Related papers: Minimax Efficient Finite-Difference Stochastic Gra…
Gradient descent is a widely used iterative algorithm for finding local minima in multivariate functions. However, the final iterations often either overshoot the minima or make minimal progress, making it challenging to determine an…
We consider black-box optimization in which only an extremely limited number of function evaluations, on the order of around 100, are affordable and the function evaluations must be performed in even fewer batches of a limited number of…
We develop an approach for estimating models described via conditional moment restrictions, with a prototypical application being non-parametric instrumental variable regression. We introduce a min-max criterion function, under which the…
We lower bound the complexity of finding $\epsilon$-stationary points (with gradient norm at most $\epsilon$) using stochastic first-order methods. In a well-studied model where algorithms access smooth, potentially non-convex functions…
Overparameterized stochastic differential equation (SDE) models have achieved remarkable success in various complex environments, such as PDE-constrained optimization, stochastic control and reinforcement learning, financial engineering,…
In this paper, we introduce a powerful and efficient framework for direct optimization of ranking metrics. The problem is ill-posed due to the discrete structure of the loss, and to deal with that, we introduce two important techniques:…
We study the problem of zero-order optimization of a strongly convex function. The goal is to find the minimizer of the function by a sequential exploration of its values, under measurement noise. We study the impact of higher order…
We study the variational inference problem of minimizing a regularized R\'enyi divergence over an exponential family. We propose to solve this problem with a Bregman proximal gradient algorithm. We propose a sampling-based algorithm to…
Deep neural networks (DNN) are typically optimized using stochastic gradient descent (SGD). However, the estimation of the gradient using stochastic samples tends to be noisy and unreliable, resulting in large gradient variance and bad…
We consider the problem of estimating a continuous distribution function $F$, as well as meaningful functions $\tau(F)$ under a large class of loss functions. We obtain best invariant estimators and establish their minimaxity for H\"{o}lder…
The problem of the mean-square optimal linear estimation of functionals which depend on the unknown values of a stationary stochastic sequence from observations of the sequence with noise is considered. In the case of spectral certainty,…
Estimating percentiles of black-box deterministic functions with random inputs is a challenging task when the number of function evaluations is severely restricted, which is typical for computer experiments. This article proposes two new…
Strong approximation errors of both finite element semi-discretization and spatio-temporal full discretization are analyzed for the stochastic Allen-Cahn equation driven by additive noise in space dimension $d \leq 3$. The full…
We introduce a theoretical and practical framework for efficient importance sampling of mini-batch samples for gradient estimation from single and multiple probability distributions. To handle noisy gradients, our framework dynamically…
We consider the problem of minimizing the sum of two convex functions: one is the average of a large number of smooth component functions, and the other is a general convex function that admits a simple proximal mapping. We assume the whole…
Derivative-free optimization (DFO) is vital in solving complex optimization problems where only noisy function evaluations are available through an oracle. Within this domain, DFO via finite difference (FD) approximation has emerged as a…
In this paper, we consider non-smooth stochastic convex optimization with two function evaluations per round under infinite noise variance. In the classical setting when noise has finite variance, an optimal algorithm, built upon the…
Derivative Free Optimization is known to be an efficient and robust method to tackle the black-box optimization problem. When it comes to noisy functions, classical comparison-based algorithms are slower than gradient-based algorithms. For…
Stochastic neurons and hard non-linearities can be useful for a number of reasons in deep learning models, but in many cases they pose a challenging problem: how to estimate the gradient of a loss function with respect to the input of such…
Functional Principal Component Analysis is a reference method for dimension reduction of curve data. Its theoretical properties are now well understood in the simplified case where the sample curves are fully observed without noise.…