Related papers: Resilience for the Littlewood-Offord Problem
In this article, we establish a $L^1$ estimate for solutions to Poisson equation with mixed boundary condition, on complete noncompact manifolds with nonnegative Ricci curvature and compact manifolds with positive Ricci curvature…
The $p$-adic Littlewood conjecture (PLC) states that $\liminf_{q\to\infty} q\cdot |q|_p \cdot ||qx|| = 0$ for every prime $p$ and every real $x$. Let $w_{CF}(x)$ be an infinite word composed of the continued fraction expansion of $x$ and…
We consider the problem of repetitive scenario design where one has to solve repeatedly a scenario design problem and can adjust the sample size (number of scenarios) to obtain a desired level of risk (constraint violation probability). We…
We study the stochastic multi-armed bandit problem with non-equivalent multiple plays where, at each step, an agent chooses not only a set of arms, but also their order, which influences reward distribution. In several problem formulations…
The Lipschitz constant of a finite normal-form game is the maximal change in some player's payoff when a single opponent changes his strategy. We prove that games with small Lipschitz constant admit pure {\epsilon}-equilibria, and pinpoint…
We provide a novel dimension-free uniform concentration bound for the empirical risk function of constrained logistic regression. Our bound yields a milder sufficient condition for a uniform law of large numbers than conditions derived by…
There are $n$ independent Bernoulli random variables with parameters $p_i$ that are observed sequentially. Two players, A and B, act in turns starting with player A. Each player has the possibility on his turn, when $I_k=1$, to choose…
We provide a tight bound on the amount of experimentation under the optimal strategy in sequential decision problems. We show the applicability of the result by providing a bound on the cut-off in a one-arm bandit problem.
We propose and study a new model for competitions, specifically sports multi-player leagues where the initial strengths of the teams are independent i.i.d. random variables that evolve during different days of the league according to…
We study the model robustness against adversarial examples, referred to as small perturbed input data that may however fool many state-of-the-art deep learning models. Unlike previous research, we establish a novel theory addressing the…
In this paper, we consider a bandit problem in which there are a number of groups each consisting of infinitely many arms. Whenever a new arm is requested from a given group, its mean reward is drawn from an unknown reservoir distribution…
We consider the problem of robust polynomial regression, where one receives samples $(x_i, y_i)$ that are usually within $\sigma$ of a polynomial $y = p(x)$, but have a $\rho$ chance of being arbitrary adversarial outliers. Previously, it…
In a recent work, Laforgue et al. introduce the model of last switch dependent (LSD) bandits, in an attempt to capture nonstationary phenomena induced by the interaction between the player and the environment. Examples include satiation,…
This paper considers a multi-armed bandit game where the number of arms is much larger than the maximum budget and is effectively infinite. We characterize necessary and sufficient conditions on the total budget for an algorithm to return…
This paper considers the multi-dimensional consensus in networked systems, where some of the agents might be misbehaving (or faulty). Despite the influence of these misbehaviors, the benign agents aim to reach an agreement while avoiding…
Fix a positive integer $N$. Select an additive composition $\xi$ of $N$ uniformly out of $2^{N-1}$ possibilities. The interplay between the number of parts in $\xi$ and the maximum part in $\xi$ is our focus. It is not surprising that…
In this paper, we investigate the online allocation problem of maximizing the overall revenue subject to both lower and upper bound constraints. Compared to the extensively studied online problems with only resource upper bounds, the…
Consider the nonlinear matrix equation X-sum_{i=1}^{m}A_{i}^{*}X^{-1}A_{i}=Q. This paper shows that there exists a unique positive definite solution to the equation without any restriction on A_{i}. Three perturbation bounds for the unique…
The stable roommates problem with $n$ agents has worst case complexity $O(n^2)$ in time and space. Random instances can be solved faster and with less memory, however. We introduce an algorithm that has average time and space complexity…
We study the probability that an AR(1) Markov chain $X_{n+1}=aX_n+\xi_{n+1}$, where $a\in(0,1)$ is a constant, stays non-negative for a long time. We find the exact asymptotics of this probability and the weak limit of $X_n$ conditioned to…