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Spectral Sparsification and Regret Minimization Beyond Matrix Multiplicative Updates
In this paper, we provide a novel construction of the linear-sized spectral sparsifiers of Batson, Spielman and Srivastava [11]. While previous constructions required Ω(n4) running time [11, 45], ourExpand
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Variance Reduction for Faster Non-Convex Optimization
We consider the fundamental problem in non-convex optimization of efficiently reaching a stationary point. In contrast to the convex case, in the long history of this basic problem, the only knownExpand
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Finding approximate local minima faster than gradient descent
We design a non-convex second-order optimization algorithm that is guaranteed to return an approximate local minimum in time which scales linearly in the underlying dimension and the number ofExpand
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Improved SVRG for Non-Strongly-Convex or Sum-of-Non-Convex Objectives
Many classical algorithms are found until several years later to outlive the confines in which they were conceived, and continue to be relevant in unforeseen settings. In this paper, we show thatExpand
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Linear Coupling: An Ultimate Unification of Gradient and Mirror Descent
First-order methods play a central role in large-scale convex optimization. Even though many variations exist, each suited to a particular problem form, almost all such methods fundamentally rely onExpand
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Even Faster Accelerated Coordinate Descent Using Non-Uniform Sampling
Accelerated coordinate descent is widely used in optimization due to its cheap per-iteration cost and scalability to large-scale problems. Up to a primal-dual transformation, it is also the same asExpand
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Finding Approximate Local Minima for Nonconvex Optimization in Linear Time
We design a non-convex second-order optimization algorithm that is guaranteed to return an approximate local minimum in time which is linear in the input representation. The time complexity of ourExpand
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Asymptotically optimal strategy-proof mechanisms for two-facility games
We consider the problem of locating facilities in a metric space to serve a set of selfish agents. The cost of an agent is the distance between her own location and the nearest facility. The socialExpand
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A simple, combinatorial algorithm for solving SDD systems in nearly-linear time
In this paper, we present a simple combinatorial algorithm that solves symmetric diagonally dominant (SDD) linear systems in nearly-linear time. It uses little of the machinery that previouslyExpand
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