相关论文: Rabbit Hunting using Set Theory and Probability

In this paper, we study the number of moves in a multidimensional elephant random walk with stops. We establish several convergence results for the number of moves, including the law of large numbers and the law of iterated logarithm. Using…

Hat problems have recently become a popular topic in combinatorics and discrete mathematics. These have been shown to be strongly related to coding theory, network coding, and auctions. We consider the following version of the hat game,…

We obtain the upper bound of the loss function for a strategy in the multi-armed bandit problem with Gaussian distributions of incomes. Considered strategy is an asymptotic generalization of the strategy proposed by J. Bather for the…

Effective solving of constraint problems often requires choosing good or specific search heuristics. However, choosing or designing a good search heuristic is non-trivial and is often a manual process. In this paper, rather than manually…

We study the problem of sequential learning of the Pareto front in multi-objective multi-armed bandits. An agent is faced with K possible arms to pull. At each turn she picks one, and receives a vector-valued reward. When she thinks she has…

We consider the best-arm identification problem in multi-armed bandits, which focuses purely on exploration. A player is given a fixed budget to explore a finite set of arms, and the rewards of each arm are drawn independently from a fixed,…

This paper is on developing some computer-assisted proof methods involving non-classical inequalities for Shannon entropy. Two areas of the applications of information inequalities are studied: Secret sharing schemes and hat guessing games.…

Hitting Set is a classic problem in combinatorial optimization. Its input consists of a set system F over a finite universe U and an integer t; the question is whether there is a set of t elements that intersects every set in F. The Hitting…

The Levine hat game requires $n$ players, each wearing an infinite random stack of black and white hats, to guess the location of a black hat on their own head seeing only the hats worn by all the other players. They are allowed a strategy…

We propose a novel approach for modelling bat motion dynamics and use it to predict roost locations using data from static acoustic detectors. Specifically, radio tracking studies of Greater Horseshoe bats demonstrate that bat movement can…

Given a set (or multiset) S of n numbers and a target number t, the subset sum problem is to decide if there is a subset of S that sums up to t. There are several methods for solving this problem, including exhaustive search,…

In the game of Matching Pennies, Alice and Bob each hold a penny, and at every tick of the clock they simultaneously display the head or the tail sides of their coins. If they both display the same side, then Alice wins Bob's penny; if they…

Exciting contemporary machine learning problems have recently been phrased in the classic formalism of tree search -- most famously, the game of Go. Interestingly, the state-space underlying these sequential decision-making problems often…

In the theory of algorithmic randomness, several notions of random sequence are defined via a game-theoretic approach, and the notions that received most attention are perhaps Martin-Loef randomness and computable randomness. The latter…

Betting games provide a natural setting to capture how information yields strategic advantage. The Kelly criterion for betting, long a cornerstone of portfolio theory and information theory, admits an interpretation in the limit of…

We consider a model of selective prediction, where the prediction algorithm is given a data sequence in an online fashion and asked to predict a pre-specified statistic of the upcoming data points. The algorithm is allowed to choose when to…

We consider a restless multi-armed bandit (RMAB) in which there are two types of arms, say A and B. Each arm can be in one of two states, say $0$ or $1.$ Playing a type A arm brings it to state $0$ with probability one and not playing it…

Roulette-wheel selection is a frequently used method in genetic and evolutionary algorithms or in modeling of complex networks. Existing routines select one of N individuals using search algorithms of O(N) or O(log(N)) complexity. We…

Machine learning relies on the assumption that unseen test instances of a classification problem follow the same distribution as observed training data. However, this principle can break down when machine learning is used to make important…

The efficiency of any metaheuristic algorithm largely depends on the way of balancing local intensive exploitation and global diverse exploration. Studies show that bat algorithm can provide a good balance between these two key components…