Contextual Combinatorial Cascading Bandits

Shuai Li, Baoxiang Wang, Shengyu Zhang, Wei Chen
Proceedings of The 33rd International Conference on Machine Learning, PMLR 48:1245-1253, 2016.

Abstract

We propose the contextual combinatorial cascading bandits, a combinatorial online learning game, where at each time step a learning agent is given a set of contextual information, then selects a list of items, and observes stochastic outcomes of a prefix in the selected items by some stopping criterion. In online recommendation, the stopping criterion might be the first item a user selects; in network routing, the stopping criterion might be the first edge blocked in a path. We consider position discounts in the list order, so that the agent’s reward is discounted depending on the position where the stopping criterion is met. We design a UCB-type algorithm, C^3-UCB, for this problem, prove an n-step regret bound \tildeO(\sqrtn) in the general setting, and give finer analysis for two special cases. Our work generalizes existing studies in several directions, including contextual information, position discounts, and a more general cascading bandit model. Experiments on synthetic and real datasets demonstrate the advantage of involving contextual information and position discounts.

Cite this Paper

BibTeX
@InProceedings{pmlr-v48-lif16, title = {Contextual Combinatorial Cascading Bandits}, author = {Li, Shuai and Wang, Baoxiang and Zhang, Shengyu and Chen, Wei}, booktitle = {Proceedings of The 33rd International Conference on Machine Learning}, pages = {1245--1253}, year = {2016}, editor = {Balcan, Maria Florina and Weinberger, Kilian Q.}, volume = {48}, series = {Proceedings of Machine Learning Research}, address = {New York, New York, USA}, month = {20--22 Jun}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v48/lif16.pdf}, url = {https://proceedings.mlr.press/v48/lif16.html}, abstract = {We propose the contextual combinatorial cascading bandits, a combinatorial online learning game, where at each time step a learning agent is given a set of contextual information, then selects a list of items, and observes stochastic outcomes of a prefix in the selected items by some stopping criterion. In online recommendation, the stopping criterion might be the first item a user selects; in network routing, the stopping criterion might be the first edge blocked in a path. We consider position discounts in the list order, so that the agent’s reward is discounted depending on the position where the stopping criterion is met. We design a UCB-type algorithm, C^3-UCB, for this problem, prove an n-step regret bound \tildeO(\sqrtn) in the general setting, and give finer analysis for two special cases. Our work generalizes existing studies in several directions, including contextual information, position discounts, and a more general cascading bandit model. Experiments on synthetic and real datasets demonstrate the advantage of involving contextual information and position discounts.} }
Endnote
%0 Conference Paper %T Contextual Combinatorial Cascading Bandits %A Shuai Li %A Baoxiang Wang %A Shengyu Zhang %A Wei Chen %B Proceedings of The 33rd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2016 %E Maria Florina Balcan %E Kilian Q. Weinberger %F pmlr-v48-lif16 %I PMLR %P 1245--1253 %U https://proceedings.mlr.press/v48/lif16.html %V 48 %X We propose the contextual combinatorial cascading bandits, a combinatorial online learning game, where at each time step a learning agent is given a set of contextual information, then selects a list of items, and observes stochastic outcomes of a prefix in the selected items by some stopping criterion. In online recommendation, the stopping criterion might be the first item a user selects; in network routing, the stopping criterion might be the first edge blocked in a path. We consider position discounts in the list order, so that the agent’s reward is discounted depending on the position where the stopping criterion is met. We design a UCB-type algorithm, C^3-UCB, for this problem, prove an n-step regret bound \tildeO(\sqrtn) in the general setting, and give finer analysis for two special cases. Our work generalizes existing studies in several directions, including contextual information, position discounts, and a more general cascading bandit model. Experiments on synthetic and real datasets demonstrate the advantage of involving contextual information and position discounts.
RIS
TY - CPAPER TI - Contextual Combinatorial Cascading Bandits AU - Shuai Li AU - Baoxiang Wang AU - Shengyu Zhang AU - Wei Chen BT - Proceedings of The 33rd International Conference on Machine Learning DA - 2016/06/11 ED - Maria Florina Balcan ED - Kilian Q. Weinberger ID - pmlr-v48-lif16 PB - PMLR DP - Proceedings of Machine Learning Research VL - 48 SP - 1245 EP - 1253 L1 - http://proceedings.mlr.press/v48/lif16.pdf UR - https://proceedings.mlr.press/v48/lif16.html AB - We propose the contextual combinatorial cascading bandits, a combinatorial online learning game, where at each time step a learning agent is given a set of contextual information, then selects a list of items, and observes stochastic outcomes of a prefix in the selected items by some stopping criterion. In online recommendation, the stopping criterion might be the first item a user selects; in network routing, the stopping criterion might be the first edge blocked in a path. We consider position discounts in the list order, so that the agent’s reward is discounted depending on the position where the stopping criterion is met. We design a UCB-type algorithm, C^3-UCB, for this problem, prove an n-step regret bound \tildeO(\sqrtn) in the general setting, and give finer analysis for two special cases. Our work generalizes existing studies in several directions, including contextual information, position discounts, and a more general cascading bandit model. Experiments on synthetic and real datasets demonstrate the advantage of involving contextual information and position discounts. ER -
APA
Li, S., Wang, B., Zhang, S. & Chen, W.. (2016). Contextual Combinatorial Cascading Bandits. Proceedings of The 33rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 48:1245-1253 Available from https://proceedings.mlr.press/v48/lif16.html.

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