Related papers: Optimization results for a generalized coupon coll…
A basic question in the PAC model of learning is whether proper learning is harder than improper learning. In the classical case, there are examples of concept classes with VC dimension $d$ that have sample complexity $\Omega\left(\frac…
The basic goal of quantization for probability distribution is to reduce the number of values, which is typically uncountable, describing a probability distribution to some finite set and thus approximation of a continuous probability…
The Coin Change problem, also known as the Change-Making problem, is a well-studied combinatorial optimization problem, which involves minimizing the number of coins needed to make a specific change amount using a given set of coin…
In "Recognizing the Maximum of a Sequence", Gilbert and Mosteller analyze a full information game where n measurements from an uniform distribution are drawn and a player (knowing n) must decide at each draw whether or not to choose that…
Nonuniform subsampling methods are effective to reduce computational burden and maintain estimation efficiency for massive data. Existing methods mostly focus on subsampling with replacement due to its high computational efficiency. If the…
We consider the problem of uniform sampling of points on an algebraic variety. Specifically, we develop a randomized algorithm that, given a small set of multivariate polynomials over a sufficiently large finite field, produces a common…
In this paper we consider the problem of minimising drawdown in a portfolio of financial assets. Here drawdown represents the relative opportunity cost of the single best missed trading opportunity over a specified time period. We formulate…
When facing many options, we narrow down our focus to very few of them. Although behaviors like this can be a sign of heuristics, they can actually be optimal under limited cognitive resources. Here we study the problem of how to optimally…
Consider $n$ independent, biased coins, each with a known probability of heads. Presented with an ordering of these coins, flip (i.e., toss) each coin once, in that order, until we have observed both a *head* and a *tail*, or flipped all…
Let $N_n=\{1,2,...,n\}$. Elements are drawn from the set $N_n$ with replacement, assuming that each element has probability $1/n$ of being drawn. We determine the limiting distributions for the waiting time until the given portion of pairs…
Currently, many e-commerce websites issue online/electronic coupons as an effective tool for promoting sales of various products and services. We focus on the problem of optimally allocating coupons to customers subject to a budget…
Quantization for a probability distribution refers to the idea of estimating a given probability by a discrete probability supported by a finite number of points. In this paper, firstly a general approach to this process is outlined using…
We study several stochastic combinatorial problems, including the expected utility maximization problem, the stochastic knapsack problem and the stochastic bin packing problem. A common technical challenge in these problems is to optimize…
This paper considers a problem where multiple users make repeated decisions based on their own observed events. The events and decisions at each time step determine the values of a utility function and a collection of penalty functions. The…
The paper deals with the distributed minimum sharing problem: a set of decision-makers compute the minimum of some local quantities of interest in a distributed and decentralized way by exchanging information through a communication…
We focus on the problem of finding an optimal strategy for a team of two players that faces an opponent in an imperfect-information zero-sum extensive-form game. Team members are not allowed to communicate during play but can coordinate…
We study coverage processes in which each draw reveals a subset of $[n]$, and the goal is to determine the expected number of draws until all items are seen at least once. A classical example is the Coupon Collector's Problem, where each…
We study the design and approximation of optimal crowdsourcing contests. Crowdsourcing contests can be modeled as all-pay auctions because entrants must exert effort up-front to enter. Unlike all-pay auctions where a usual design objective…
This technical note studies the distributed optimization problem of a sum of nonsmooth convex cost functions with local constraints. At first, we propose a novel distributed continuous-time projected algorithm, in which each agent knows its…
The problem of drawing samples from a discrete distribution can be converted into a discrete optimization problem. In this work, we show how sampling from a continuous distribution can be converted into an optimization problem over…