Algorithmic Learning Theory: 25th International Conference, by Peter Auer, Alexander Clark, Thomas Zeugmann, Sandra Zilles

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By Peter Auer, Alexander Clark, Thomas Zeugmann, Sandra Zilles

This ebook constitutes the complaints of the twenty fifth foreign convention on Algorithmic studying concept, ALT 2014, held in Bled, Slovenia, in October 2014, and co-located with the seventeenth overseas convention on Discovery technology, DS 2014. The 21 papers provided during this quantity have been rigorously reviewed and chosen from 50 submissions. moreover the e-book comprises four complete papers summarizing the invited talks. The papers are equipped in topical sections named: inductive inference; unique studying from queries; reinforcement studying; on-line studying and studying with bandit details; statistical studying thought; privateness, clustering, MDL, and Kolmogorov complexity.

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Extra resources for Algorithmic Learning Theory: 25th International Conference, ALT 2014, Bled, Slovenia, October 8-10, 2014. Proceedings

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Concretely, three different goals of the learner are considered, depending on whether the application calls for the prediction of a single arm, a full ranking of all arms, or the entire probability distribution: – The MPI problem consists of finding the most preferred item i∗ , namely the item whose probability of being top-ranked is maximal: i∗ = argmax Er∼P I{ri = 1} = argmax 1≤i≤K where I{·} denotes the indicator function. 1≤i≤K P(r) , r∈L(ri =1) A Survey of Preference-Based Online Learning 31 – The MPR problem consists of finding the most probable ranking r∗ : r∗ = argmax P(r) r∈SK – The KLD problem calls for producing a good estimate P of the distribution P, that is, an estimate with small KL divergence: P(r) log KL P, P = r∈SK P(r) P(r) < All three goals are meant to be achieved with probability at least 1 − δ.

Another way to look at the problem is to start from the pairwise preferences Q themselves, that is to say, to consider the pairwise probabilities qi,j as the ground truth. In tournaments in sports, for example, the qi,j may express the probabilities of one team ai beating another one aj . In this case, there is no underlying ground truth ranking from which these probabilities are derived. Instead, it is just the other way around: A ranking is derived from the pairwise comparisons. Moreover, there is no reason for why the qi,j should be consistent in a specific sense.

The aim of this paper is to provide a survey of the state-of-the-art in this field, that we refer to as preference-based multi-armed bandits. To this end, we provide an overview of problems that have been considered in the literature as well as methods for tackling them. Our systematization is mainly based on the assumptions made by these methods about the data-generating process and, related to this, the properties of the preference-based feedback. Keywords: Multi-armed bandits, online learning, preference learning, ranking, top-k selection, exploration/exploitation, cumulative regret, sample complexity, PAC learning.

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