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This paper proposes a differentially private gradient-tracking-based distributed stochastic optimization algorithm over directed graphs. In particular, privacy noises are incorporated into each agent's state and tracking variable to…

Systems and Control · Electrical Eng. & Systems 2026-04-15 Jialong Chen , Jimin Wang , Ji-Feng Zhang

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 propose a Dimension-Reduced Second-Order Method (DRSOM) for convex and nonconvex (unconstrained) optimization. Under a trust-region-like framework, our method preserves the convergence of the second-order method while…

Optimization and Control · Mathematics 2023-07-04 Chuwen Zhang , Dongdong Ge , Chang He , Bo Jiang , Yuntian Jiang , Yinyu Ye

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

Differentially private stochastic gradient descent (DP-SGD) has become the standard algorithm for training machine learning models with rigorous privacy guarantees. Despite its widespread use, the theoretical understanding of its long-run…

Machine Learning · Computer Science 2025-11-21 Amartya Mukherjee , Jun Liu

In this paper, we propose a new randomized second-order optimization algorithm---Stochastic Subspace Cubic Newton (SSCN)---for minimizing a high dimensional convex function $f$. Our method can be seen both as a {\em stochastic} extension of…

Optimization and Control · Mathematics 2020-02-25 Filip Hanzely , Nikita Doikov , Peter Richtárik , Yurii Nesterov

Differentially private (DP) optimization is the standard paradigm to learn large neural networks that are accurate and privacy-preserving. The computational cost for DP deep learning, however, is notoriously heavy due to the per-sample…

Machine Learning · Computer Science 2023-09-20 Zhiqi Bu , Yu-Xiang Wang , Sheng Zha , George Karypis

We present the online Newton's method, a single-step second-order method for online nonconvex optimization. We analyze its performance and obtain a dynamic regret bound that is linear in the cumulative variation between round optima. We…

Optimization and Control · Mathematics 2020-12-11 Antoine Lesage-Landry , Joshua A. Taylor , Iman Shames

Optimization plays a key role in machine learning. Recently, stochastic second-order methods have attracted much attention due to their low computational cost in each iteration. However, these algorithms might perform poorly especially if…

Machine Learning · Computer Science 2017-10-25 Haishan Ye , Zhihua Zhang

Motivated by applications of large embedding models, we study differentially private (DP) optimization problems under sparsity of individual gradients. We start with new near-optimal bounds for the classic mean estimation problem but with…

Machine Learning · Computer Science 2024-11-01 Badih Ghazi , Cristóbal Guzmán , Pritish Kamath , Ravi Kumar , Pasin Manurangsi

The hidden state threat model of differential privacy (DP) assumes that the adversary has access only to the final trained machine learning (ML) model, without seeing intermediate states during training. However, the current privacy…

Machine Learning · Computer Science 2025-05-27 Rob Romijnders , Antti Koskela

In this paper, we present a new Hyperfast Second-Order Method with convergence rate $O(N^{-5})$ up to a logarithmic factor for the convex function with Lipshitz the third derivative. This method based on two ideas. The first comes from the…

Optimization and Control · Mathematics 2020-06-30 Dmitry Kamzolov , Alexander Gasnikov

Newton's method may exhibit slower convergence than vanilla Gradient Descent in its initial phase on strongly convex problems. Classical Newton-type multilevel methods mitigate this but, like Gradient Descent, achieve only linear…

Optimization and Control · Mathematics 2026-02-25 Nick Tsipinakis , Panos Parpas , Matthias Voigt

Newton's method may exhibit slower convergence than vanilla Gradient Descent in its initial phase on strongly convex problems. Classical Newton-type multilevel methods mitigate this but, like Gradient Descent, achieve only linear…

Optimization and Control · Mathematics 2026-03-05 Nick Tsipinakis , Panagiotis Tigkas , Panos Parpas

In this paper, we attempt to compare two distinct branches of research on second-order optimization methods. The first one studies self-concordant functions and barriers, the main assumption being that the third derivative of the objective…

Optimization and Control · Mathematics 2024-08-21 Pavel Dvurechensky , Yurii Nesterov

Many high-stakes applications require machine learning models that protect user privacy and provide well-calibrated, accurate predictions. While Differential Privacy (DP) is the gold standard for protecting user privacy, standard DP…

Machine Learning · Computer Science 2025-05-09 Ossi Räisä , Stratis Markou , Matthew Ashman , Wessel P. Bruinsma , Marlon Tobaben , Antti Honkela , Richard E. Turner

Distributed optimization is widely used in large-scale and privacy-preserving machine learning, where each agent stores a local objective and communicates only with its neighbors in a connected network. We study decentralized second-order…

We extend the standard notion of self-concordance to non-convex optimization and develop a family of second-order algorithms with global convergence guarantees. In particular, two function classes -- \textit{weakly self-concordant}…

Optimization and Control · Mathematics 2026-04-07 Donald Goldfarb , Lexiao Lai , Tianyi Lin , Jiayu Zhang

In this paper, we propose new structured second-order methods and structured adaptive-gradient methods obtained by performing natural-gradient descent on structured parameter spaces. Natural-gradient descent is an attractive approach to…

Machine Learning · Statistics 2022-02-22 Wu Lin , Frank Nielsen , Mohammad Emtiyaz Khan , Mark Schmidt

While the superior performance of second-order optimization methods such as Newton's method is well known, they are hardly used in practice for deep learning because neither assembling the Hessian matrix nor calculating its inverse is…

Machine Learning · Computer Science 2020-09-16 Siyuan Shen , Tianjia Shao , Kun Zhou , Chenfanfu Jiang , Feng Luo , Yin Yang