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SketchySGD improves upon existing stochastic gradient methods in machine learning by using randomized low-rank approximations to the subsampled Hessian and by introducing an automated stepsize that works well across a wide range of convex…
Stochastic Gradient Descent (SGD) is a workhorse in machine learning, yet its slow convergence can be a computational bottleneck. Variance reduction techniques such as SAG, SVRG and SAGA have been proposed to overcome this weakness,…
In this thesis, we propose new theoretical frameworks for the analysis of stochastic and distributed methods with error compensation and local updates. Using these frameworks, we develop more than 20 new optimization methods, including the…
Accelerated stochastic gradient descent (ASGD) is a workhorse in deep learning and often achieves better generalization performance than SGD. However, existing optimization theory can only explain the faster convergence of ASGD, but cannot…
Distributed stochastic optimization has drawn great attention recently due to its effectiveness in solving large-scale machine learning problems. Though numerous algorithms have been proposed and successfully applied to general practical…
In centralized settings, it is well known that stochastic gradient descent (SGD) avoids saddle points and converges to local minima in nonconvex problems. However, similar guarantees are lacking for distributed first-order algorithms. The…
We study diffusion and consensus based optimization of a sum of unknown convex objective functions over distributed networks. The only access to these functions is through stochastic gradient oracles, each of which is only available at a…
Recent advances in the theoretical understanding of SGD led to a formula for the optimal batch size minimizing the number of effective data passes, i.e., the number of iterations times the batch size. However, this formula is of no…
The Lookahead optimizer enhances deep learning models by employing a dual-weight update mechanism, which has been shown to improve the performance of underlying optimizers such as SGD. However, most theoretical studies focus on its…
A widely recognized difficulty in federated learning arises from the statistical heterogeneity among clients: local datasets often originate from distinct yet not entirely unrelated probability distributions, and personalization is,…
In this work, we investigate the dynamics of stochastic gradient descent (SGD) when training a single-neuron autoencoder with linear or ReLU activation on orthogonal data. We show that for this non-convex problem, randomly initialized SGD…
Stochastic gradient descent (SGD) has been a go-to algorithm for nonconvex stochastic optimization problems arising in machine learning. Its theory however often requires a strong framework to guarantee convergence properties. We hereby…
Stochastic gradient descent (SGD) is a well known method for regression and classification tasks. However, it is an inherently sequential algorithm at each step, the processing of the current example depends on the parameters learned from…
Distributed parallel stochastic gradient descent algorithms are workhorses for large scale machine learning tasks. Among them, local stochastic gradient descent (Local SGD) has attracted significant attention due to its low communication…
In distributed machine learning, where agents collaboratively learn from diverse private data sets, there is a fundamental tension between consensus and optimality. In this paper, we build on recent algorithmic progresses in distributed…
Stochastic optimization lies at the core of most statistical learning models. The recent great development of stochastic algorithmic tools focused significantly onto proximal gradient iterations, in order to find an efficient approach for…
Stochastic Gradient Descent (SGD) is a fundamental algorithm in machine learning, representing the optimization backbone for training several classic models, from regression to neural networks. Given the recent practical focus on…
This work characterizes the benefits of averaging schemes widely used in conjunction with stochastic gradient descent (SGD). In particular, this work provides a sharp analysis of: (1) mini-batching, a method of averaging many samples of a…
Training large neural networks requires distributing learning across multiple workers, where the cost of communicating gradients can be a significant bottleneck. signSGD alleviates this problem by transmitting just the sign of each…
Stochastic Gradient Descent (SGD) is being used routinely for optimizing non-convex functions. Yet, the standard convergence theory for SGD in the smooth non-convex setting gives a slow sublinear convergence to a stationary point. In this…