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

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

This publication constitutes the refereed lawsuits of the 20 th foreign convention on Algorithmic studying thought, ALT 2009, held in Porto, Portugal, in October 2009, co-located with the twelfth foreign convention on Discovery technology, 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, lively studying and question studying, statistical studying, inductive inference, and semisupervised and unsupervised studying. the quantity 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 via Exploring the ability of hyperlinks, Yishay Mansour, studying and area edition; Fernando C.N. Pereira, studying on the internet.

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

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Theorem 1, among others, will however indicate some connections between rn and Rn . Goal and structure of the paper: We study the links between simple and cumulative regrets. Intuitively, an efficient allocation strategy for the simple regret should rely on some exploration–exploitation trade-off. Our main contribution (Theorem 1, Section 3) is a lower bound on the simple regret in terms of the cumulative regret suffered in the exploration phase, showing that the trade-off involved in the minimization of the simple regret is somewhat different from the one for the cumulative regret.

Yn , grouped according to the arms as Xj,1 , . . , Xj,Tj (n) , for j = 1, . . , n Empirical distribution of plays (EDP) Draws a recommendation using the probability distribution ψn = Empirical best arm (EBA) Only considers arms j with Tj (n) μj,n 1 n n δIt . t=1 1, computes their associated empirical means 1 = Tj (n) Tj (n) Xj,s , s=1 and forms a deterministic recommendation (conditionally to the history), ψn = δJn∗ where Jn∗ ∈ argmax μj,n j (ties broken in some way). Most played arm (MPA) Forms a deterministic recommendation (conditionally to the history), ψn = δJn∗ where Jn∗ ∈ argmax Tj (n) .

Proof. The part “if” is obvious, so we will only prove the part “only if”. Let λ be η-mixable and proper. Suppose there exists π such that the shift A1 of e−ηx + e−ηy = 1 passing through Λπ and having Λπ as its π-point has some superpredictions strictly to its Southwest. Let s be such a superprediction, and let A2 be the tangent to A1 at the point Λπ . The image Eη (A1 ) is a straight Prediction with Expert Evaluators’ Advice 19 line in [0, 1]2 , and the curve Eη (A2 ) touches Eη (A1 ) at Eη (Λπ ) and lies at the same side of Eη (A1 ) as Eη (s).

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