Online Learning with Feedback Graphs: Beyond Bandits

Noga Alon, Nicolò Cesa-Bianchi, Ofer Dekel, Tomer Koren
; Proceedings of The 28th Conference on Learning Theory, PMLR 40:23-35, 2015.

Abstract

We study a general class of online learning problems where the feedback is specified by a graph. This class includes online prediction with expert advice and the multi-armed bandit problem, but also several learning problems where the online player does not necessarily observe his own loss. We analyze how the structure of the feedback graph controls the inherent difficulty of the induced T-round learning problem. Specifically, we show that any feedback graph belongs to one of three classes: \emphstrongly observable graphs, \emphweakly observable graphs, and \emphunobservable graphs. We prove that the first class induces learning problems with \widetildeΘ(α^1/2 T^1/2) minimax regret, where αis the independence number of the underlying graph; the second class induces problems with \widetildeΘ(δ^1/3T^2/3) minimax regret, where δis the domination number of a certain portion of the graph; and the third class induces problems with linear minimax regret. Our results subsume much of the previous work on learning with feedback graphs and reveal new connections to partial monitoring games. We also show how the regret is affected if the graphs are allowed to vary with time.

Cite this Paper


BibTeX
@InProceedings{pmlr-v40-Alon15, title = {Online Learning with Feedback Graphs: Beyond Bandits}, author = {Noga Alon and Nicolò Cesa-Bianchi and Ofer Dekel and Tomer Koren}, booktitle = {Proceedings of The 28th Conference on Learning Theory}, pages = {23--35}, year = {2015}, editor = {Peter Grünwald and Elad Hazan and Satyen Kale}, volume = {40}, series = {Proceedings of Machine Learning Research}, address = {Paris, France}, month = {03--06 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v40/Alon15.pdf}, url = {http://proceedings.mlr.press/v40/Alon15.html}, abstract = {We study a general class of online learning problems where the feedback is specified by a graph. This class includes online prediction with expert advice and the multi-armed bandit problem, but also several learning problems where the online player does not necessarily observe his own loss. We analyze how the structure of the feedback graph controls the inherent difficulty of the induced T-round learning problem. Specifically, we show that any feedback graph belongs to one of three classes: \emphstrongly observable graphs, \emphweakly observable graphs, and \emphunobservable graphs. We prove that the first class induces learning problems with \widetildeΘ(α^1/2 T^1/2) minimax regret, where αis the independence number of the underlying graph; the second class induces problems with \widetildeΘ(δ^1/3T^2/3) minimax regret, where δis the domination number of a certain portion of the graph; and the third class induces problems with linear minimax regret. Our results subsume much of the previous work on learning with feedback graphs and reveal new connections to partial monitoring games. We also show how the regret is affected if the graphs are allowed to vary with time. } }
Endnote
%0 Conference Paper %T Online Learning with Feedback Graphs: Beyond Bandits %A Noga Alon %A Nicolò Cesa-Bianchi %A Ofer Dekel %A Tomer Koren %B Proceedings of The 28th Conference on Learning Theory %C Proceedings of Machine Learning Research %D 2015 %E Peter Grünwald %E Elad Hazan %E Satyen Kale %F pmlr-v40-Alon15 %I PMLR %J Proceedings of Machine Learning Research %P 23--35 %U http://proceedings.mlr.press %V 40 %W PMLR %X We study a general class of online learning problems where the feedback is specified by a graph. This class includes online prediction with expert advice and the multi-armed bandit problem, but also several learning problems where the online player does not necessarily observe his own loss. We analyze how the structure of the feedback graph controls the inherent difficulty of the induced T-round learning problem. Specifically, we show that any feedback graph belongs to one of three classes: \emphstrongly observable graphs, \emphweakly observable graphs, and \emphunobservable graphs. We prove that the first class induces learning problems with \widetildeΘ(α^1/2 T^1/2) minimax regret, where αis the independence number of the underlying graph; the second class induces problems with \widetildeΘ(δ^1/3T^2/3) minimax regret, where δis the domination number of a certain portion of the graph; and the third class induces problems with linear minimax regret. Our results subsume much of the previous work on learning with feedback graphs and reveal new connections to partial monitoring games. We also show how the regret is affected if the graphs are allowed to vary with time.
RIS
TY - CPAPER TI - Online Learning with Feedback Graphs: Beyond Bandits AU - Noga Alon AU - Nicolò Cesa-Bianchi AU - Ofer Dekel AU - Tomer Koren BT - Proceedings of The 28th Conference on Learning Theory PY - 2015/06/26 DA - 2015/06/26 ED - Peter Grünwald ED - Elad Hazan ED - Satyen Kale ID - pmlr-v40-Alon15 PB - PMLR SP - 23 DP - PMLR EP - 35 L1 - http://proceedings.mlr.press/v40/Alon15.pdf UR - http://proceedings.mlr.press/v40/Alon15.html AB - We study a general class of online learning problems where the feedback is specified by a graph. This class includes online prediction with expert advice and the multi-armed bandit problem, but also several learning problems where the online player does not necessarily observe his own loss. We analyze how the structure of the feedback graph controls the inherent difficulty of the induced T-round learning problem. Specifically, we show that any feedback graph belongs to one of three classes: \emphstrongly observable graphs, \emphweakly observable graphs, and \emphunobservable graphs. We prove that the first class induces learning problems with \widetildeΘ(α^1/2 T^1/2) minimax regret, where αis the independence number of the underlying graph; the second class induces problems with \widetildeΘ(δ^1/3T^2/3) minimax regret, where δis the domination number of a certain portion of the graph; and the third class induces problems with linear minimax regret. Our results subsume much of the previous work on learning with feedback graphs and reveal new connections to partial monitoring games. We also show how the regret is affected if the graphs are allowed to vary with time. ER -
APA
Alon, N., Cesa-Bianchi, N., Dekel, O. & Koren, T.. (2015). Online Learning with Feedback Graphs: Beyond Bandits. Proceedings of The 28th Conference on Learning Theory, in PMLR 40:23-35

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