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In modern decentralized applications, ensuring communication efficiency and privacy for the users are the key challenges. In order to train machine-learning models, the algorithm has to communicate to the data center and sample data for its…
Recent advances in distributed optimization and learning have shown that communication compression is one of the most effective means of reducing communication. While there have been many results on convergence rates under communication…
Reducing communication - either between levels of a memory hierarchy or between processors over a network - is a key component of performance optimization (in both time and energy) for many problems, including dense linear algebra, particle…
Given a graph $G = (V,E)$, an $(\alpha, \beta)$-ruling set is a subset $S \subseteq V$ such that the distance between any two vertices in $S$ is at least $\alpha$, and the distance between any vertex in $V$ and the closest vertex in $S$ is…
The branch-and-bound algorithm based on decision diagrams introduced by Bergman et al. in 2016 is a framework for solving discrete optimization problems with a dynamic programming formulation. It works by compiling a series of bounded-width…
Dynamic data race detection has emerged as a key technique for ensuring reliability of concurrent software in practice. However, dynamic approaches can often miss data races owing to nondeterminism in the thread scheduler. Predictive race…
We introduce a new class of optimal-transport-regularized divergences, $D^c$, constructed via an infimal convolution between an information divergence, $D$, and an optimal-transport (OT) cost, $C$, and study their use in distributionally…
We consider a general class of two-stage distributionally robust optimization (DRO) problems where the ambiguity set is constrained by fixed marginal probability laws that are not necessarily discrete. We derive primal and dual formulations…
In their seminal paper that initiated the field of algorithmic mechanism design, \citet{NR99} studied the problem of designing strategyproof mechanisms for scheduling jobs on unrelated machines aiming to minimize the makespan. They provided…
We revisit the vertex-failure connectivity oracle problem. This is one of the most basic graph data structure problems under vertex updates, yet its complexity is still not well-understood. We essentially settle the complexity of this…
By definition, a rigid graph in $\mathbb{R}^d$ (or on a sphere) has a finite number of embeddings up to rigid motions for a given set of edge length constraints. These embeddings are related to the real solutions of an algebraic system.…
We present a deterministic algorithm for solving a wide range of dynamic programming problems in trees in $O(\log D)$ rounds in the massively parallel computation model (MPC), with $O(n^\delta)$ words of local memory per machine, for any…
We study distributed (strongly convex) optimization problems over a network of agents, with no centralized nodes. The loss functions of the agents are assumed to be \textit{similar}, due to statistical data similarity or otherwise. In order…
Decentralized optimization with time-varying networks is an emerging paradigm in machine learning. It saves remarkable communication overhead in large-scale deep training and is more robust in wireless scenarios especially when nodes are…
We prove the first nontrivial worst-case lower bounds for two closely related problems. First, $\Omega(n^{3/2})$ degree-1 reductions, series-parallel reductions, and $\Delta$Y transformations are required in the worst case to reduce an…
We present a new threshold phenomenon in data structure lower bounds where slightly reduced update times lead to exploding query times. Consider incremental connectivity, letting t_u be the time to insert an edge and t_q be the query time.…
In nonadaptive group testing, the main research objective is to design an efficient algorithm to identify a set of up to $t$ positive elements among $n$ samples with as few tests as possible. Disjunct matrices and separable matrices are two…
Decentralization is a promising method of scaling up parallel machine learning systems. In this paper, we provide a tight lower bound on the iteration complexity for such methods in a stochastic non-convex setting. Our lower bound reveals a…
This paper presents a novel methodology for tractably solving optimal control and offline reinforcement learning problems for high-dimensional systems. This work is motivated by the ongoing challenges of safety, computation, and optimality…
We propose Adaptive Compressed Gradient Descent (AdaCGD) - a novel optimization algorithm for communication-efficient training of supervised machine learning models with adaptive compression level. Our approach is inspired by the recently…