Related papers: On Communication Complexity of Fixed Point Computa…
It is well known that a fixed point iteration for solving a linear equation system converges if and only if the spectral radius of the iteration matrix is less than one. A method is presented which guarantees the Fixed Point, even if this…
We consider the problem of minimizing a convex function over the intersection of finitely many simple sets which are easy to project onto. This is an important problem arising in various domains such as machine learning. The main difficulty…
This work studies distributed learning in the spirit of Yao's model of communication complexity: consider a two-party setting, where each of the players gets a list of labelled examples and they communicate in order to jointly perform some…
We prove a fixed point theorem for closed-graphed, decomposable-valued correspondences whose domain and range is a decomposable set of functions from an atomless measure space to a topological space. One consequence is an improvement of the…
For a topological space $X$ a topological contraction on $X$ is a closed mapping $f:X\to X$ such that for every open cover of $X$ there is a positive integer $n$ such that the image of the space $X$ via the $n$th iteration of $f$ is a…
In $\mathcal{N}=1$ superconformal theories in four dimensions the two-point function of superconformal multiplets is known up to an overall constant. A superconformal multiplet contains several conformal primary operators, whose two-point…
Cooperation through repetition is an important theme in game theory. In this regard, various celebrated ``folk theorems'' have been proposed for repeated games in increasingly more complex environments. There has, however, been insufficient…
We establish common fixed point theorems for two pairs of weakly compatible self-mappings using an auxiliary function of two variables. Unlike classical results, our theorems do not assume continuity of the mappings and require completeness…
Banach's fixed point theorem for contraction maps has been widely used to analyze the convergence of iterative methods in non-convex problems. It is a common experience, however, that iterative maps fail to be globally contracting under the…
Theoreticians have studied distributed algorithms in the radio network model for close to three decades. A significant fraction of this work focuses on lower bounds for basic communication problems such as wake-up (symmetry breaking among…
Recent work by Atserias and Dawar (J. Log. Comp 2019) and Tucker-Foltz (LMCS 2024) has established undefinability results in fixed-point logic with counting (FPC) corresponding to many classical complexity results from the hardness of…
This study develops a fixed-time convergent saddle point dynamical system for solving min-max problems under a relaxation of standard convexity-concavity assumption. In particular, it is shown that by leveraging the dynamical systems…
Max-min bilinear optimization models, where one agent maximizes and an adversary minimizes a common bilinear objective, serve as canonical saddle-point formulations in optimization theory. They capture, among others, two-player zero-sum…
Consider the "Number in Hand" multiparty communication complexity model, where k players holding inputs x_1,...,x_k in {0,1}^n communicate to compute the value f(x_1,...,x_k) of a function f known to all of them. The main lower bound…
We introduce a new coordination problem in distributed computing that we call the population stability problem. A system of agents each with limited memory and communication, as well as the ability to replicate and self-destruct, is…
We study learning dynamics induced by strategic agents who repeatedly play a game with an unknown payoff-relevant parameter. In each step, an information system estimates a belief distribution of the parameter based on the players'…
We study the computational complexity of basic decision problems for one-counter simple stochastic games (OC-SSGs), under various objectives. OC-SSGs are 2-player turn-based stochastic games played on the transition graph of classic…
We introduce a new theoretical framework for deriving lower bounds on data movement in bilinear algorithms. Bilinear algorithms are a general representation of fast algorithms for bilinear functions, which include computation of matrix…
Information theoretically secure multi-party computation (MPC) is a central primitive of modern cryptography. However, relatively little is known about the communication complexity of this primitive. In this work, we develop powerful…
In communication systems where users share common resources, users' selfish behavior usually results in suboptimal resource utilization. There have been extensive works that model communication systems with selfish users as one-shot games…