arXiv subjects

Théo Guyard

Publications and source records attributed to Théo Guyard.

7 recordsLinked to original sources

arXiv2026

Linear Decision Tree Policies for Integer Linear Programs

We study optimal decision policies, represented as linear decision trees, for integer linear programs with a fixed feasible set and varying cost vectors. Once synthesized for a given feasible set, they return an optimal solution for any queried cost vector through a sequence of linear tests. We show that there exists a policy performing this operation in a polynomial number of arithmetic operations in the worst case. In contrast, deciding whether there exists an exact policy with a prescribed maximum number of leaves is $Σ_2^p$-complete. Alongside these theoretical results, we develop a practical construction framework to synthesize policies within a specific subclass of linear decision trees. Our computational experiments show that, although policy synthesis can be time-intensive, it allows one to retrieve optimal solutions orders of magnitude faster than classical and specialized solution methods on repeated queries. Overall, this paradigm provides a different perspective on the solution of integer linear programs and offers a principled offline-online approach for repeated optimization.

math.OC↗

arXiv2026

PACE: Prune-And-Compress Ensemble Models

Ensemble models achieve state-of-the-art performance on prediction tasks, but usually require aggregating a large number of weak learners. This can hinder deployment, interpretability, and downstream tasks such as robustness verification. Remedies to this issue fall into two main camps: pruning, which discards redundant learners, and compression, which generates new ones from scratch. We introduce PACE, a framework that interleaves these paradigms in a two-phase strategy. First, new learners are actively generated via a theoretically grounded procedure to enhance the diversity of the initial ensemble. When no more relevant learners can be found, a second phase of pruning is performed on this enriched ensemble. During both operations, PACE allows fine control on the faithfulness to the original ensemble. Experiments show that our method outperforms prior pruning and compression methods while offering principled control of faithfulness guarantees.

cs.LG↗

arXiv2025

A Generic Branch-and-Bound Algorithm for $\ell_0$-Penalized Problems with Supplementary Material

We present a generic Branch-and-Bound procedure designed to solve L0-penalized optimization problems. Existing approaches primarily focus on quadratic losses and construct relaxations using "Big-M" constraints and/or L2-norm penalties. In contrast, our method accommodates a broader class of loss functions and allows greater flexibility in relaxation design through a general penalty term, encompassing existing techniques as special cases. We establish theoretical results ensuring that all key quantities required for the Branch-and-Bound implementation admit closed-form expressions under the general blanket assumptions considered in our work. Leveraging this framework, we introduce El0ps, an open-source Python solver with a plug-and-play workflow that enables user-defined losses and penalties in L0-penalized problems. Through extensive numerical experiments, we demonstrate that El0ps achieves state-of-the-art performance on classical instances and extends computational feasibility to previously intractable ones.

math.OC↗

arXiv2025

El0ps: An Exact L0-regularized Problems Solver

This paper presents El0ps, a Python toolbox providing several utilities to handle L0-regularized problems related to applications in machine learning, statistics, and signal processing, among other fields. In contrast to existing toolboxes, El0ps allows users to define custom instances of these problems through a flexible framework, provides a dedicated solver achieving state-of-the-art performance, and offers several built-in machine learning pipelines. Our aim with El0ps is to provide a comprehensive tool which opens new perspectives for the integration of L0-regularized problems in practical applications.

cs.MS↗

arXiv2023

Safe Peeling for L0-Regularized Least-Squares with supplementary material

We introduce a new methodology dubbed ``safe peeling'' to accelerate the resolution of L0-regularized least-squares problems via a Branch-and-Bound (BnB) algorithm. Our procedure enables to tighten the convex relaxation considered at each node of the BnB decision tree and therefore potentially allows for more aggressive pruning. Numerical simulations show that our proposed methodology leads to significant gains in terms of number of nodes explored and overall solving time.s show that our proposed methodology leads to significant gains in terms of number of nodes explored and overall solving time.

cs.LG↗

arXiv2022

Screen & Relax: Accelerating the resolution of Elastic-net by safe identification of the solution support

In this paper, we propose a procedure to accelerate the resolution of the well-known "Elastic-Net" problem. Our procedure is based on the (partial) identification of the solution support and the reformulation of the original problem into a problem of reduced dimension. The identification of the support leverages the novel concept of "safe relaxing" where one aims to identify non-zero coefficients of the solution. It can be viewed as a dual approach to "safe screening" introduced in the last decade and allowing to reduce the problem dimension using the identification of zero coefficients of the solution. We show numerically that combining both methodologies in a "Screen & Relax" strategy enables to significantly improve the tradeoff between complexity and accuracy achievable by standard resolution techniques.

math.OC↗

arXiv2022

Node-screening tests for L0-penalized least-squares problem with supplementary material

We present a novel screening methodology to safely discard irrelevant nodes within a generic branch-and-bound (BnB) algorithm solving the l0-penalized least-squares problem. Our contribution is a set of two simple tests to detect sets of feasible vectors that cannot yield optimal solutions. This allows to prune nodes of the BnB search tree, thus reducing the overall optimization time. One cornerstone of our contribution is a nesting property between tests at different nodes that allows to implement them with a low computational cost. Our work leverages the concept of safe screening, well known for sparsity-inducing convex problems, and some recent advances in this field for l0-penalized regression problems.

eess.SP↗