Related papers: Resilience for the Littlewood-Offord Problem
This article describes an absolutely stable, first-order constraint solverfor multi-rigid body systems that calculates (predicts) constraint forces for typical bilateral and unilateral constraints, contact constraints with friction, and…
Order statistics theory is applied in this paper to probabilistic robust control theory to compute the minimum sample size needed to come up with a reliable estimate of an uncertain quantity under continuity assumption of the related…
Given natural parameters s and r, where $2\leq s\leq r$, we consider the distribution of a random variable $\xi=\sum\limits_{k=1}^{\infty}s^{-k}\xi_k\equiv\Delta^{r_s}_{\xi_1\xi_2...\xi_k...},$ where $(\xi_k)$ is a sequence of independent…
We study a class of adversarial bandit optimization problems in which the loss functions may be non-convex and non-smooth. In each round, the learner observes a loss that consists of an underlying linear component together with an…
Given a star-shaped domain $K\subseteq \mathbb R^d$, $n$ vectors $v_1,\dots,v_n \in \mathbb R^d$, a number $R>0$, and i.i.d. random variables $\eta_1,\dots,\eta_n$, we study the geometric and arithmetic structure of the set of vectors $V =…
Let $X=\{X_n: n\in\mathbb{N}\}$ be a linear process in which the coefficients are of the form $a_i=i^{-1}\ell(i)$ with $\ell$ being a slowly varying function at the infinity and the innovations are independent and identically distributed…
We prove concentration bounds for random Euclidean combinatorial optimization problems with $p$--costs. For bipartite matching and for the (mono- and bi-partite) traveling salesperson problem in dimension $d\ge 3$, we obtain concentration…
Several recent papers have discussed utilizing Lipschitz constants to limit the susceptibility of neural networks to adversarial examples. We analyze recently proposed methods for computing the Lipschitz constant. We show that the Lipschitz…
We consider an adversarial variant of the classic $K$-armed linear contextual bandit problem where the sequence of loss functions associated with each arm are allowed to change without restriction over time. Under the assumption that the…
Machine learning approaches relying on such criteria as adversarial robustness or multi-agent settings have raised the need for solving game-theoretic equilibrium problems. Of particular relevance to these applications are methods targeting…
In the area of symbolic-numerical computation within computer algebra, an interesting question is how "close" a random input is to the "critical" ones, like the singular matrices in linear algebra or the polynomials with multiple roots for…
The dynamics of interacting structured populations can be modeled by $\frac{dx_i}{dt}= A_i (x)x_i$ where $x_i\in \R^{n_i}$, $x=(x_1,\dots,x_k)$, and $A_i(x)$ are matrices with non-negative off-diagonal entries. These models are permanent if…
We consider a bandit optimization problem for nonconvex and non-smooth functions, where in each trial the loss function is the sum of a linear function and a small but arbitrary perturbation chosen after observing the player's choice. We…
We consider the classical stochastic multi-armed bandit but where, from time to time and roughly with frequency $\epsilon$, an extra observation is gathered by the agent for free. We prove that, no matter how small $\epsilon$ is the agent…
By well known results of probability theory, any sequence of random variables with bounded second moments has a subsequence satisfying the central limit theorem and the law of the iterated logarithm in a randomized form. In this paper we…
Recently, Abebe et al. (KDD 2018) and Chan et al. (WWW 2019) have considered an opinion dynamics optimization problem that is based on a popular model for social opinion dynamics, in which each agent has some fixed innate opinion, and a…
We investigate the stability of the equilibrium-induced optimal value in one-dimensional diffusion setting for a time-inconsistent stopping problem under non-exponential discounting. We show that the optimal value is semi-continuous with…
Let $\xi$ be a random integer vector, having uniform distribution \[\mathbf{P} \{\xi = (i_1,i_2,...,i_n) = 1/n^n \} \ \hbox{for} \ 1 \leq i_1,i_2,...,i_n\leq n.\] A realization $(i_1,i_2,...,i_n)$ of $\xi$ is called \textit{good}, if its…
The stable marriage and stable roommates problems have been extensively studied due to their high applicability in various real-world scenarios. However, it might happen that no stable solution exists, or stable solutions do not meet…
In this paper, we study the relationship between resilience and accuracy in the resilient distributed multi-dimensional consensus problem. We consider a network of agents, each of which has a state in $\mathbb{R}^d$. Some agents in the…