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We study differentially private (DP) algorithms for stochastic convex optimization (SCO). In this problem the goal is to approximately minimize the population loss given i.i.d. samples from a distribution over convex and Lipschitz loss…

Machine Learning · Computer Science 2019-08-28 Raef Bassily , Vitaly Feldman , Kunal Talwar , Abhradeep Thakurta

One of the most effective algorithms for differentially private learning and optimization is objective perturbation. This technique augments a given optimization problem (e.g. deriving from an ERM problem) with a random linear term, and…

Machine Learning · Computer Science 2021-01-01 Seth Neel , Aaron Roth , Giuseppe Vietri , Zhiwei Steven Wu

In this paper, we focus on the problem of stochastic optimization where the objective function can be written as an expectation function over a closed convex set. We also consider multiple expectation constraints which restrict the domain…

Statistics Theory · Mathematics 2019-06-18 Kinjal Basu , Preetam Nandy

This paper resolves a longstanding open question pertaining to the design of near-optimal first-order algorithms for smooth and strongly-convex-strongly-concave minimax problems. Current state-of-the-art first-order algorithms find an…

Optimization and Control · Mathematics 2021-07-27 Tianyi Lin , Chi Jin , Michael. I. Jordan

In this paper, we study private optimization problems for non-smooth convex functions $F(x)=\mathbb{E}_i f_i(x)$ on $\mathbb{R}^d$. We show that modifying the exponential mechanism by adding an $\ell_2^2$ regularizer to $F(x)$ and sampling…

Data Structures and Algorithms · Computer Science 2022-07-29 Sivakanth Gopi , Yin Tat Lee , Daogao Liu

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…

Machine Learning · Computer Science 2021-11-11 Raef Bassily , Cristóbal Guzmán , Michael Menart

This paper is devoted to a new modification of a recently proposed adaptive stochastic mirror descent algorithm for constrained convex optimization problems in the case of several convex functional constraints. Algorithms, standard and its…

Optimization and Control · Mathematics 2020-01-22 Mohammad S. Alkousa

We study stochastic convex optimization with heavy-tailed data under the constraint of differential privacy (DP). Most prior work on this problem is restricted to the case where the loss function is Lipschitz. Instead, as introduced by…

Machine Learning · Computer Science 2022-11-02 Gautam Kamath , Xingtu Liu , Huanyu Zhang

This paper studies the lower bound complexity for the optimization problem whose objective function is the average of $n$ individual smooth convex functions. We consider the algorithm which gets access to gradient and proximal oracle for…

Optimization and Control · Mathematics 2019-08-23 Guangzeng Xie , Luo Luo , Zhihua Zhang

We provide a first-order oracle complexity lower bound for finding stationary points of min-max optimization problems where the objective function is smooth, nonconvex in the minimization variable, and strongly concave in the maximization…

Optimization and Control · Mathematics 2021-04-20 Haochuan Li , Yi Tian , Jingzhao Zhang , Ali Jadbabaie

In this work, we give efficient algorithms for privately estimating a Gaussian distribution in both pure and approximate differential privacy (DP) models with optimal dependence on the dimension in the sample complexity. In the pure DP…

Data Structures and Algorithms · Computer Science 2023-06-02 Daniel Alabi , Pravesh K. Kothari , Pranay Tankala , Prayaag Venkat , Fred Zhang

Minimizing a convex, quadratic objective of the form $f_{\mathbf{A},\mathbf{b}}(x) := \frac{1}{2}x^\top \mathbf{A} x - \langle \mathbf{b}, x \rangle$ for $\mathbf{A} \succ 0 $ is a fundamental problem in machine learning and optimization.…

Machine Learning · Computer Science 2019-04-17 Max Simchowitz

We study private empirical risk minimization (ERM) problem for losses satisfying the $(\gamma,\kappa)$-Kurdyka-{\L}ojasiewicz (KL) condition. The Polyak-{\L}ojasiewicz (PL) condition is a special case of this condition when $\kappa=2$.…

Machine Learning · Computer Science 2024-04-04 Michael Menart , Enayat Ullah , Raman Arora , Raef Bassily , Cristóbal Guzmán

In this paper, we revisit the problem of private stochastic convex optimization. We propose an algorithm based on noisy mirror descent, which achieves optimal rates both in terms of statistical complexity and number of queries to a…

Machine Learning · Computer Science 2020-11-18 Raman Arora , Teodor V. Marinov , Enayat Ullah

In this paper, we investigate unconstrained and constrained sample-based federated optimization, respectively. For each problem, we propose a privacy preserving algorithm using stochastic successive convex approximation (SSCA) techniques,…

Machine Learning · Computer Science 2021-03-18 Chencheng Ye , Ying Cui

This paper develops a novel differentially private framework to solve convex optimization problems with sensitive optimization data and complex physical or operational constraints. Unlike standard noise-additive algorithms, that act…

Cryptography and Security · Computer Science 2020-06-23 Vladimir Dvorkin , Ferdinando Fioretto , Pascal Van Hentenryck , Jalal Kazempour , Pierre Pinson

We study the problem of differentially private optimization with linear constraints when the right-hand-side of the constraints depends on private data. This type of problem appears in many applications, especially resource allocation.…

Machine Learning · Computer Science 2020-11-05 Andrés Muñoz Medina , Umar Syed , Sergei Vassilvitskii , Ellen Vitercik

We introduce a new zeroth-order algorithm for private stochastic optimization on nonconvex and nonsmooth objectives. Given a dataset of size $M$, our algorithm ensures $(\alpha,\alpha\rho^2/2)$-R\'enyi differential privacy and finds a…

Optimization and Control · Mathematics 2024-07-01 Qinzi Zhang , Hoang Tran , Ashok Cutkosky

We study the optimization of (strongly) quasar-convex functions, a class that arises naturally in many machine learning and data science applications due to its favorable properties. The fundamental properties of this class are first…

Optimization and Control · Mathematics 2026-04-30 Masoud Ahookhosh , Jose M. M. de Brito , Alireza Kabgani , Felipe Lara , Jinyun Yuan

Bilevel optimization minimizes an objective function, defined by an upper-level problem whose feasible region is the solution of a lower-level problem. We study the oracle complexity of finding an $\epsilon$-stationary point with…

Optimization and Control · Mathematics 2025-12-01 Lesi Chen , Jingzhao Zhang