Related papers: Implicit Differentiation for Hyperparameter Tuning…
We propose a bilevel optimization approach for the estimation of parameters in nonlocal image denoising models. The parameters we consider are both the fidelity weight and weights within the kernel of the nonlocal operator. In both cases we…
Bilevel optimization is a hierarchical framework where an upper-level optimization problem is constrained by a lower-level problem, commonly used in machine learning applications such as hyperparameter optimization. Existing bilevel…
Solving different types of optimization models (including parameters fitting) for support vector machines on large-scale training data is often an expensive computational task. This paper proposes a multilevel algorithmic framework that…
This paper addresses the problem of learning an undirected graph from data gathered at each nodes. Within the graph signal processing framework, the topology of such graph can be linked to the support of the conditional correlation matrix…
We propose an optimization proxy in terms of iterative implicit gradient methods for solving constrained optimization problems with nonconvex loss functions. This framework can be applied to a broad range of machine learning settings,…
Bilevel programs are optimization problems where some variables are solutions to optimization problems themselves, and they arise in a variety of control applications, including: control of vehicle traffic networks, inverse reinforcement…
This paper investigates simple bilevel optimization problems where we minimize an upper-level objective over the optimal solution set of a convex lower-level objective. Existing methods for such problems either only guarantee asymptotic…
Jacobian and Hessian regularization aim to reduce the magnitude of the first and second-order partial derivatives with respect to neural network inputs, and they are predominantly used to ensure the adversarial robustness of image…
Hypergraph matching has recently become a popular approach for solving correspondence problems in computer vision as it allows to integrate higher-order geometric information. Hypergraph matching can be formulated as a third-order…
This paper introduces a novel double regularization scheme for bilevel optimization problems whose lower-level problem is composite and convex, but not necessarily strongly convex, in the lower-level variable. The analysis focuses on the…
With a Bayesian approach, the linear optics correction algorithm for storage rings is revisited. Starting from the Bayes' theorem, a complete linear optics model is simplified as "likelihood functions" and "prior probability distributions".…
Bilevel optimization aims to optimize an outer objective function that depends on the solution to an inner optimization problem. It is routinely used in Machine Learning, notably for hyperparameter tuning. The conventional method to compute…
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…
In this paper we present a bilevel optimization scheme for the solution of a general image deblurring problem, in which a parametric variational-like approach is encapsulated within a machine learning scheme to provide a high quality…
The graph partitioning problem is a well-known NP-hard problem. In this paper, we formulate a 0-1 quadratic integer programming model for the graph partitioning problem with vertex weight constraints and fixed vertex constraints, and…
We investigate the choice of tuning parameters for a Bayesian multi-level group lasso model developed for the joint analysis of neuroimaging and genetic data. The regression model we consider relates multivariate phenotypes consisting of…
We propose a general dual ascent framework for Lagrangean decomposition of combinatorial problems. Although methods of this type have shown their efficiency for a number of problems, so far there was no general algorithm applicable to…
This paper considers the problem of estimating multiple related Gaussian graphical models from a $p$-dimensional dataset consisting of different classes. Our work is based upon the formulation of this problem as group graphical lasso. This…
Bilevel optimization has gained prominence in various applications. In this study, we introduce a framework for solving bilevel optimization problems, where the variables in both the lower and upper levels are constrained on Riemannian…
We consider heuristic algorithm for solving graph isomorphism problem. The algorithm based on a successive splitting of the eigenvalues of the matrices which are modifications (to positive defined) of graphs' adjacency matrices.…