Geodesic
Box-constrained optimization for minimax supervised learning
Cyprien Gilet1 ; Susana Barbosa2 ; Lionel Fillatre1
1 University of Côte d’Azur, CNRS, I3S laboratory, Sophia-Antipolis, France
2 University of Côte d’Azur, CNRS, laboratory IPMC, Sophia-Antipolis, France
ESAIM. Proceedings, Tome 71 (2021), pp. 101-113.

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In this paper, we present the optimization procedure for computing the discrete boxconstrained minimax classifier introduced in [1, 2]. Our approach processes discrete or beforehand discretized features. A box-constrained region defines some bounds for each class proportion independently. The box-constrained minimax classifier is obtained from the computation of the least favorable prior which maximizes the minimum empirical risk of error over the box-constrained region. After studying the discrete empirical Bayes risk over the probabilistic simplex, we consider a projected subgradient algorithm which computes the prior maximizing this concave multivariate piecewise affine function over a polyhedral domain. The convergence of our algorithm is established.
DOI : 10.1051/proc/202171109

Cyprien Gilet 1 ; Susana Barbosa 2 ; Lionel Fillatre 1

1 University of Côte d’Azur, CNRS, I3S laboratory, Sophia-Antipolis, France
2 University of Côte d’Azur, CNRS, laboratory IPMC, Sophia-Antipolis, France 
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     author = {Cyprien Gilet and Susana Barbosa and Lionel Fillatre},
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Cyprien Gilet; Susana Barbosa; Lionel Fillatre. Box-constrained optimization for minimax supervised learning. ESAIM. Proceedings, Tome 71 (2021), pp. 101-113. doi : 10.1051/proc/202171109. http://geodesic.mathdoc.fr/articles/10.1051/proc/202171109/

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