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09/14/2023
Adaptive approximation of monotone functions
We study the classical problem of approximating a non-decreasing functio...
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08/02/2023
Certified Multi-Fidelity Zeroth-Order Optimization
We consider the problem of multi-fidelity zeroth-order optimization, whe...
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06/09/2022
A general approximation lower bound in L^p norm, with applications to feed-forward neural networks
We study the fundamental limits to the expressive power of neural networ...
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07/28/2021
Global minimizers, strict and non-strict saddle points, and implicit regularization for deep linear neural networks
In non-convex settings, it is established that the behavior of gradient-...
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06/23/2021
Numerical influence of ReLU'(0) on backpropagation
In theory, the choice of ReLU'(0) in [0, 1] for a neural network has a n...
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03/18/2021
White Paper Machine Learning in Certified Systems
Machine Learning (ML) seems to be one of the most promising solution to ...
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02/03/2021
The Sample Complexities of Global Lipschitz Optimization
We study the problem of black-box optimization of a Lipschitz function f...
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10/26/2020
The sample complexity of level set approximation
We study the problem of approximating the level set of an unknown functi...
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10/05/2020
Diversity-Preserving K-Armed Bandits, Revisited
We consider the bandit-based framework for diversity-preserving recommen...
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02/06/2020
Regret analysis of the Piyavskii-Shubert algorithm for global Lipschitz optimization
We consider the problem of maximizing a non-concave Lipschitz multivaria...
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07/09/2018
Optimization of a SSP's Header Bidding Strategy using Thompson Sampling
Over the last decade, digital media (web or app publishers) generalized ...
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05/29/2018
Uniform regret bounds over R^d for the sequential linear regression problem with the square loss
We consider the setting of online linear regression for arbitrary determ...
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01/10/2018
Optimal functional supervised classification with separation condition
We consider the binary supervised classification problem with the Gaussi...
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02/27/2017
Algorithmic Chaining and the Role of Partial Feedback in Online Nonparametric Learning
We investigate contextual online learning with nonparametric (Lipschitz)...
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05/24/2016
Refined Lower Bounds for Adversarial Bandits
We provide new lower bounds on the regret that must be suffered by adver...
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02/26/2015
A Chaining Algorithm for Online Nonparametric Regression
We consider the problem of online nonparametric regression with arbitrar...
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05/20/2011
Adaptive and Optimal Online Linear Regression on L1-balls
We consider the problem of online linear regression on individual sequen...
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01/05/2011