By Sanjay Jain, Rémi Munos, Frank Stephan, Thomas Zeugmann

ISBN-10: 3642409342

ISBN-13: 9783642409349

ISBN-10: 3642409350

ISBN-13: 9783642409356

This booklet constitutes the lawsuits of the twenty fourth foreign convention on Algorithmic studying thought, ALT 2013, held in Singapore in October 2013, and co-located with the sixteenth overseas convention on Discovery technological know-how, DS 2013. The 23 papers offered during this quantity have been rigorously reviewed and chosen from 39 submissions. furthermore the ebook includes three complete papers of invited talks. The papers are prepared in topical sections named: on-line studying, inductive inference and grammatical inference, educating and studying from queries, bandit idea, statistical studying conception, Bayesian/stochastic studying, and unsupervised/semi-supervised learning.

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More precisely, if the convex hull of C is a base polyhedron defined by a submodular function f , then the two procedures can be computed in polynomial time, assuming that f can be evaluated in polynomial time. This result implies that we obtain an essentially one low-regret online algorithm for all concept classes in this family. The family includes the classes of k-sets, permutations, truncated permutations, spanning trees, and more. In Section 3, we will show the result in slightly more details.

The main task underlying such 16 N. Ailon systems is often referred to as “ranking”, because the retrieved documents are typically outputted to the user in an ordered list from top (most relevant) to bottom. It should be mentioned that most work on optimizing such systems assumes that the basic source of information used in the optimization task is a sequence of tuples (qi , di , ri ), where ri is a relevance score of document di for query qi . The relevance score is an ordinal value, usually from a finite scale, and is provided by an expert.

Online Algorithm under Assumption 2 1. For (a) (b) (c) (d) t = 1, . . , T Run Algorithm B one step and get a prediction xt ∈ P. Run the metarounding with xt and get ct ∈ C. Receive t ∈ L and incur loss ct · t . Feed t to B and resume it. Now we state the main theorems. Theorem 8. Under Assumption 2, Algorithm 3 runs in polynomial time per trial and achieves α-regret to be at most αReg B (T ). Theorem 9. Under Assumption 1, there exists an algorithm that runs in poly(n, 1/ ) time and achieves (α + )-regret to be at most (α + )Reg B (T ), where > 0 is a parameter that can be arbitrarily chosen.

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Algorithmic Learning Theory: 24th International Conference, ALT 2013, Singapore, October 6-9, 2013. Proceedings by Sanjay Jain, Rémi Munos, Frank Stephan, Thomas Zeugmann

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