Related papers: A Primal-Dual Approach to Bilevel Optimization wit…
This paper studies the distributed optimization problem when the objective functions might be nondifferentiable and subject to heterogeneous set constraints. Unlike existing subgradient methods, we focus on the case when the exact…
In recent years, a variety of gradient-based methods have been developed to solve Bi-Level Optimization (BLO) problems in machine learning and computer vision areas. However, the theoretical correctness and practical effectiveness of these…
We consider a bilevel learning framework for learning linear operators. In this framework, the learnable parameters are optimized via a loss function that also depends on the minimizer of a convex optimization problem (denoted lower-level…
Bilevel optimization has arisen as a powerful tool in modern machine learning. However, due to the nested structure of bilevel optimization, even gradient-based methods require second-order derivative approximations via Jacobian- or/and…
We present in this paper novel accelerated fully first-order methods in \emph{Bilevel Optimization} (BLO). Firstly, for BLO under the assumption that the lower-level functions admit the typical strong convexity assumption, the…
We propose efficient methods for solving stochastic simple bilevel optimization problems with convex inner levels, where the goal is to minimize an outer stochastic objective function subject to the solution set of an inner stochastic…
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.…
A learning approach to selecting regularization parameters in multi-penalty Tikhonov regularization is investigated. It leads to a bilevel optimization problem, where the lower level problem is a Tikhonov regularized problem parameterized…
Bilevel optimization problems are a class of challenging optimization problems, which contain two levels of optimization tasks. In these problems, the optimal solutions to the lower level problem become possible feasible candidates to the…
Bilevel optimization and bilevel minimax optimization have recently emerged as unifying frameworks for a range of machine-learning tasks, including hyperparameter optimization and reinforcement learning. The existing literature focuses on…
Distributed and decentralized optimization are key for the control of networked systems. Application examples include distributed model predictive control and distributed sensing or estimation. Non-linear systems, however, lead to problems…
Existing methods for nonconvex bilevel optimization (NBO) require prior knowledge of first- and second-order problem-specific parameters (e.g., Lipschitz constants and the Polyak-{\L}ojasiewicz (P{\L}) parameters) to set step sizes, a…
In this paper, we study a class of bilevel programming problem where the inner objective function is strongly convex. More specifically, under some mile assumptions on the partial derivatives of both inner and outer objective functions, we…
We consider stochastic unconstrained bilevel optimization problems when only the first-order gradient oracles are available. While numerous optimization methods have been proposed for tackling bilevel problems, existing methods either tend…
This paper presents a new approach and algorithm for solving a class of constrained Bi-Level Optimization (BLO) problems in which the lower-level problem involves constraints coupling both upper-level and lower-level variables. Such…
In this paper, we revisit the bilevel optimization problem, in which the upper-level objective function is generally nonconvex and the lower-level objective function is strongly convex. Although this type of problem has been studied…
In optimization-based image restoration models, the correct selection of hyperparameters is crucial for achieving superior performance. However, current research typically involves manual tuning of these hyperparameters, which is highly…
We propose and analyse primal-dual interior-point algorithms for convex optimization problems in conic form. The families of algorithms we analyse are so-called short-step algorithms and they match the current best iteration complexity…
In this work, we propose different formulations and gradient-based algorithms for deterministic and stochastic bilevel problems with conflicting objectives in the lower level. Such problems have received little attention in the…
Gradient-based Bi-Level Optimization (BLO) methods have been widely applied to handle modern learning tasks. However, most existing strategies are theoretically designed based on restrictive assumptions (e.g., convexity of the lower-level…