相关论文: Comparing BilevelJuMP.jl Formulations: Support Vec…

This article studies Gauss-Newton-type methods for over-determined systems to find solutions to bilevel programming problems. To proceed, we use the lower-level value function reformulation of bilevel programs and consider necessary…

Proper hyperparameter tuning is essential for achieving optimal performance of modern machine learning (ML) methods in predictive tasks. While there is an extensive literature on tuning ML learners for prediction, there is only little…

Hyperparameter optimization in machine learning is often achieved using naive techniques that only lead to an approximate set of hyperparameters. Although techniques such as Bayesian optimization perform an intelligent search on a given…

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…

We present \texttt{MathOptAI.jl}, an open-source Julia library for embedding trained machine learning predictors into a JuMP model. \texttt{MathOptAI.jl} can embed a wide variety of neural networks, decision trees, and Gaussian Processes…

Bilevel optimisation is used in inverse imaging problems for hyperparameter learning/identification and experimental design, for instance, to find optimal regularisation parameters and forward operators. However, computationally, the…

Linear bilevel programs (linear BLPs) have been widely used in computational mathematics and optimization in several applications. Single-level reformulation for linear BLPs replaces the lower-level linear program with its…

We present DataDeps.jl: a julia package for the reproducible handling of static datasets to enhance the repeatability of scripts used in the data and computational sciences. It is used to automate the data setup part of running software…

We review some recent learning approaches in variational imaging, based on bilevel optimisation, and emphasize the importance of their treatment in function space. The paper covers both analytical and numerical techniques. Analytically, we…

We investigate relaxations for a class of discrete bilevel programs where the interaction constraints linking the leader and the follower are linear. Our approach reformulates the upper-level optimality constraints by projecting the…

We present a Julia package HypersurfaceRegions.jl for computing all connected components in the complement of an arrangement of real algebraic hypersurfaces in $\mathbb{R}^n$.

Motivation: Estimating model parameters from experimental observations is one of the key challenges in systems biology and can be computationally very expensive. While the Julia programming language was recently developed as a high-level…

Recently, Serfling and Xiao (2007) extended the L-moment theory (Hosking, 1990) to the multivariate setting. In the present paper, we focus on the two-dimension random vectors to establish a link between the bivariate L-moments (BLM) and…

It is common within the deep learning community to first pre-train a deep neural network from a large-scale dataset and then fine-tune the pre-trained model to a specific downstream task. Recently, both supervised and unsupervised…

We study a general class of bilevel problems, consisting in the minimization of an upper-level objective which depends on the solution to a parametric fixed-point equation. Important instances arising in machine learning include…

MultiPrecisionArrays.jl is a Julia package. This package provides data structures and solvers for several variants of iterative refinement. It will become much more useful when half precision (aka Float16) is fully supported in LAPACK/BLAS.…

Many optimization problems require hyperparameters, i.e., parameters that must be pre-specified in advance, such as regularization parameters and parametric regularizers in variational regularization methods for inverse problems, and…

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…

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…

Bilevel reinforcement learning (RL), which features intertwined two-level problems, has attracted growing interest recently. The inherent non-convexity of the lower-level RL problem is, however, to be an impediment to developing bilevel…