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Gradient clipping is a popular modification to standard (stochastic) gradient descent, at every iteration limiting the gradient norm to a certain value $c >0$. It is widely used for example for stabilizing the training of deep learning…
When implementing the gradient descent method in low precision, the employment of stochastic rounding schemes helps to prevent stagnation of convergence caused by the vanishing gradient effect. Unbiased stochastic rounding yields zero bias…
Stochastic gradient descent (SGD) still is the workhorse for many practical problems. However, it converges slow, and can be difficult to tune. It is possible to precondition SGD to accelerate its convergence remarkably. But many attempts…
Stress, edge crossings, and crossing angles play an important role in the quality and readability of graph drawings. Most standard graph drawing algorithms optimize one of these criteria which may lead to layouts that are deficient in other…
In this work we investigate the practicality of stochastic gradient descent and recently introduced variants with variance-reduction techniques in imaging inverse problems. Such algorithms have been shown in the machine learning literature…
This paper considers a distributed stochastic strongly convex optimization, where agents connected over a network aim to cooperatively minimize the average of all agents' local cost functions. Due to the stochasticity of gradient estimation…
A stochastic gradient method for finite-sum minimization subject to deterministic linear constraints is proposed and analyzed. The procedure presented adapts the projected gradient method on convex set to the use of both a stochastic…
In this paper, we propose a method of distributed stochastic gradient descent (SGD), with low communication load and computational complexity, and still fast convergence. To reduce the communication load, at each iteration of the algorithm,…
Stochastic gradient descent method and its variants constitute the core optimization algorithms that achieve good convergence rates for solving machine learning problems. These rates are obtained especially when these algorithms are…
We consider a discrete-time model of continuous-time distributed optimization over dynamic directed-graphs (digraphs) with applications to distributed learning. Our optimization algorithm works over general strongly connected dynamic…
Optimization problems with continuous data appear in, e.g., robust machine learning, functional data analysis, and variational inference. Here, the target function is given as an integral over a family of (continuously) indexed target…
Sampling methods (e.g., node-wise, layer-wise, or subgraph) has become an indispensable strategy to speed up training large-scale Graph Neural Networks (GNNs). However, existing sampling methods are mostly based on the graph structural…
Stochastic gradient descent (SGD) holds as a classical method to build large scale machine learning models over big data. A stochastic gradient is typically calculated from a limited number of samples (known as mini-batch), so it…
Graph Visualization, also known as Graph Drawing, aims to find geometric embeddings of graphs that optimize certain criteria. Stress is a widely used metric; stress is minimized when every pair of nodes is positioned at their shortest path…
In this paper, we provide a theoretical study of noise geometry for minibatch stochastic gradient descent (SGD), a phenomenon where noise aligns favorably with the geometry of local landscape. We propose two metrics, derived from analyzing…
Neural networks are usually trained by some form of stochastic gradient descent (SGD)). A number of strategies are in common use intended to improve SGD optimization, such as learning rate schedules, momentum, and batching. These are…
We study finite-sum nonconvex optimization problems, where the objective function is an average of $n$ nonconvex functions. We propose a new stochastic gradient descent algorithm based on nested variance reduction. Compared with…
We consider the problem of minimizing a convex function that is evolving according to unknown and possibly stochastic dynamics, which may depend jointly on time and on the decision variable itself. Such problems abound in the machine…
Stochastic gradient descent is the method of choice for large-scale machine learning problems, by virtue of its light complexity per iteration. However, it lags behind its non-stochastic counterparts with respect to the convergence rate,…
Feedback optimization is an increasingly popular control paradigm to optimize dynamical systems, accounting for control objectives that concern the system operation at steady-state. Existing feedback optimization techniques heavily rely on…