The general multi-armed bandit problem is reformulated and solved as a control problem over a partially ordered set. The approach taken provides a technically convenient framework for bandit-like problems. It also adds insight to the structure of strategies over partially ordered sets.

Discrete multi-armed bandits and multi-parameter processes

This article examines a series of Schelling-like models of residential segregation, in which agents prefer to be in the minority. We demonstrate that as long as agents care about the characteristics of their wider community, they tend to end up in a segregated state. We then investigate the process that causes this and conclude that the result hinges on the similarity of informational states among agents of the same type. This is quite different from Schelling-like behavior and suggests (in his terms) that segregation is an instance of macrobehavior that can arise from a wide variety of micromotives.

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Segregation That No One Seeks

ε-Optimality of a general class of learning algorithms

Stochastic Models for Learning

Learning automaton (LA) as one of artificial intelligence techniques is a stochastic model operating in the framework of the reinforcement learning. LA has been found to be a useful tool for solving many complex and real world problems where a large amount of uncertainty exists or there is no access to the whole information regarding the environment. In this chapter, learning automaton and suitable variants of LA models for distributed and decentralized environments (e.g., social networks) will be introduced. Also, recent models and applications of learning automata will be presented.

Introduction to Learning Automata Models

The paper is initially concerned with monotonic properties of the posterior success probabilities when the prior success probabilities are distributed according to an arbitrary joint distribution function (Bayesian approach). Next a dynamic programming model is proposed and monotonic properties of the optimal expected cumulative discounted reward are proved. Finally, optimality properties are given for the case when one prior success probability is known.

On the Bernoulli two-armed bandit problem

On a general class of absorbing-barrier learning algorithms

The purpose of this short note is to correct some oversights in [1]. More precisely, we point out that stronger assumptions have to be imposed on the decision model (in order to use results in [2]) and present a counterexample to a comment to [1, Theorem 3.1].

A note on `monotone optimal policies for markov decision processes'

Mathematical Learning Models — Theory and Algorithms

We consider a stochastic dynamic single product inventory model with finite horizon and allow the demand process to be dependent. Conditions are found for the optimally of a (z Z) strategy. In case of an independent demand process the results carry over to the optimality of an (s S) strategy.

Dieter Kalin

Papers

On the Bernoulli two-armed bandit problem

On a general class of absorbing-barrier learning algorithms

A note on `monotone optimal policies for markov decision processes'

Mathematical Learning Models — Theory and Algorithms

Zur optimalität von (z Z) - strategien. bei berücksichtigimg von beiarfstrenis