Related papers: On the Complexity of Robust Bilevel Optimization W…
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…
Stochastic bilevel optimization, which captures the inherent nested structure of machine learning problems, is gaining popularity in many recent applications. Existing works on bilevel optimization mostly consider either unconstrained…
In this paper, we study the problem of solving a simple bilevel optimization problem, where the upper-level objective is minimized over the solution set of the lower-level problem. We focus on the general setting in which both the upper-…
This paper investigates a class of stochastic bilevel optimization problems where the upper-level function is nonconvex with potentially unbounded smoothness and the lower-level problem is strongly convex. These problems have significant…
In this paper we study constraint qualifications and optimality conditions for bilevel programming problems. We strive to derive checkable constraint qualifications in terms of problem data and applicable optimality conditions. For the…
We study multilevel techniques, commonly used in PDE multigrid literature, to solve structured optimization problems. For a given hierarchy of levels, we formulate a coarse model that approximates the problem at each level and provides a…
We consider an unconstrained continuous optimization problem where, in each iteration, gradient estimates may be arbitrarily corrupted with a probability greater than 1/2. Additionally, function value estimates may exhibit heavy-tailed…
Bilevel optimization enjoys a wide range of applications in emerging machine learning and signal processing problems such as hyper-parameter optimization, image reconstruction, meta-learning, adversarial training, and reinforcement…
As machine learning (ML) applications grow increasingly complex in recent years, modern ML frameworks often need to address multiple potentially conflicting objectives with coupled decision variables across different layers. This creates a…
In this paper, we develop a two-stage data-driven approach to address the adjustable robust optimization problem, where the uncertainty set is adjustable to manage infeasibility caused by significant or poorly quantified uncertainties. In…
Bilevel learning has gained prominence in machine learning, inverse problems, and imaging applications, including hyperparameter optimization, learning data-adaptive regularizers, and optimizing forward operators. The large-scale nature of…
The addition of lower level integrality constraints to a bi-level linear program is known to result in significantly weaker analytical properties. Most notably, the upper level goal function in the optimistic setting lacks lower…
Bilevel optimization has been applied to a wide variety of machine learning models, and numerous stochastic bilevel optimization algorithms have been developed in recent years. However, most existing algorithms restrict their focus on the…
In this paper, we consider an adaptive approach to address optimization problems with uncertain cost parameters. Here, the decision maker selects an initial decision, observes the realization of the uncertain cost parameters, and then is…
In high-dimensional data analysis, bi-level sparsity is often assumed when covariates function group-wisely and sparsity can appear either at the group level or within certain groups. In such cases, an ideal model should be able to…
We consider class of equilibrium models including the implicit Walras supply-demand and competitive models. Such a model in this class, in general, is ill-posed. We formulate such a model in the form a variational inequality having certain…
Bilevel optimization has become a powerful framework in various machine learning applications including meta-learning, hyperparameter optimization, and network architecture search. There are generally two classes of bilevel optimization…
In this work we study binary two-stage robust optimization problems with objective uncertainty. We present an algorithm to calculate efficiently lower bounds for the binary two-stage robust problem by solving alternately the underlying…
We study the problem of bipedal robot navigation in complex environments with uncertain and rough terrain. In particular, we consider a scenario in which the robot is expected to reach a desired goal location by traversing an environment…
This paper considers the smooth bilevel optimization in which the lower-level problem is strongly convex and the upper-level problem is possibly nonconvex. We focus on the stochastic setting where the algorithm can access the unbiased…