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Adam Ouorou

Publications and source records attributed to Adam Ouorou.

6 recordsLinked to original sources
arXiv2020

From Weakly Supervised Learning to Biquality Learning: an Introduction

The field of Weakly Supervised Learning (WSL) has recently seen a surge of popularity, with numerous papers addressing different types of "supervision deficiencies". In WSL use cases, a variety of situations exists where the collected "information" is imperfect. The paradigm of WSL attempts to list and cover these problems with associated solutions. In this paper, we review the research progress on WSL with the aim to make it as a brief introduction to this field. We present the three axis of WSL cube and an overview of most of all the elements of their facets. We propose three measurable quantities that acts as coordinates in the previously defined cube namely: Quality, Adaptability and Quantity of information. Thus we suggest that Biquality Learning framework can be defined as a plan of the WSL cube and propose to re-discover previously unrelated patches in WSL literature as a unified Biquality Learning literature.

cs.LG↗
arXiv2020

Fast proximal algorithms for nonsmooth convex optimization

In the lines of our approach in \cite{Ouorou2019}, where we exploit Nesterov fast gradient concept \cite{Nesterov1983} to the Moreau-Yosida regularization of a convex function, we devise new proximal algorithms for nonsmooth convex optimization. These algorithms need no bundling mechanism to update the stability center while preserving the complexity estimates established in \cite{Ouorou2019}. We report some preliminary computational results on some academic test problem to give a first estimate of their performance in relation with the classical proximal bundle algorithm.

math.OC↗
arXiv2020

Proximal bundle algorithms for nonsmooth convex optimization via fast gradient smooth methods

We propose new proximal bundle algorithms for minimizing a nonsmooth convex function. These algorithms are derived from the application of Nesterov fast gradient methods for smooth convex minimization to the so-called Moreau-Yosida regularization $F_\mu$ of $f$ w.r.t. some $\mu>0$. Since the exact values and gradients of $F_\mu$ are difficult to evaluate, we use approximate proximal points thanks to a bundle strategy to get implementable algorithms. One of these algorithms appears as an implementable version of a special case of inertial proximal algorithm. We give their complexity estimates in terms of the original function values, and report some preliminary numerical results.

math.OC↗
arXiv2018

A Lagrange decomposition based Branch and Bound algorithm for the Optimal Mapping of Cloud Virtual Machines

One of the challenges of cloud computing is to optimally and efficiently assign virtual ma- chines to physical machines. The aim of telecommunication operators is to minimize the map- ping cost while respecting constraints regarding location, assignment and capacity. In this paper we first propose an exact formulation leading to a 0-1 bilinear constrained problem. Then we introduce a variety of linear cuts by exploiting the problem structure and present a Lagrange decomposition based B&B algorithm to obtain optimal solutions efficiently. Numerically, we show that our valid inequalities close over 80% of the optimality gap incurred by the well-known McCormick relaxation, and demonstrate the computational advantage of the proposed B&B algorithm with extensive numerical experiments.

math.OC↗
arXiv2016

Multipolar robust optimization

We consider linear programs involving uncertain parameters and propose a new tractable robust counterpart which contains and generalizes several other models including the existing Affinely Adjustable Robust Counterpart and the Fully Adjustable Robust Counterpart. It consists in selecting a set of poles whose convex hull contains some projection of the uncertainty set, and computing a recourse strategy for each data scenario as a convex combination of some optimized recourses (one for each pole). We show that the proposed multipolar robust counterpart is tractable and its complexity is controllable. Further, we show that under some mild assumptions, two sequences of upper and lower bounds converge to the optimal value of the fully adjustable robust counterpart. To illustrate the approach, a robust problem related to lobbying under some uncertain opinions of authorities is studied. Several numerical experiments are carried out showing the advantages of the proposed robustness framework and evaluating the benefit of adaptability.

math.OC↗