Related papers: Local Adaption for Approximation and Minimization …
We develop algorithms for private stochastic convex optimization that adapt to the hardness of the specific function we wish to optimize. While previous work provide worst-case bounds for arbitrary convex functions, it is often the case…
We propose an algorithm for an optimal adaptive selection of points from the design domain of input random variables that are needed for an accurate estimation of failure probability and the determination of the boundary between safe and…
The universal approximation theorem is generalised to uniform convergence on the (noncompact) input space $\mathbb{R}^n$. All continuous functions that vanish at infinity can be uniformly approximated by neural networks with one hidden…
We provide general adaptive upper bounds for estimating nonparametric functionals based on second order U-statistics arising from finite dimensional approximation of the infinite dimensional models. We then provide examples of functionals…
A sequence of works in unconstrained online convex optimisation have investigated the possibility of adapting simultaneously to the norm $U$ of the comparator and the maximum norm $G$ of the gradients. In full generality, matching upper and…
We describe approximation algorithms in Linial's classic LOCAL model of distributed computing to find maximum-weight matchings in a hypergraph of rank $r$. Our main result is a deterministic algorithm to generate a matching which is an…
We present an optimization algorithm that can identify a global minimum of a potentially nonconvex smooth function with high probability, assuming the Gibbs measure of the potential satisfies a logarithmic Sobolev inequality. Our…
One of the basic principles of Approximation Theory is that the quality of approximations increase with the smoothness of the function to be approximated. Functions that are smooth in certain subdomains will have good approximations in…
The motivation for this paper stems from the desire to develop an adaptive sampling method for solving constrained optimization problems in which the objective function is stochastic and the constraints are deterministic. The method…
In this work, we propose a computationally efficient algorithm for the problem of global optimization in univariate loss functions. For the performance evaluation, we study the cumulative regret of the algorithm instead of the simple regret…
This paper proposes a stochastic gradient descent method with an adaptive Gaussian noise term for the global minimization of nearly convex functions, which are nonconvex and possess multiple strict local minimizers. The noise term,…
We give sublinear-time approximation algorithms for some optimization problems arising in machine learning, such as training linear classifiers and finding minimum enclosing balls. Our algorithms can be extended to some kernelized versions…
A regularization algorithm using inexact function values and inexact derivatives is proposed and its evaluation complexity analyzed. This algorithm is applicable to unconstrained problems and to problems with inexpensive constraints (that…
Reliable uncertainty estimates are an important tool for helping autonomous agents or human decision makers understand and leverage predictive models. However, existing approaches to estimating uncertainty largely ignore the possibility of…
The Expectation-Maximization (EM) algorithm is an iterative method to maximize the log-likelihood function for parameter estimation. Previous works on the convergence analysis of the EM algorithm have established results on the asymptotic…
Weak submodularity is a natural relaxation of the diminishing return property, which is equivalent to submodularity. Weak submodularity has been used to show that many (monotone) functions that arise in practice can be efficiently maximized…
We propose an anytime online algorithm for the problem of learning a sequence of adversarial convex cost functions while approximately satisfying another sequence of adversarial online convex constraints. A sequential algorithm is called…
Investigation of the degree of personalization in federated learning algorithms has shown that only maximizing the performance of the global model will confine the capacity of the local models to personalize. In this paper, we advocate an…
We study the sample complexity of learning a uniform approximation of an $n$-dimensional cumulative distribution function (CDF) within an error $\epsilon > 0$, when observations are restricted to a minimal one-bit feedback. This serves as a…
An adaptive regularization algorithm for unconstrained nonconvex optimization is presented in which the objective function is never evaluated, but only derivatives are used. This algorithm belongs to the class of adaptive regularization…