Related papers: Approximation Methods for Bilevel Programming
Single-objective bilevel optimization is a specialized form of constraint optimization problems where one of the constraints is an optimization problem itself. These problems are typically non-convex and strongly NP-Hard. Recently, there…
In this paper we consider a class of optimization problems with a strongly convex objective function and the feasible set given by an intersection of a simple convex set with a set given by a number of linear equality and inequality…
Bilevel optimization is defined as a mathematical program, where an optimization problem contains another optimization problem as a constraint. These problems have received significant attention from the mathematical programming community.…
Bilevel optimization has arisen as a powerful tool for many machine learning problems such as meta-learning, hyperparameter optimization, and reinforcement learning. In this paper, we investigate the nonconvex-strongly-convex bilevel…
In this paper, we studied the federated bilevel optimization problem, which has widespread applications in machine learning. In particular, we developed two momentum-based algorithms for optimizing this kind of problem and established the…
Chance constraints are a valuable tool for the design of safe decisions in uncertain environments; they are used to model satisfaction of a constraint with a target probability. However, because of possible non-convexity and non-smoothness,…
The goal of coreset selection in supervised learning is to produce a weighted subset of data, so that training only on the subset achieves similar performance as training on the entire dataset. Existing methods achieved promising results in…
Bilevel optimization has recently attracted growing interests due to its wide applications in modern machine learning problems. Although recent studies have characterized the convergence rate for several such popular algorithms, it is still…
Invex programs are a special kind of non-convex problems which attain global minima at every stationary point. While classical first-order gradient descent methods can solve them, they converge very slowly. In this paper, we propose new…
Bilevel optimization is an important formulation for many machine learning problems. Current bilevel optimization algorithms assume that the gradient of the upper-level function is Lipschitz. However, recent studies reveal that certain…
Practical optimization problems may contain different kinds of difficulties that are often not tractable if one relies on a particular optimization method. Different optimization approaches offer different strengths that are good at…
This paper introduces and studies the convergence properties of a new class of explicit $\epsilon$-subgradient methods for the task of minimizing a convex function over the set of minimizers of another convex minimization problem. The…
Bilevel optimization has found successful applications in various machine learning problems, including hyper-parameter optimization, data cleaning, and meta-learning. However, its huge computational cost presents a significant challenge for…
In this paper, we introduce a \textit{Bi-level OPTimization} (BiOPT) framework for minimizing the sum of two convex functions, where both can be nonsmooth. The BiOPT framework involves two levels of methodologies. At the upper level of…
In this paper, we study multi-block min-max bilevel optimization problems, where the upper level is non-convex strongly-concave minimax objective and the lower level is a strongly convex objective, and there are multiple blocks of dual…
In this paper, we discuss the problem of minimizing the sum of two convex functions: a smooth function plus a non-smooth function. Further, the smooth part can be expressed by the average of a large number of smooth component functions, and…
We study the problem of optimizing nonlinear objective functions over bipartite matchings. While the problem is generally intractable, we provide several efficient algorithms for it, including a deterministic algorithm for maximizing convex…
Bilevel programming has recently received attention in the literature due to its wide range of applications, including reinforcement learning and hyper-parameter optimization. However, it is widely assumed that the underlying bilevel…
Convex optimization problems arising in applications often have favorable objective functions and complicated constraints, thereby precluding first-order methods from being immediately applicable. We describe an approach that exchanges the…
We propose techniques for approximating bilevel optimization problems with non-smooth lower level problems that can have a non-unique solution. To this end, we substitute the expression of a minimizer of the lower level minimization problem…