arXiv subjects

Sirine Louati

Publications and source records attributed to Sirine Louati.

3 recordsLinked to original sources

arXiv2026

Gradient-free stochastic optimization of derivatives under strong convexity

We consider the problem of minimizing the $k$-th order partial derivative $f=\partial_j^k g$ of an unknown function $g$ along a fixed coordinate direction $j$, based on noisy queries of $g$. Assuming that $g$ has Hölder regularity ${β+k}$ for some $β\ge 2$, that $f$ is strongly convex on a compact convex set $Θ\subset\mathbb{R}^d$ and that $g$ and $f$ satisfy mild boundedness and Lipschitz regularity conditions on $Θ$, we propose a kernel-based estimator of $\nabla f$ and analyze the projected stochastic gradient algorithm driven by this estimator. We obtain a non-asymptotic upper bound on the optimization error of the order $d^{(2β+k-1)/(β+k)}\,N^{-(β-1)/(β+k)}$, where $N$ is the total number of queries. We also establish a minimax lower bound of the order $N^{-(β-1)/(β+k)}$ showing that this rate is optimal in $N$ over all sequential algorithms.

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arXiv2025

Estimation of discrete distributions with high probability under $χ^2$-divergence

We investigate the high-probability estimation of discrete distributions from an \iid sample under $χ^2$-divergence loss. Although the minimax risk in expectation is well understood, its high-probability counterpart remains largely unexplored. We provide sharp upper and lower bounds for the classical Laplace estimator, showing that it achieves optimal performance among estimators that do not rely on the confidence level. We further characterize the minimax high-probability risk for any estimator and demonstrate that it can be attained through a simple smoothing strategy. Our analysis highlights an intrinsic separation between asymptotic and non-asymptotic guarantees, with the latter suffering from an unavoidable overhead. This work sharpens existing guarantees and advances the theoretical understanding of divergence-based estimation.

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arXiv2025

Performance of the empirical median for location estimation in heteroscedastic settings

We investigate the performance of the empirical median for location estimation in heteroscedastic settings. Specifically, we consider independent symmetric real-valued random variables that share a common but unknown location parameter while having different and unknown scale parameters. Estimation under heteroscedasticity arises naturally in many practical situations and has recently attracted considerable attention. In this work, we analyze the empirical median as an estimator of the common location parameter and derive matching non-asymptotic upper and lower bounds on its estimation error. These results fully characterize the behavior of the empirical median in heteroscedastic settings, clarifying both its robustness and its intrinsic limitations and offering a precise understanding of its performance in modern settings where data quality may vary across sources.

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