Algorithmic Learning Theory: 20th International Conference, - download pdf or read online

By Sanjoy Dasgupta (auth.), Ricard Gavaldà , Gábor Lugosi, Thomas Zeugmann, Sandra Zilles (eds.)

ISBN-10: 3642044131

ISBN-13: 9783642044137

This e-book constitutes the refereed complaints of the 20 th overseas convention on Algorithmic studying idea, 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 awarded 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 energetic studying; Hector Geffner, Inference and

Learning in making plans; Jiawei Han, Mining Heterogeneous; info Networks through Exploring the facility of hyperlinks, Yishay Mansour, studying and area edition; Fernando C.N. Pereira, studying on the net.

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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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We prove this result under an extra assumption that the volume of the game grows slowly, lim inf vt /ta+δ > 0, where δ > 0 is arbitrary. Corollary 1 shows that our t→∞ algorithm is also Hannan consistent when δ > 12 . 1 2 Allenberg et al. [2] considered losses −∞ < sit < ∞. This means that (1) holds with probability 1, where E is omitted. The Follow Perturbed Leader Algorithm 41 At the end of Section 2 we consider some applications of our algorithm for the case of standard time-scaling. 2 The Follow Perturbed Leader Algorithm with Adaptive Weights We consider a game of prediction with expert advice with unbounded one-step losses.

72 . . 4 Without loss of generality we suppose that γ(t) < min{1, (e2 − 1)/(1 + ln N )} for all t. Then 0 < αt < 1 for all t. We consider an FPL algorithm with a variable learning rate t = 1 , μt vt−1 (9) where μt is defined by (8) and the volume vt−1 depends on experts actions on steps < t. By definition vt ≥ vt−1 and μt ≤ μt−1 for t = 1, 2, . .. Also, by definition μt → 0 as t → ∞. 4 The choice of the optimal value of αt will be explained later. It will be obtained by minimization of the corresponding member of the sum (44).

When the experts one-step losses are bounded, this problem has been solved using randomization of the experts cumulative losses. The method of following the perturbed leader was discovered by Hannan [3]. Kalai and Vempala [5] rediscovered this method and published a simple proof of the main result of Hannan. They called an algorithm of this type FPL (Following the Perturbed Leader). The FPL algorithm outputs prediction of an expert i which minimizes 1 si1:t−1 − ξ i , where ξ i , i = 1, . . N , t = 1, 2, .

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Algorithmic Learning Theory: 20th International Conference, ALT 2009, Porto, Portugal, October 3-5, 2009. Proceedings by Sanjoy Dasgupta (auth.), Ricard Gavaldà , Gábor Lugosi, Thomas Zeugmann, Sandra Zilles (eds.)


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