Related papers: Optimal Ball Recycling
We revisit a version of the classic occupancy scheme, where balls are thrown until almost all boxes receive a given number of balls. Special cases are widely known as coupon-collectors and dixie cup problems. We show that as the number of…
This paper develops a highly simplified model with which to analyze the phenomenon of sleep. Motivated by Crick's suggestion that sleep is the brain's way of ``taking out the trash,'' a suggestion that is supported by emerging evidence, we…
We develop a worst-case analysis of aggregation of classifier ensembles for binary classification. The task of predicting to minimize error is formulated as a game played over a given set of unlabeled data (a transductive setting), where…
This paper proposes to use probabilistic model checking to synthesize optimal robot policies in multi-tasking autonomous systems that are subject to human-robot interaction. Given the convincing empirical evidence that human behavior can be…
This paper presents theoretical and practical results for the bin packing problem with scenarios, a generalization of the classical bin packing problem which considers the presence of uncertain scenarios, of which only one is realized. For…
We consider perfect-information reachability stochastic games for 2 players on infinite graphs. We identify a subclass of such games, and prove two interesting properties of it: first, Player Max always has optimal strategies in games from…
We study a sequential coin-flipping game in which a player starts with~$n$ coins, each landing heads independently with probability~$p$. In each round the player flips all remaining coins and must set aside at least one coin showing heads;…
In Multi-Goal Reinforcement Learning, an agent learns to achieve multiple goals with a goal-conditioned policy. During learning, the agent first collects the trajectories into a replay buffer, and later these trajectories are selected…
When P indistinguishable balls are randomly distributed among L distinguishable boxes, and considering the dense system in which P much greater than L, our natural intuition tells us that the box with the average number of balls has the…
This paper presents a new safety specification method that is robust against errors in the probability distribution of disturbances. Our proposed distributionally robust safe policy maximizes the probability of a system remaining in a…
This paper introduces a sampling-based strategy synthesis algorithm for nondeterministic hybrid systems with complex continuous dynamics under temporal and reachability constraints. We model the evolution of the hybrid system as a…
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…
Reactive synthesis is a class of methods to construct a provably-correct control system, referred to as a robot, with respect to a temporal logic specification in the presence of a dynamic and uncontrollable environment. This is achieved by…
We present a rapid method for the exact calculation of the cumulative distribution function of the maximum of multinomially distributed random variables. The method runs in time $O(mn)$, where $m$ is the desired maximum and $n$ is the…
Enormous successes have been made by quantum algorithms during the last decade. In this paper, we combine the quantum game with the problem of data clustering, and then develop a quantum-game-based clustering algorithm, in which data points…
Adversarial optimal transport has been proven useful as a mathematical formulation to model resource allocation problems to maximize the efficiency of transportation with an adversary, who modifies the data. It is often the case, however,…
``When in a difficult situation, it is sometimes better to give up and start all over again''. While this empirical truth has been regularly observed in a wide range of circumstances, quantifying the effectiveness of such a heuristic…
Two-player, turn-based, stochastic games with reachability conditions are considered, where the maximizer has no information (he is blind) and is restricted to deterministic strategies whereas the minimizer is perfectly informed. We ask the…
Game Theory concepts have been successfully applied in a wide variety of domains over the past decade. Sports and games are one of the popular areas of game theory application owing to its merits and benefits in solving complex scenarios.…
We study the effects of randomness on competitions based on an elementary random process in which there is a finite probability that a weaker team upsets a stronger team. We apply this model to sports leagues and sports tournaments, and…