic constrained multi-level optimization. In this context, the objective function is a nested composition of several smooth functions, and the decision set is closed and convex.…
Gradient-based optimization methods for hyperparameter tuning guarantee theoretical convergence to stationary solutions when for fixed upper-level variable values, the lower level of the bilevel program is strongly convex (LLSC) and smooth…