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Block coordinate descent methods and stochastic subgradient methods have been extensively studied in optimization and machine learning. By combining randomized block sampling with stochastic subgradient methods based on dual averaging, we…
Federated learning is an emerging data-private distributed learning framework, which, however, is vulnerable to adversarial attacks. Although several heuristic defenses are proposed to enhance the robustness of federated learning, they do…
Due to the high communication cost in distributed and federated learning problems, methods relying on compression of communicated messages are becoming increasingly popular. While in other contexts the best performing gradient-type methods…
We study federated machine learning at the wireless network edge, where limited power wireless devices, each with its own dataset, build a joint model with the help of a remote parameter server (PS). We consider a bandwidth-limited fading…
Stochastic convex optimization is a basic and well studied primitive in machine learning. It is well known that convex and Lipschitz functions can be minimized efficiently using Stochastic Gradient Descent (SGD). The Normalized Gradient…
Minimax optimization is gaining increasing attention in modern machine learning applications. Driven by large-scale models and massive volumes of data collected from edge devices, as well as the concern to preserve client privacy,…
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…
While Nesterov's Accelerated Gradient Descent (AGD) efficiently solves constrained problems when the constraint set $X \subseteq \mathbb{R}^n$ is simple and easy to project onto, it remains an open question whether function-constrained…
Classical machine learning models such as deep neural networks are usually trained by using Stochastic Gradient Descent-based (SGD) algorithms. The classical SGD can be interpreted as a discretization of the stochastic gradient flow. In…
Stochastic gradient descent (\textsc{Sgd}) methods are the most powerful optimization tools in training machine learning and deep learning models. Moreover, acceleration (a.k.a. momentum) methods and diagonal scaling (a.k.a. adaptive…
Averaging scheme has attracted extensive attention in deep learning as well as traditional machine learning. It achieves theoretically optimal convergence and also improves the empirical model performance. However, there is still a lack of…
Gradient descent is an important class of iterative algorithms for minimizing convex functions. Classically, gradient descent has been a sequential and synchronous process. Distributed and asynchronous variants of gradient descent have been…
Federated Learning (FL), a distributed learning paradigm that scales on-device learning collaboratively, has emerged as a promising approach for decentralized AI applications. Local optimization methods such as Federated Averaging (FedAvg)…
Stochastic Gradient Descent (SGD) has become popular for solving large scale supervised machine learning optimization problems such as SVM, due to their strong theoretical guarantees. While the closely related Dual Coordinate Ascent (DCA)…
In recent years, nonconvex minimax problems have attracted significant attention due to their broad applications in machine learning, including generative adversarial networks, robust optimization and adversarial training. Most existing…
Stochastic Gradient Descent (SGD) is a popular optimization method which has been applied to many important machine learning tasks such as Support Vector Machines and Deep Neural Networks. In order to parallelize SGD, minibatch training is…
We consider the distributed optimization problem where $n$ agents each possessing a local cost function, collaboratively minimize the average of the $n$ cost functions over a connected network. Assuming stochastic gradient information is…
Stochastic gradient descent with momentum (SGDM) methods have become fundamental optimization tools in machine learning, combining the computational efficiency of stochastic gradients with the acceleration benefits of momentum. Despite…
Stochastic gradient descent ascent (SGDA) and its variants have been the workhorse for solving minimax problems. However, in contrast to the well-studied stochastic gradient descent (SGD) with differential privacy (DP) constraints, there is…
Stochastic gradient descent (SGD) is a widely used algorithm in machine learning, particularly for neural network training. Recent studies on SGD for canonical quadratic optimization or linear regression show it attains well generalization…