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Combinatorial Penalties: Which structures are preserved by convex relaxations?

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Publications associées (39)

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Industry 4.0 Technologies and Customer-centricity for Digital Supply Chains

Rachel Agnès Laetitia Rosemonde Marie Lacroix

The last few years have experienced the emergence of Industry 4.0 (I4.0), ultra-customization, and the explosion of demand for ethical, fair trade, and sustainable consumption. Organizations have therefore started a digital transformation of their SCs and ...

EPFL2021

Vehicle-to-Grid for Reliable Frequency Regulation

Dirk Lauinger

Future low-carbon societies will need to store vast amounts of electricity to stabilize electricity grids and to power electric vehicles. Vehicle-to-grid allows vehicle owners and grid operators to share the costs of electricity storage by making the batte ...

EPFL2022

Addressing fairness in classification with a model-agnostic multi-objective algorithm

Boi Faltings, Diego Matteo Antognini, Claudiu-Cristian Musat

The goal of fairness in classification is to learn a classifier that does not discriminate against groups of individuals based on sensitive attributes, such as race and gender. One approach to designing fair algorithms is to use relaxations of fairness not ...

2021

An Accelerated First-Order Method for Non-convex Optimization on Manifolds

Christopher Arnold Criscitiello, Nicolas Boumal

We describe the first gradient methods on Riemannian manifolds to achieve accelerated rates in the non-convex case. Under Lipschitz assumptions on the Riemannian gradient and Hessian of the cost function, these methods find approximate first-order critical ...

SPRINGER2022

Integrating advanced discrete choice models in mixed integer linear optimization

Michel Bierlaire, Meritxell Pacheco Paneque

In many transportation systems, a mismatch between the associated design and planning decisions and the demand is typically encountered. A tailored system is not only appealing to operators, which could have a better knowledge of their operational costs, b ...

PERGAMON-ELSEVIER SCIENCE LTD2021

Learning of Continuous and Piecewise-Linear Functions With Hessian Total-Variation Regularization

Michaël Unser, Shayan Aziznejad, Joaquim Gonçalves Garcia Barreto Campos

We develop a novel 2D functional learning framework that employs a sparsity-promoting regularization based on second-order derivatives. Motivated by the nature of the regularizer, we restrict the search space to the span of piecewise-linear box splines shi ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2022

Implications of ANEC for SCFTs in four dimensions

Alessandro Vichi, Andrea Manenti

We explore consequences of the Averaged Null Energy Condition (ANEC) for scaling dimensions Delta of operators in four-dimensional N = 1 superconformal field theories. We show that in many cases the ANEC bounds are stronger than the corresponding unitarity ...

Springer Nature2020

Convergence without Convexity: Sampling, Optimization, and Games

Ya-Ping Hsieh

Many important problems in contemporary machine learning involve solving highly non- convex problems in sampling, optimization, or games. The absence of convexity poses significant challenges to convergence analysis of most training algorithms, and in some ...

EPFL2020

Reliable Frequency Regulation through Vehicle-to-Grid: Encoding Legislation with Robust Constraints

Daniel Kuhn, François Richard Vuille, Dirk Lauinger

Problem definition: Vehicle-to-grid increases the low utilization rate of privately owned electric vehicles by making their batteries available to electricity grids. We formulate a robust optimization problem that maximizes a vehicle owner’s expected profi ...

2024

A first-order primal-dual method with adaptivity to local smoothness

Volkan Cevher, Maria-Luiza Vladarean

We consider the problem of finding a saddle point for the convex-concave objective

\min_x \max_y f(x) + \langle Ax, y\rangle - g^*(y)

, where

f

is a convex function with locally Lipschitz gradient and

g

is convex and possibly non-smooth. We propose an ...

2021

Scalable Semidefinite Programming

Volkan Cevher, Alp Yurtsever

Semidefinite programming (SDP) is a powerful framework from convex optimization that has striking potential for data science applications. This paper develops a provably correct algorithm for solving large SDP problems by economizing on both the storage an ...

2021

An Optimal-Storage Approach to Semidefinite Programming Using Approximate Complementarity

Volkan Cevher, Alp Yurtsever

This paper develops a new storage-optimal algorithm that provably solves almost all semidefinite programs (SDPs). This method is particularly effective for weakly constrained SDPs under appropriate regularity conditions. The key idea is to formulate an app ...

SIAM Publications2021

Generalization error in high-dimensional perceptrons: Approaching Bayes error with convex optimization

Lenka Zdeborová, Florent Gérard Krzakala

We consider a commonly studied supervised classification of a synthetic dataset whose labels are generated by feeding a one-layer non-linear neural network with random iid inputs. We study the generalization performances of standard classifiers in the high ...

Curran Associates, Inc.2020

Adaptive Gradient Descent without Descent

We present a strikingly simple proof that two rules are sufficient to automate gradient descent: 1) don’t increase the stepsize too fast and 2) don’t overstep the local curvature. No need for functional values, no line search, no information about the func ...

2020

Adaptation in Stochastic Algorithms: From Nonsmooth Optimization to Min-Max Problems and Beyond

Ahmet Alacaoglu

Stochastic gradient descent (SGD) and randomized coordinate descent (RCD) are two of the workhorses for training modern automated decision systems. Intriguingly, convergence properties of these methods are not well-established as we move away from the spec ...

EPFL2021

Convex optimization in sums of Banach spaces

Michaël Unser, Shayan Aziznejad

We characterize the solution of a broad class of convex optimization problems that address the reconstruction of a function from a finite number of linear measurements. The underlying hypothesis is that the solution is decomposable as a finite sum of compo ...

2021

Second-Order Guarantees In Federated Learning

Ali H. Sayed, Stefan Vlaski, Elsa Rizk

Federated learning is a useful framework for centralized learning from distributed data under practical considerations of heterogeneity, asynchrony, and privacy. Federated architectures are frequently deployed in deep learning settings, which generally giv ...

IEEE2020

A Unified Theory of Robust and Distributionally Robust Optimization via the Primal-Worst-Equals-Dual-Best Principle

Daniel Kuhn, Wolfram Wiesemann, Jianzhe Zhen

Robust and distributionally robust optimization are modeling paradigms for decision-making under uncertainty where the uncertain parameters are only known to reside in an uncertainty set or are governed by any probability distribution from within an ambigu ...

2023

Good Vibrations and Unknown Excitations

Dalia Salem Hassan Fahmy El Badawy

Inspired by the human ability to localize sounds, even with only one ear, as well as to recognize objects using active echolocation, we investigate the role of sound scattering and prior knowledge in regularizing ill-posed inverse problems in acoustics. In ...

EPFL2020