Related papers: Optimal Algorithms for Differentially Private Stoc…
Saddle-point optimization problems are an important class of optimization problems with applications to game theory, multi-agent reinforcement learning and machine learning. A majority of the rich literature available for saddle-point…
We study fundamental limits of first-order stochastic optimization in a range of nonconvex settings, including L-smooth functions satisfying Quasar-Convexity (QC), Quadratic Growth (QG), and Restricted Secant Inequalities (RSI). While the…
An increasing number of machine learning problems, such as robust or adversarial variants of existing algorithms, require minimizing a loss function that is itself defined as a maximum. Carrying a loop of stochastic gradient ascent (SGA)…
Finding efficient, easily implementable differentially private (DP) algorithms that offer strong excess risk bounds is an important problem in modern machine learning. To date, most work has focused on private empirical risk minimization…
Differentially Private Stochastic Gradient Descent (DP-SGD) has become a widely used technique for safeguarding sensitive information in deep learning applications. Unfortunately, DPSGD's per-sample gradient clipping and uniform noise…
Recently, Stochastic Variational Inference (SVI) has been increasingly attractive thanks to its ability to find good posterior approximations of probabilistic models. It optimizes the variational objective with stochastic optimization,…
We study non-smooth stochastic decentralized optimization problems over time-varying networks, where objective functions are distributed across nodes and network connections may intermittently appear or break. Specifically, we consider two…
We study the performance of stochastic first-order methods for finding saddle points of convex-concave functions. A notorious challenge faced by such methods is that the gradients can grow arbitrarily large during optimization, which may…
We analyze the variance of stochastic gradients along negative curvature directions in certain non-convex machine learning models and show that stochastic gradients exhibit a strong component along these directions. Furthermore, we show…
Differentially private (DP) mechanisms face the challenge of providing accurate results while protecting their inputs: the privacy-utility trade-off. A simple but powerful technique for DP adds noise to sensitivity-bounded query outputs to…
In this paper, a general stochastic optimization procedure is studied, unifying several variants of the stochastic gradient descent such as, among others, the stochastic heavy ball method, the Stochastic Nesterov Accelerated Gradient…
We study differentially private stochastic optimization in convex and non-convex settings. For the convex case, we focus on the family of non-smooth generalized linear losses (GLLs). Our algorithm for the $\ell_2$ setting achieves optimal…
For finite-dimensional problems, stochastic approximation methods have long been used to solve stochastic optimization problems. Their application to infinite-dimensional problems is less understood, particularly for nonconvex objectives.…
This paper considers the smooth bilevel optimization in which the lower-level problem is strongly convex and the upper-level problem is possibly nonconvex. We focus on the stochastic setting where the algorithm can access the unbiased…
Stochastic gradient descent (SGD) is a prevalent optimization technique for large-scale distributed machine learning. While SGD computation can be efficiently divided between multiple machines, communication typically becomes a bottleneck…
In recent centralized nonconvex distributed learning and federated learning, local methods are one of the promising approaches to reduce communication time. However, existing work has mainly focused on studying first-order optimality…
In this work, we study the stochastic optimal control problem (SOC) mainly from the probabilistic view point, i.e. via the Stochastic Maximum principle (SMP) \cite{Peng4}. We adopt the sample-wise backpropagation scheme proposed in…
In this paper, we study federated optimization for solving stochastic variational inequalities (VIs), a problem that has attracted growing attention in recent years. Despite substantial progress, a significant gap remains between existing…
We develop two compression based stochastic gradient algorithms to solve a class of non-smooth strongly convex-strongly concave saddle-point problems in a decentralized setting (without a central server). Our first algorithm is a…
Traditionally, the random noise is equally injected when training with different data instances in the field of differential privacy (DP). In this paper, we first give sharper excess risk bounds of DP stochastic gradient descent (SGD)…