Download Algorithmic Learning Theory: 20th International Conference, by Ricard Gavaldà, Gabor Lugosi, Thomas Zeugmann, Sandra Zilles PDF

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

This booklet constitutes the refereed court cases of the 20 th foreign convention on Algorithmic studying conception, ALT 2009, held in Porto, Portugal, in October 2009, co-located with the twelfth foreign convention on Discovery technological know-how, DS 2009. The 26 revised complete papers offered including the abstracts of five invited talks have been rigorously reviewed and chosen from 60 submissions. The papers are divided into topical sections of papers on on-line studying, studying graphs, lively studying and question studying, statistical studying, inductive inference, and semisupervised and unsupervised studying. the amount additionally includes 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 through Exploring the ability of hyperlinks, Yishay Mansour, studying and area model; Fernando C.N. Pereira, studying on the internet.

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Extra resources for Algorithmic Learning Theory: 20th International Conference, ALT 2009, Porto, Portugal, October 3-5, 2009, Proceedings

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K For each round t = 1, 2, . . , (1) the forecaster chooses ϕt ∈ P{1, . . , K} and pulls It at random according to ϕt ; (2) the environment draws the reward Yt for that action (also denoted by XIt ,TIt (t) with the notation introduced in the text); (3) the forecaster outputs a recommendation ψt ∈ P{1, . . , K}; (4) If the environment sends a stopping signal, then the game takes an end; otherwise, the next round starts. Fig. 1. The pure exploration problem for multi-armed bandits Pure Exploration in Multi-armed Bandits Problems 25 perform exploration during a random number of rounds T and aim at identifying an ε–best arm.

The distinguishing feature from the classical multi-armed bandit problem is that the exploration phase and the evaluation phase are separated. We now illustrate why this is a natural framework for numerous applications. Historically, the first occurrence of multi-armed bandit problems was given by medical trials. In the case of a severe disease, ill patients only are included in the trial and the cost of picking the wrong treatment is high (the associated reward would equal a large negative value).

By s11:t and s21:t denote the cumulative losses of these experts incurred at steps ≤ t, let vt be the corresponding volume, where t = 1, 2, . .. Define v0 = 1 and Mt = 4vt−1 / for all t ≥ 1. For t ≥ 1, define s1t = 0 and 2 st = Mt if P {It = 1} ≥ 12 , and define s1t = Mt and s2t = 0 otherwise. Let st be one-step loss of the master algorithm and s1:t be its cumulative loss at step t ≥ 1. We have E(s1:t ) ≥ E(st ) = s1t P {It = 1} + s2t P {It = 2} ≥ 1 Mt 2 for all t ≥ 1. Also, since vt = vt−1 + Mt = (1 + 4/ )vt−1 and min si1:t ≤ vt−1 , the i normalized expected regret of the master algorithm is bounded from below 1 2/ − 1 1 ≥ (1 − ).

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