Online learning for structured loss spaces

Barman, S and Gopalan, A and Saha, A (2018) Online learning for structured loss spaces. In: 32nd AAAI Conference on Artificial Intelligence, AAAI 2018, 2 - 7 February 2018, New Orleans, pp. 2696-2703.

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Abstract

We consider prediction with expert advice when the loss vectors are assumed to lie in a set described by the sum of atomic norm balls. We derive a regret bound for a general version of the online mirror descent (OMD) algorithm that uses a combination of regularizers, each adapted to the constituent atomic norms. The general result recovers standard OMD regret bounds, and yields regret bounds for new structured settings where the loss vectors are (i) noisy versions of vectors from a low-dimensional subspace, (ii) sparse vectors corrupted with noise, and (iii) sparse perturbations of low-rank vectors. For the problem of online learning with structured losses, we also show lower bounds on regret in terms of rank and sparsity of the loss vectors, which implies lower bounds for the above additive loss settings as well.

Item Type:	Conference Paper
Publication:	32nd AAAI Conference on Artificial Intelligence, AAAI 2018
Publisher:	AAAI press
Additional Information:	The copyright for this article belongs to the AAAI press.
Keywords:	Artificial intelligence; Vectors, General version; Low-dimensional subspace; Lower bounds; Noisy versions; Online learning; Prediction with expert advice; Regret bounds; Sparse vectors, E-learning
Department/Centre:	Division of Electrical Sciences > Computer Science & Automation
Date Deposited:	18 Aug 2022 06:12
Last Modified:	18 Aug 2022 06:12
URI:	https://eprints.iisc.ac.in/id/eprint/75955

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