Related papers: Efficient Second Order Online Learning by Sketchin…
In this paper, we propose a quasi-Newton method for solving smooth and monotone nonlinear equations, including unconstrained minimization and minimax optimization as special cases. For the strongly monotone setting, we establish two global…
This paper addresses the optimization problem of minimizing non-convex continuous functions, which is relevant in the context of high-dimensional machine learning applications characterized by over-parametrization. We analyze a randomized…
Motivated by recent advances in serverless cloud computing, in particular the "function as a service" (FaaS) model, we consider the problem of minimizing a convex function in a massively parallel fashion, where communication between workers…
We investigate the problem of sequential linear data prediction for real life big data applications. The second order algorithms, i.e., Newton-Raphson Methods, asymptotically achieve the performance of the "best" possible linear data…
The power of randomized algorithms in numerical methods have led to fast solutions which use the Singular Value Decomposition (SVD) as a core routine. However, given the large data size of modern and the modest runtime of SVD, most…
Leveraging the kernel trick in both the input and output spaces, surrogate kernel methods are a flexible and theoretically grounded solution to structured output prediction. If they provide state-of-the-art performance on complex data sets…
We propose a randomized algorithm with quadratic convergence rate for convex optimization problems with a self-concordant, composite, strongly convex objective function. Our method is based on performing an approximate Newton step using a…
Online linear programming plays an important role in both revenue management and resource allocation, and recent research has focused on developing efficient first-order online learning algorithms. Despite the empirical success of…
Randomized algorithms are important for solving large-scale optimization problems. In this paper, we propose a fast sketching algorithm for least square problems regularized by convex or nonconvex regularization functions, Sketching for…
Stochastic optimization methods have become a class of popular optimization tools in machine learning. Especially, stochastic gradient descent (SGD) has been widely used for machine learning problems such as training neural networks due to…
Projection-based iterative methods for solving large over-determined linear systems are well-known for their simplicity and computational efficiency. It is also known that the correct choice of a sketching procedure (i.e., preprocessing…
Consumer electronics used to follow the miniaturization trend described by Moore's Law. Despite increased processing power in Microcontroller Units (MCUs), MCUs used in the smallest appliances are still not capable of running even…
In this book, I introduce the basic concepts of Online Learning through the modern view of Online Convex Optimization. Here, online learning refers to the framework of regret minimization under worst-case assumptions. I present first-order…
The computational bottleneck in applying online learning to massive data sets is usually the projection step. We present efficient online learning algorithms that eschew projections in favor of much more efficient linear optimization steps…
In online learning, the data is provided in a sequential order, and the goal of the learner is to make online decisions to minimize overall regrets. This note is concerned with continuous-time models and algorithms for several online…
A new, fast second-order method is proposed that achieves the optimal $\mathcal{O}\left(|\log(\epsilon)|\epsilon^{-3/2}\right)$ complexity to obtain first-order $\epsilon$-stationary points. Crucially, this is deduced without assuming the…
We show that the Subgradient algorithm is universal for online learning on the simplex in the sense that it simultaneously achieves $O(\sqrt N)$ regret for adversarial costs and $O(1)$ pseudo-regret for i.i.d costs. To the best of our…
In order to safely deploy Deep Neural Networks (DNNs) within the perception pipelines of real-time decision making systems, there is a need for safeguards that can detect out-of-training-distribution (OoD) inputs both efficiently and…
Sketching is a powerful dimensionality reduction technique for accelerating algorithms for data analysis. A crucial step in sketching methods is to compute a subspace embedding (SE) for a large matrix $\mathbf{A} \in \mathbb{R}^{N \times…
We improve the theoretical and empirical performance of neural-network(NN)-based active learning algorithms for the non-parametric streaming setting. In particular, we introduce two regret metrics by minimizing the population loss that are…