Related papers: Trading information complexity for error
Despite the apparent similarity between shared randomness and shared entanglement in the context of Communication Complexity, our understanding of the latter is not as good as of the former. In particular, there is no known "entanglement…
We consider a private discrete distribution estimation problem with one-bit communication constraint. The privacy constraints are imposed with respect to the local differential privacy and the maximal leakage. The estimation error is…
We study the scalability of consensus-based distributed optimization algorithms by considering two questions: How many processors should we use for a given problem, and how often should they communicate when communication is not free?…
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…
Communication complexity, which quantifies the minimum communication required for distributed computation, offers a natural setting for investigating the capabilities and limitations of quantum mechanics in information processing. We…
The process of state preparation, its transmission and subsequent measurement can be classically simulated through the communication of some amount of classical information. Recently, we proved that the minimal communication cost is the…
We consider the communication complexity of finding an approximate maximum matching in a graph in a multi-party message-passing communication model. The maximum matching problem is one of the most fundamental graph combinatorial problems,…
We study the maximum $k$-set coverage problem in the following distributed setting. A collection of sets $S_1,\ldots,S_m$ over a universe $[n]$ is partitioned across $p$ machines and the goal is to find $k$ sets whose union covers the most…
A distributed binary hypothesis testing (HT) problem involving two parties, a remote observer and a detector, is studied. The remote observer has access to a discrete memoryless source, and communicates its observations to the detector via…
We study lower bounds on the worst-case error of numerical integration in tensor product spaces. As reference we use the $N$-th minimal error of linear rules that use $N$ function values. The information complexity is the minimal number $N$…
In this work we focus our attention on distributed optimization problems in the context where the communication time between the server and the workers is non-negligible. We obtain novel methods supporting bidirectional compression (both…
We study the setup where each of $n$ users holds an element from a discrete set, and the goal is to count the number of distinct elements across all users, under the constraint of $(\epsilon, \delta)$-differentially privacy: - In the…
In this paper, we study the sample complexity lower bounds for the exact recovery of parameters and for a positive excess risk of a feed-forward, fully-connected neural network for binary classification, using information-theoretic tools.…
We consider the problem of option hedging in a market with proportional transaction costs. Since super-replication is very costly in such markets, we replace perfect hedging with an expected loss constraint. Asymptotic analysis for small…
We deal with the problem, initiated in [8], of finding randomized and quantum complexity of initial-value problems. We showed in [8] that a speed-up in both settings over the worst-case deterministic complexity is possible. In the present…
We study the effect of rounds of interaction on the common randomness generation (CRG) problem. In the CRG problem, two parties, Alice and Bob, receive samples $X_i$ and $Y_i$, respectively, drawn jointly from a source distribution $\mu$.…
The multiplayer promise set disjointness is one of the most widely used problems from communication complexity in applications. In this problem there are $k$ players with subsets $S^1, \ldots, S^k$, each drawn from $\{1, 2, \ldots, n\}$,…
Alice and Bob are given $n$-bit integer pairs $(x,y)$ and $(a,b)$, respectively, and they must decide if $y=ax+b$. We prove that the randomised communication complexity of this Point--Line Incidence problem is $\Theta(\log n)$. This…
We present efficient and practical algorithms for a large, distributed system of processors to achieve reliable computations in a secure manner. Specifically, we address the problem of computing a general function of several private inputs…
We consider a setting of non-cooperative communication where a receiver wants to recover randomly generated sequences of symbols that are observed by a strategic sender. The sender aims to maximize an average utility that may not align with…