arXiv subjects

Sofiane Tanji

Publications and source records attributed to Sofiane Tanji.

3 recordsLinked to original sources

arXiv2026

Fairness-informed Pareto Optimization : An Efficient Bilevel Framework

Despite their promise, fair machine learning methods often yield Pareto-inefficient models, in which the performance of certain groups can be improved without degrading that of others. This issue arises frequently in traditional in-processing approaches such as fairness-through-regularization. In contrast, existing Pareto-efficient approaches are biased towards a certain perspective on fairness and fail to adapt to the broad range of fairness metrics studied in the literature. In this paper, we present BADR, a simple framework to recover the optimal Pareto-efficient model for any fairness metric. Our framework recovers its models through a Bilevel Adaptive Rescalarisation procedure. The lower level is a weighted empirical risk minimization task where the weights are a convex combination of the groups, while the upper level optimizes the chosen fairness objective. We equip our framework with two novel large-scale, single-loop algorithms, BADR-GD and BADR-SGD, and establish their convergence guarantees. We release badr, an open-source Python toolbox implementing our framework for a variety of learning tasks and fairness metrics. Finally, we conduct extensive numerical experiments demonstrating the advantages of BADR over existing Pareto-efficient approaches to fairness.

cs.LG↗

arXiv2025

Dual first-order methods for efficient computation of convex hull prices

Convex Hull (CH) pricing, used in US electricity markets and raising interest in Europe, is a pricing rule designed to handle markets with non-convexities such as startup costs and minimum up and down times. In such markets, the market operator makes side payments to generators to cover lost opportunity costs, and CH prices minimize the total "lost opportunity costs", which include both actual losses and missed profit opportunities. These prices can also be obtained by solving a (partial) Lagrangian dual of the original mixed-integer program, where power balance constraints are dualized. Computing CH prices then amounts to minimizing a sum of nonsmooth convex objective functions, where each term depends only on a single generator. The subgradient of each of those terms can be obtained independently by solving smaller mixed-integer programs. In this work, we benchmark a large panel of first-order methods to solve the above dual CH pricing problem. We test several dual methods, most of which not previously considered for CH pricing, namely a proximal variant of the bundle level method, subgradient methods with three different stepsize strategies, two recent parameter-free methods and an accelerated gradient method combined with smoothing. We compare those methods on two representative sets of real-world large-scale instances and complement the comparison with a (Dantzig-Wolfe) primal column generation method shown to be efficient at computing CH prices, for reference. Our numerical experiments show that the bundle proximal level method and two variants of the subgradient method perform the best among all dual methods and compare favorably with the Dantzig-Wolfe primal method.

math.OC↗

arXiv2023

Snacks: a fast large-scale kernel SVM solver

Kernel methods provide a powerful framework for non parametric learning. They are based on kernel functions and allow learning in a rich functional space while applying linear statistical learning tools, such as Ridge Regression or Support Vector Machines. However, standard kernel methods suffer from a quadratic time and memory complexity in the number of data points and thus have limited applications in large-scale learning. In this paper, we propose Snacks, a new large-scale solver for Kernel Support Vector Machines. Specifically, Snacks relies on a Nyström approximation of the kernel matrix and an accelerated variant of the stochastic subgradient method. We demonstrate formally through a detailed empirical evaluation, that it competes with other SVM solvers on a variety of benchmark datasets.

cs.LG↗