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We present a new accelerated gradient-based method for solving smooth unconstrained optimization problems. The goal is to embed a heavy-ball type of momentum into the Fast Gradient Method (FGM). For this purpose, we devise a generalization…

In this work, we study the iteration complexity of gradient methods for minimizing convex quadratic functions regularized by powers of Euclidean norms. We show that, due to the uniform convexity of the objective, gradient methods have…

Traffic prediction is a critical task in spatial-temporal forecasting with broad applications in travel planning and urban management. To model the complex spatial-temporal dependencies in traffic data, Spatial-Temporal Graph Convolutional…

The proximal bundle method (PBM) is a powerful and widely used approach for minimizing nonsmooth convex functions. However, for smooth objectives, its best-known convergence rate remains suboptimal, and whether PBM can be accelerated…

We propose a novel block-row partitioning method in order to improve the convergence rate of the block Cimmino algorithm for solving general sparse linear systems of equations. The convergence rate of the block Cimmino algorithm depends on…

We consider the problem of classifying data manifolds where each manifold represents invariances that are parameterized by continuous degrees of freedom. Conventional data augmentation methods rely upon sampling large numbers of training…

We outline a new approach for solving optimization problems which enforce triangle inequalities on output variables. We refer to this as metric-constrained optimization, and give several examples where problems of this form arise in machine…

The error exponent in lossy source coding characterizes the asymptotic decay rate of error probability with respect to blocklength. The Marton's error exponent provides the theoretically optimal bound on this rate. However, computation…

Unstructured pruning reduces the memory footprint in deep neural networks (DNNs). Recently, researchers proposed different types of structural pruning intending to reduce also the computation complexity. In this work, we first suggest a new…

Existing multi-view learning methods based on kernel function either require the user to select and tune a single predefined kernel or have to compute and store many Gram matrices to perform multiple kernel learning. Apart from the huge…

Graph-based machine learning has seen an increased interest over the last decade with many connections to other fields of applied mathematics. Learning based on partial differential equations, such as the phase-field Allen-Cahn equation,…

In many statistical learning problems, it is desired that the optimal solution conforms to an a priori known sparsity structure represented by a directed acyclic graph. Inducing such structures by means of convex regularizers requires…

We consider the problem of minimizing a non-convex function over a smooth manifold $\mathcal{M}$. We propose a novel algorithm, the Orthogonal Directions Constrained Gradient Method (ODCGM) which only requires computing a projection onto a…

One issue limiting the adaption of large-scale multi-region segmentation is the sometimes prohibitive memory requirements. This is especially troubling considering advances in massively parallel computing and commercial graphics processing…

To overcome the curse of dimensionality and curse of modeling in Dynamic Programming (DP) methods for solving classical Markov Decision Process (MDP) problems, Reinforcement Learning (RL) algorithms are popular. In this paper, we consider…

The aim of this paper is to design computationally-efficient and optimal algorithms for the online and stochastic exp-concave optimization settings. Typical algorithms for these settings, such as the Online Newton Step (ONS), can guarantee…

This paper considers the distributed optimization problem over a network, where the objective is to optimize a global function formed by a sum of local functions, using only local computation and communication. We develop an Accelerated…

Over the past two decades, descent methods have received substantial attention within the multiobjective optimization field. Nonetheless, both theoretical analyses and empirical evidence reveal that existing first-order methods for…

We develop several new algorithms for learning Markov Decision Processes in an infinite-horizon average-reward setting with linear function approximation. Using the optimism principle and assuming that the MDP has a linear structure, we…

Incremental methods for structure learning of pairwise Markov random fields (MRFs), such as grafting, improve scalability by avoiding inference over the entire feature space in each optimization step. Instead, inference is performed over an…