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We extend, in the free probability framework, an invariance principle for multilinear homogeneous sums with low influences recently established in [E. Mossel, R. O'Donnell and K. Oleszkiewicz (2010). Noise stability of functions with low…
Cowan and Zabczyk (1978) introduced a continuous-time generalisation of the secretary problem, where offers arrive at epochs of a homogeneous Poisson process. We expand their work to encompass the last-success problem under the…
Inspired by real-world applications such as the assignment of pupils to schools or the allocation of social housing, the one-sided matching problem studies how a set of agents can be assigned to a set of objects when the agents have…
We study the problem of bounding the posterior distribution of discrete probabilistic programs with unbounded support, loops, and conditioning. Loops pose the main difficulty in this setting: even if exact Bayesian inference is possible,…
In social choice settings with linear preferences, random dictatorship is known to be the only social decision scheme satisfying strategyproofness and ex post efficiency. When also allowing indifferences, random serial dictatorship (RSD) is…
We consider the stochastic gradient method with random reshuffling ($\mathsf{RR}$) for tackling smooth nonconvex optimization problems. $\mathsf{RR}$ finds broad applications in practice, notably in training neural networks. In this work,…
Reinforcement learning is generally difficult for partially observable Markov decision processes (POMDPs), which occurs when the agent's observation is partial or noisy. To seek good performance in POMDPs, one strategy is to endow the agent…
This paper presents a novel solution paradigm of general optimization under both exogenous and endogenous uncertainties. This solution paradigm consists of a probability distribution (PD)-free method of obtaining deterministic equivalents…
Best-response mechanisms (Nisan, Schapira, Valiant, Zohar, 2011) provide a unifying framework for studying various distributed protocols in which the participants are instructed to repeatedly best respond to each others' strategies. Two…
Maximality, interval dominance, and E-admissibility are three well-known criteria for decision making under severe uncertainty using lower previsions. We present a new fast algorithm for finding maximal gambles. We compare its performance…
In this paper we consider the problem of binary hypothesis testing with finite memory systems. Let $X_1,X_2,\ldots$ be a sequence of independent identically distributed Bernoulli random variables, with expectation $p$ under $\mathcal{H}_0$…
A celebrated result of Hastad established that, for any constant $\varepsilon>0$, it is NP-hard to find an assignment satisfying a $(1/|G|+\varepsilon)$-fraction of the constraints of a given 3-LIN instance over an Abelian group $G$ even if…
A probabilistic structure on sequential dynamical systems is introduced here, the new model will be called Probabilistic Sequential Network, PSN. The morphisms of Probabilistic Sequential Networks are defined using two algebraic conditions.…
We consider the infinite-horizon average-reward restless bandit problem. We propose a novel \emph{two-set policy} that maintains two dynamic subsets of arms: one subset of arms has a nearly optimal state distribution and takes actions…
A system $(P_\alpha: \alpha\in\mathcal{A})$ of probability distributions on a partially ordered set (poset) $\mathcal{S}$ indexed by another poset $\mathcal{A}$ can be realized by a system of $\mathcal{S}$-valued random variables…
In school districts where assignments are exclusively determined by a clearinghouse students can only appeal their assignment with a valid reason. An assignment is incontestable if it is appeal-proof. We study incontestability when students…
In party-approval multiwinner elections the goal is to allocate the seats of a fixed-size committee to parties based on the approval ballots of the voters over the parties. In particular, each voter can approve multiple parties and each…
Recently, a scalable approach to system analysis and controller synthesis for homogeneous multi-agent systems with Bernoulli distributed packet loss has been proposed. As a key result of that line of work, it was shown how to obtain upper…
Enhancing the stability of machine learning algorithms under distributional shifts is at the heart of the Out-of-Distribution (OOD) Generalization problem. Derived from causal learning, recent works of invariant learning pursue strict…
We consider the allocation of indivisible objects when agents have preferences over their own allocations, but share the ownership of the resources to be distributed. Examples might include seats in public schools, faculty offices, and time…