arXiv subjects

Pierre-Yves Bouchet

Publications and source records attributed to Pierre-Yves Bouchet.

4 recordsLinked to original sources

arXiv2026

Optimization by Directional Attacks: Solving Problems with Neural Network Surrogates

This paper tackles optimization problems whose objective and constraints involve a trained Neural Network (NN), where the goal is to maximize $f(Φ(x))$ subject to $c(Φ(x)) \leq 0$, with $f$ smooth, $c$ general and non-stringent, and $Φ$ a NN already trained and not given as a glass-box. We address two challenges regarding this problem: identifying ascent directions for local search, and ensuring reliable convergence towards relevant local solutions. To this end, we re-purpose the notion of directional NN attacks as efficient optimization subroutines, since directional NN attacks are designed to efficiently compute perturbations of $x$ that steer $Φ(x)$ in prescribed directions. Precisely, we develop an attack operator that computes attacks of $Φ$ at any $x$ along the direction $\nabla f(Φ(x))$. Then, we propose a hybrid algorithm combining the attack operator with derivative-free optimization (DFO) techniques, designed for numerical reliability by remaining oblivious to the structure of the problem. We consider the Covering Direct Search Method (CDSM), which offers asymptotic guarantees to converge to a local solution under mild assumptions on the problem. The resulting method alternates between attack-based steps for heuristic yet fast local improvements of the current incumbent solution and CDSM steps for certified convergence and numerical reliability. Experiments on three problems show that this hybrid approach outperforms standard baselines.

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arXiv2026

A Partitioned Optimization Framework for Structure-Aware Problems

This work tackles a class of optimization problems in which fixing some well-chosen combinations of the variables makes the problem substantially easier to solve. We consider that the variables space may be partitioned into subsets that fix these combinations to given values, so that the restriction of the problem to any of the partition sets admits a tractable solution. Then, we exhibit a reformulation of the problem that consists in searching for the partition set index that minimizes the objective value of the solution to the restricted problem. We name partitioned optimization framework (POf) the formalization of this class of problems and this reformulation process. As we prove in this work, the POf allows solving the original problem by focusing on the reformulated problem: all solutions to the reformulated problem are partition indices for which the solution to the associated restricted problem is also a solution to the original problem. Second, we introduce a derivative-free partitioned optimization method (DFPOm) to efficiently solve problems that fit in the POf. We prove that the reformulated problem is nicely handled by derivative-free optimization (DFO) algorithms with a covering step. Then the DFPOm consists in solving the reformulated problem using such DFO algorithm with a covering step to obtain an optimal partition index, and to return the solution to the associated restricted problem as a solution to the initial problem. Finally, we illustrate how the \pof allows solving some classes of problems. We first focus on an infinite-dimensional case, by solving analytically an optimal control problem that challenges standard methods from the literature. Then, we apply the DFPOm on a class of finite-dimensional problems called composite greybox problems, and we highlight the gain in numerical performance provided by the DFPOm by comparing it to two popular DFO solvers.

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arXiv2022

Erratum, counterexample and an additional revealing poll step for a result of "Analysis of direct searches for discontinuous functions''

This note provides a counterexample to a theorem announced in the last part of the paper ''Analysis of direct searches for discontinuous functions'', Mathematical Programming Vol. 133, pp.~299--325, 2012. The counterexample involves an objective function $f: \mathbb{R} \to \mathbb{R}$ which satisfies all the assumptions required by the theorem but contradicts some of its conclusions. A corollary of this theorem is also affected by this counterexample. The main flaw revealed by the counterexample is the possibility that a directional direct search method (dDSM) generates a sequence of trial points $(x_k)_k$ converging to a point $x_*$ where $f$ is discontinuous and whose objective function value $f(x_*)$ is strictly less than $\lim_{k\to\infty} f(x_k)$. Moreover the dDSM generates no trial point in one of the two branches of $f$ near $x_*$. This note also investigates the proof of the theorem to highlight the inexact statements in the original paper. Finally this work concludes with a modification of the dDSM that allows to recover the properties broken by the counterexample.

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arXiv2019

Optimization of noisy blackboxes with adaptive precision

In derivative-free and blackbox optimization, the objective function is often evaluated through the execution of a computer program seen as a blackbox. It can be noisy, in the sense that its outputs are contaminated by random errors. Sometimes, the source of these errors is identified and controllable, in the sense that it is possible to reduce the standard deviation of the stochastic noise it generates. A common strategy to deal with such a situation is to monotonically diminish this standard deviation, to asymptotically make it converge to zero and ensure convergence of algorithms because the noise is dismantled. This work presents MpMads, an algorithm which follows this approach. However, in practice a reduction of the standard deviation increases the computation time, and makes the optimization process long. Therefore, a second algorithm called DpMads is introduced to explore another strategy, which does not force the standard deviation to monotonically diminish. Although these strategies are proved to be theoretically equivalents, tests on analytical problems and an industrial blackbox are presented to illustrate practical differences.

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