Get Algorithmic Learning Theory: 20th International Conference, PDF

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

ISBN-10: 3642044131

ISBN-13: 9783642044137

This publication constitutes the refereed court cases of the twentieth overseas 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 rigorously 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 energetic studying; Hector Geffner, Inference and studying in making plans; Jiawei Han, Mining Heterogeneous; details Networks through Exploring the facility of hyperlinks, Yishay Mansour, studying and area model; Fernando C.N. Pereira, studying on the internet.

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

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Chernov and V. Vovk Let us fix a constant η > 0. The prediction set of the generalized log loss function (3) is the curve {(x, y) | e−ηx + e−ηy = 1} in IR2 . , the point 1 1 − ln(1 − π), − ln π η η . Since the generalized log loss function is proper, the minimum of (1 − π)x + πy (geometrically, of the dot product of (1 − π, π) and (x, y)) on the curve e−ηx + e−ηy = 1 is attained at the π-point; in other words, the tangent of e−ηx +e−ηy = 1 at the π-point is orthogonal to the vector (1 − π, π). , it is a parallel translation of e−ηx + e−ηy = 1 by some vector (α, β)).

Thus, using that Δj 1 for all j, Ern = EΔJn∗ P Tj (n) aj n . j:Δj >0 A side-result extracted from the proof of [ACBF02, Theorem 1] states that for all suboptimal arms j and all rounds t K + 1, P It = j and Tj (t − 1) 2 t1−2p whenever 4p ln n . Δ2j (2) This yields that for a suboptimal arm j and since by the assumptions on n and the aj , the choice = aj n − 1 satisfies K + 1 and (4p ln n)/Δ2j , Pure Exploration in Multi-armed Bandits Problems 35 n P Tj (n) P Tj (t − 1) = aj n − 1 and It = j aj n t=aj n n 2 t1−2p t=aj n 1 (aj n)2(1−p) p−1 (3) where we used a union bound for the second inequality and (2) for the third inequality.

This completes the proof of the lemma: by Lemma 2, the superprediction set indeed lies to the Northeast of that shift. 20 8 A. Chernov and V. Vovk Defensive Forecasting for Specialist Experts and the AA In this section we will find a more explicit version of defensive forecasting in the case of specialist experts. Our algorithm will achieve a slightly more general version of the bound (6); namely, we will replace the ln N in (6) by − ln pn where pn is an a priori chosen weight for Expert n: all pn are non-negative and sum to 1.

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Algorithmic Learning Theory: 20th International Conference, ALT 2009, Porto, Portugal, October 3-5, 2009, Proceedings by Ricard Gavaldà, Gabor Lugosi, Thomas Zeugmann, Sandra Zilles

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