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The strong converse for a coding theorem shows that the optimal asymptotic rate possible with vanishing error cannot be improved by allowing a fixed error. Building on a method introduced by Gu and Effros for centralized coding problems, we…
We consider the task of minimizing the sum of smooth and strongly convex functions stored in a decentralized manner across the nodes of a communication network whose links are allowed to change in time. We solve two fundamental problems for…
Communication lower bounds have long been established for matrix multiplication algorithms. However, most methods of asymptotic analysis have either ignored the constant factors or not obtained the tightest possible values. Recent work has…
Population protocols are a well-studied model of distributed computation in which a group of anonymous finite-state agents communicates via pairwise interactions. Together they decide whether their initial configuration, that is, the…
Our work proves rigidity theorems for initial data sets associated with compact smooth spin manifolds with boundary and with compact convex polytopes, subject to the dominant energy condition. For manifolds with smooth boundary, this is…
Coded source compression, also known as source compression with helpers, has been a major variant of distributed source compression, but has hitherto received little attention in the quantum regime. This work treats and solves the…
Randomized smoothing is a popular way of providing robustness guarantees against adversarial attacks: randomly-smoothed functions have a universal Lipschitz-like bound, allowing for robustness certificates to be easily computed. In this…
Lipschitz constants are connected to many properties of neural networks, such as robustness, fairness, and generalization. Existing methods for computing Lipschitz constants either produce relatively loose upper bounds or are limited to…
We give a new version of the adversary method for proving lower bounds on quantum query algorithms. The new method is based on analyzing the eigenspace structure of the problem at hand. We use it to prove a new and optimal strong direct…
Let $f : \{0,1\}^n \times \{0,1\}^n \rightarrow \{0,1\}$ be a 2-party function. For every product distribution $\mu$ on $\{0,1\}^n \times \{0,1\}^n$, we show that $$\mathsf{CC}^\mu_{0.49}(f) = O\left(\left(\log \mathsf{prt}_{1/8}(f) \cdot…
In this paper, we prove a general hardness amplification scheme for optimization problems based on the technique of direct products. We say that an optimization problem $\Pi$ is direct product feasible if it is possible to efficiently…
A general scenario for an $N$-sequential conclusive state discrimination introduced recently in Loubenets and Namkung [arXiv:2102.04747] can provide a multipartite quantum communication realizable in the presence of a noise. In the present…
We study common randomness where two parties have access to i.i.d. samples from a known random source, and wish to generate a shared random key using limited (or no) communication with the largest possible probability of agreement. This…
Motivated by the increasing need to understand the distributed algorithmic foundations of large-scale graph computations, we study some fundamental graph problems in a message-passing model for distributed computing where $k \geq 2$…
Using tail bounds, we introduce a new probabilistic condition for function estimation in stochastic derivative-free optimization which leads to a reduction in the number of samples and eases algorithmic analyses. Moreover, we develop simple…
This paper considers a variation of the full-information secretary problem where the random variables to be observed are independent but not necessary identically distributed. The main result is a sharp lower bound for the optimal win…
Distributionally robust optimization has been shown to offer a principled way to regularize learning models. In this paper, we find that Tikhonov regularization is distributionally robust in an optimal transport sense (i.e., if an adversary…
We consider the task of decentralized minimization of the sum of smooth strongly convex functions stored across the nodes of a network. For this problem, lower bounds on the number of gradient computations and the number of communication…
We examine fixed-price mechanisms in bilateral trade through the lens of regret minimization. Our main results are twofold. (i) For independent values, a near-optimal $\widetilde{\Theta}(T^{2/3})$ tight bound for $\textsf{Global Budget…
In a celebrated work, Blais, Brody, and Matulef developed a technique for proving property testing lower bounds via reductions from communication complexity. Their work focused on testing properties of functions, and yielded new lower…