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Found 18 papers, 2 papers with code
Adaptive approximation of monotone functions
We prove that GreedyBox achieves an optimal sample complexity for any function $f$, up to logarithmic factors.
Certified Multi-Fidelity Zeroth-Order Optimization
We also prove an $f$-dependent lower bound showing that this algorithm has a near-optimal cost complexity.
A general approximation lower bound in $L^p$ norm, with applications to feed-forward neural networks
Given two sets $F$, $G$ of real-valued functions, we first prove a general lower bound on how well functions in $F$ can be approximated in $L^p(\mu)$ norm by functions in $G$, for any $p \geq 1$ and any probability measure $\mu$.
The loss landscape of deep linear neural networks: a second-order analysis
We characterize, among all critical points, which are global minimizers, strict saddle points, and non-strict saddle points.
Numerical influence of ReLU'(0) on backpropagation
In theory, the choice of ReLU(0) in [0, 1] for a neural network has a negligible influence both on backpropagation and training.
Numerical influence of ReLU’(0) on backpropagation
In theory, the choice of ReLU(0) in [0, 1] for a neural network has a negligible influence both on backpropagation and training.
White Paper Machine Learning in Certified Systems
Machine Learning (ML) seems to be one of the most promising solution to automate partially or completely some of the complex tasks currently realized by humans, such as driving vehicles, recognizing voice, etc.
Instance-Dependent Bounds for Zeroth-order Lipschitz Optimization with Error Certificates
We study the problem of zeroth-order (black-box) optimization of a Lipschitz function $f$ defined on a compact subset $\mathcal X$ of $\mathbb R^d$, with the additional constraint that algorithms must certify the accuracy of their recommendations.
The sample complexity of level set approximation
We study the problem of approximating the level set of an unknown function by sequentially querying its values.
Diversity-Preserving K-Armed Bandits, Revisited
We consider the bandit-based framework for diversity-preserving recommendations introduced by Celis et al. (2019), who approached it in the case of a polytope mainly by a reduction to the setting of linear bandits.
Regret analysis of the Piyavskii-Shubert algorithm for global Lipschitz optimization
We consider the problem of maximizing a non-concave Lipschitz multivariate function over a compact domain by sequentially querying its (possibly perturbed) values.
Optimization of a SSP's Header Bidding Strategy using Thompson Sampling
The SSP acts as an intermediary between an advertiser wanting to buy ad spaces and a web publisher wanting to sell its ad spaces, and needs to define a bidding strategy to be able to deliver to the advertisers as many ads as possible while spending as little as possible.
Uniform regret bounds over $R^d$ for the sequential linear regression problem with the square loss
In the case of sequentially revealed features, we also derive an asymptotic regret bound of $d B^2 \ln T$ for any individual sequence of features and bounded observations.
Algorithmic Chaining and the Role of Partial Feedback in Online Nonparametric Learning
We investigate contextual online learning with nonparametric (Lipschitz) comparison classes under different assumptions on losses and feedback information.
Refined Lower Bounds for Adversarial Bandits
First, the existence of a single arm that is optimal in every round cannot improve the regret in the worst case.
A Chaining Algorithm for Online Nonparametric Regression
We consider the problem of online nonparametric regression with arbitrary deterministic sequences.
Adaptive and optimal online linear regression on $\ell^1$-balls
We first present regret bounds with optimal dependencies on $d$, $T$, and on the sizes $U$, $X$ and $Y$ of the $\ell^1$-ball, the input data and the observations.
Sparsity regret bounds for individual sequences in online linear regression
We consider the problem of online linear regression on arbitrary deterministic sequences when the ambient dimension d can be much larger than the number of time rounds T. We introduce the notion of sparsity regret bound, which is a deterministic online counterpart of recent risk bounds derived in the stochastic setting under a sparsity scenario.
