By Ricard Gavaldà, Gabor Lugosi, Thomas Zeugmann, Sandra Zilles

This booklet constitutes the refereed complaints of the twentieth overseas convention on Algorithmic studying conception, ALT 2009, held in Porto, Portugal, in October 2009, co-located with the twelfth overseas convention on Discovery technological know-how, DS 2009. The 26 revised complete papers offered including the abstracts of five invited talks have been conscientiously reviewed and chosen from 60 submissions. The papers are divided into topical sections of papers on on-line studying, studying graphs, energetic studying and question studying, statistical studying, inductive inference, and semisupervised and unsupervised studying. the quantity additionally comprises abstracts of the invited talks: Sanjoy Dasgupta, the 2 Faces of lively studying; Hector Geffner, Inference and studying in making plans; Jiawei Han, Mining Heterogeneous; info Networks by means of Exploring the ability of hyperlinks, Yishay Mansour, studying and area edition; Fernando C.N. Pereira, studying on the net.

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A key example is the multi-armed bandit problem [Rob52], a sequential decision problem where, at each stage, the forecaster has to pull one out of K given stochastic arms and gets a reward drawn at random according to the distribution of the chosen arm. The usual assessment criterion of a strategy is given by its cumulative regret, the sum of differences between the expected reward of the best arm and the obtained rewards. Typical good strategies, like the UCB strategies of [ACBF02], trade off between exploration and exploitation.

D random variables distributed according to the exponential distribution with the density p(x) = exp{−x}, and is a learning rate. ,N log N , where is a positive real number such that 0 < < 1 is a learning rate, N is the number of experts. Hutter and Poland [4] presented a further developments of the FPL algorithm for countable class of experts, arbitrary weights and adaptive learning rate. Also, FPL algorithm is usually considered for bounded one-step losses: 0 ≤ sit ≤ 1 for all i and t. Most papers on prediction with expert advice either consider bounded losses or assume the existence of a speciﬁc loss function (see [7]).

Pure Exploration in Multi-armed Bandits Problems 37 6 Pure Exploration for Bandit Problems in Topological Spaces These results are of theoretical interest. We summarize them very briefly; statements and proofs can be found in the extended version [BMS09]. , [Kle04, BMSS09] and (re)define the notions of cumulative and simple regrets. The topological set X is a large possibly non-parametric space but the associated mean-payoff function is continuous. We show that, without any assumption on X , there exists a strategy with cumulative regret ERn = o(n) if and only if there exist an allocation and a recommendation strategy with simple regret Ern = o(1).