We consider the partial observability model for multi-armed bandits, introduced by Mannor and Shamir [14]. Our main result is a characterization of regret in the directed observability model in terms of the dominating and independence numbers of the observability graph (which must be accessible before selecting an action). In the undirected case, we show that the learner can achieve optimal regret without even accessing the observability graph before selecting an action. Both results are shown using variants of the Exp3 algorithm operating on the observability graph in a time-efficient manner.
From bandits to experts : a tale of domination and independence / N. Alon, N. Cesa-Bianchi, C. Gentile, Y. Mansour - In: Advances in neural information processing systems / [a cura di] C.J.C. Burges, L. Bottou, M. Welling, Z. Ghahramani, K.Q. Weinberger. - [s.l] : Neural information processing systems foundation, 2013. (( Intervento presentato al 27. convegno Conference on Neural Information Processing Systems tenutosi a South Lake Tahoe, USA nel 2013.
From bandits to experts : a tale of domination and independence
N. Cesa-Bianchi;
2013
Abstract
We consider the partial observability model for multi-armed bandits, introduced by Mannor and Shamir [14]. Our main result is a characterization of regret in the directed observability model in terms of the dominating and independence numbers of the observability graph (which must be accessible before selecting an action). In the undirected case, we show that the learner can achieve optimal regret without even accessing the observability graph before selecting an action. Both results are shown using variants of the Exp3 algorithm operating on the observability graph in a time-efficient manner.
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