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We consider a scenario where $N$ users send packets to a common access point. The receiver decodes the message of each user by treating the other user's signals as noise. Associated with each user is its channel state and a finite queue…

This article is concerned with stability analysis and stabilization of randomly switched nonlinear systems. These systems may be regarded as piecewise deterministic stochastic systems: the discrete switches are triggered by a stochastic…

Motivated by data on coauthorships in scientific publications, we analyze a team formation process that generalizes matching models and network formation models, allowing for overlapping teams of heterogeneous size. We apply different…

In this paper, we study the consensus problem for networked dynamic systems with arbitrary initial states, and present some structural characterization and direct construction of consensus functions. For the consensus problem under similar…

We explore the possibility of designing matching mechanisms that can accommodate non-standard choice behavior. We pin down the necessary and sufficient conditions on participants' choice behavior for the existence of stable and incentive…

We propose two solution concepts for matchings under preferences: robustness and near stability. The former strengthens while the latter relaxes the classic definition of stability by Gale and Shapley (1962). Informally speaking, robustness…

The aim of this paper is to obtain quantitative bounds for solutions to the optimal matching problem in dimension two. These bounds show that up to a logarithmically divergent shift, the optimal transport maps are close to be the identity…

In this paper, we consider large-scale ranking problems where one is given a set of (possibly non-redundant) pairwise comparisons and the underlying ranking explained by those comparisons is desired. We show that stochastic gradient descent…

Learning controllers merely based on a performance metric has been proven effective in many physical and non-physical tasks in both control theory and reinforcement learning. However, in practice, the controller must guarantee some notion…

This paper develops the first class of algorithms that enable unbiased estimation of steady-state expectations for multidimensional reflected Brownian motion. In order to explain our ideas, we first consider the case of compound Poisson…

Arrival processes to service systems often display fluctuations that are larger than anticipated under the Poisson assumption, a phenomenon that is referred to as overdispersion. Motivated by this, we analyze a class of discrete stochastic…

In this paper, we study a matching market model on a bipartite network where agents on each side arrive and depart stochastically by a Poisson process. For such a dynamic model, we design a mechanism that decides not only which agents to…

The efficient computation of large matchings with desirable guarantees is a crucial objective in market design. However, even in simple two-sided matching markets with weak ordinal preferences, finding a maximum-size stable matching is…

In computing, as in many aspects of life, changes incur cost. Many optimization problems are formulated as a one-time instance starting from scratch. However, a common case that arises is when we already have a set of prior assignments, and…

We consider deterministic Markov decision processes (MDPs) and apply max-plus algebra tools to approximate the value iteration algorithm by a smaller-dimensional iteration based on a representation on dictionaries of value functions. The…

Machine learning in the context of noise is a challenging but practical setting to plenty of real-world applications. Most of the previous approaches in this area focus on the pairwise relation (casual or correlational relationship) with…

Learned models and policies can generalize effectively when evaluated within the distribution of the training data, but can produce unpredictable and erroneous outputs on out-of-distribution inputs. In order to avoid distribution shift when…

We study dynamic matching in an infinite-horizon stochastic market. While all agents are potentially compatible with each other, some are hard-to-match and others are easy-to-match. Agents prefer to be matched as soon as possible and…

We focus on the solutions of second-order stable linear difference equations and demonstrate that their behavior can be non-monotone and exhibit peak effects depending on initial conditions. The results are applied to the analysis of the…

We study the dynamical properties of a broad class of high-dimensional random dynamical systems exhibiting chaotic as well as fixed point and periodic attractors. We consider cases in which attractors can co-exists in some regions of the…