Related papers: Streaming Complexity of SVMs
Stochastic gradient descent (SGD) is a popular algorithm for optimization problems arising in high-dimensional inference tasks. Here one produces an estimator of an unknown parameter from independent samples of data by iteratively…
We identify a sharp separation in the streaming space complexity of Maximum Cut when the algorithm must output an approximate cut (rather than only the approximate value). For dense graphs, we show that $O(n/\varepsilon^2)$ space is…
Large-scale constrained optimization problems are at the core of many tasks in control, signal processing, and machine learning. Notably, problems with functional constraints arise when, beyond a performance{\nobreakdash-}centric goal…
Stochastic gradient descent (SGD) and its variants are the main workhorses for solving large-scale optimization problems with nonconvex objective functions. Although the convergence of SGDs in the (strongly) convex case is well-understood,…
Gradient clipping is a standard training technique used in deep learning applications such as large-scale language modeling to mitigate exploding gradients. Recent experimental studies have demonstrated a fairly special behavior in the…
We study space-pass tradeoffs in graph streaming algorithms for parameter estimation and property testing problems such as estimating the size of maximum matchings and maximum cuts, weight of minimum spanning trees, or testing if a graph is…
We study high-dimensional robust statistics tasks in the streaming model. A recent line of work obtained computationally efficient algorithms for a range of high-dimensional robust estimation tasks. Unfortunately, all previous algorithms…
SGD (Stochastic Gradient Descent) is a popular algorithm for large scale optimization problems due to its low iterative cost. However, SGD can not achieve linear convergence rate as FGD (Full Gradient Descent) because of the inherent…
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 study streaming algorithms for two fundamental geometric problems: computing the cost of a Minimum Spanning Tree (MST) of an $n$-point set $X \subset \{1,2,\dots,\Delta\}^d$, and computing the Earth Mover Distance (EMD) between two…
We introduce a new computational model for data streams: asymptotically exact streaming algorithms. These algorithms have an approximation ratio that tends to one as the length of the stream goes to infinity while the memory used by the…
Streaming algorithms are generally judged by the quality of their solution, memory footprint, and computational complexity. In this paper, we study the problem of maximizing a monotone submodular function in the streaming setting with a…
Classical stochastic gradient methods are well suited for minimizing expected-value objective functions. However, they do not apply to the minimization of a nonlinear function involving expected values or a composition of two expected-value…
There has been a growing effort in studying the distributed optimization problem over a network. The objective is to optimize a global function formed by a sum of local functions, using only local computation and communication. Literature…
In this paper, we propose a novel kernel stochastic gradient descent (SGD) algorithm for large-scale supervised learning with general losses. Compared to traditional kernel SGD, our algorithm improves efficiency and scalability through an…
In this paper, we study streaming algorithms that minimize the number of changes made to their internal state (i.e., memory contents). While the design of streaming algorithms typically focuses on minimizing space and update time, these…
Stochastic Gradient Descent (SGD), a widely used optimization algorithm in deep learning, is often limited to converging to local optima due to the non-convex nature of the problem. Leveraging these local optima to improve model performance…
Stochastic Gradient Descent (SGD) has proven to be remarkably effective in optimizing deep neural networks that employ ever-larger numbers of parameters. Yet, improving the efficiency of large-scale optimization remains a vital and highly…
We consider in this work a system of two stochastic differential equations named the perturbed compositional gradient flow. By introducing a separation of fast and slow scales of the two equations, we show that the limit of the slow motion…
A fundamental question in streaming complexity is whether every space-efficient turnstile algorithm is implicitly a linear sketch. The landmark work of Li, Nguyen, and Woodruff [LNW14] established an equivalence between the two, but their…