Efficient Learning in Large-Scale Combinatorial Semi-Bandits

Zheng Wen, Branislav Kveton, Azin Ashkan
Proceedings of the 32nd International Conference on Machine Learning, PMLR 37:1113-1122, 2015.

Abstract

A stochastic combinatorial semi-bandit is an online learning problem where at each step a learning agent chooses a subset of ground items subject to combinatorial constraints, and then observes stochastic weights of these items and receives their sum as a payoff. In this paper, we consider efficient learning in large-scale combinatorial semi-bandits with linear generalization, and as a solution, propose two learning algorithms called Combinatorial Linear Thompson Sampling (CombLinTS) and Combinatorial Linear UCB (CombLinUCB). Both algorithms are computationally efficient as long as the offline version of the combinatorial problem can be solved efficiently. We establish that CombLinTS and CombLinUCB are also provably statistically efficient under reasonable assumptions, by developing regret bounds that are independent of the problem scale (number of items) and sublinear in time. We also evaluate CombLinTS on a variety of problems with thousands of items. Our experiment results demonstrate that CombLinTS is scalable, robust to the choice of algorithm parameters, and significantly outperforms the best of our baselines.

Cite this Paper


BibTeX
@InProceedings{pmlr-v37-wen15, title = {Efficient Learning in Large-Scale Combinatorial Semi-Bandits}, author = {Wen, Zheng and Kveton, Branislav and Ashkan, Azin}, booktitle = {Proceedings of the 32nd International Conference on Machine Learning}, pages = {1113--1122}, year = {2015}, editor = {Bach, Francis and Blei, David}, volume = {37}, series = {Proceedings of Machine Learning Research}, address = {Lille, France}, month = {07--09 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v37/wen15.pdf}, url = { http://proceedings.mlr.press/v37/wen15.html }, abstract = {A stochastic combinatorial semi-bandit is an online learning problem where at each step a learning agent chooses a subset of ground items subject to combinatorial constraints, and then observes stochastic weights of these items and receives their sum as a payoff. In this paper, we consider efficient learning in large-scale combinatorial semi-bandits with linear generalization, and as a solution, propose two learning algorithms called Combinatorial Linear Thompson Sampling (CombLinTS) and Combinatorial Linear UCB (CombLinUCB). Both algorithms are computationally efficient as long as the offline version of the combinatorial problem can be solved efficiently. We establish that CombLinTS and CombLinUCB are also provably statistically efficient under reasonable assumptions, by developing regret bounds that are independent of the problem scale (number of items) and sublinear in time. We also evaluate CombLinTS on a variety of problems with thousands of items. Our experiment results demonstrate that CombLinTS is scalable, robust to the choice of algorithm parameters, and significantly outperforms the best of our baselines.} }
Endnote
%0 Conference Paper %T Efficient Learning in Large-Scale Combinatorial Semi-Bandits %A Zheng Wen %A Branislav Kveton %A Azin Ashkan %B Proceedings of the 32nd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2015 %E Francis Bach %E David Blei %F pmlr-v37-wen15 %I PMLR %P 1113--1122 %U http://proceedings.mlr.press/v37/wen15.html %V 37 %X A stochastic combinatorial semi-bandit is an online learning problem where at each step a learning agent chooses a subset of ground items subject to combinatorial constraints, and then observes stochastic weights of these items and receives their sum as a payoff. In this paper, we consider efficient learning in large-scale combinatorial semi-bandits with linear generalization, and as a solution, propose two learning algorithms called Combinatorial Linear Thompson Sampling (CombLinTS) and Combinatorial Linear UCB (CombLinUCB). Both algorithms are computationally efficient as long as the offline version of the combinatorial problem can be solved efficiently. We establish that CombLinTS and CombLinUCB are also provably statistically efficient under reasonable assumptions, by developing regret bounds that are independent of the problem scale (number of items) and sublinear in time. We also evaluate CombLinTS on a variety of problems with thousands of items. Our experiment results demonstrate that CombLinTS is scalable, robust to the choice of algorithm parameters, and significantly outperforms the best of our baselines.
RIS
TY - CPAPER TI - Efficient Learning in Large-Scale Combinatorial Semi-Bandits AU - Zheng Wen AU - Branislav Kveton AU - Azin Ashkan BT - Proceedings of the 32nd International Conference on Machine Learning DA - 2015/06/01 ED - Francis Bach ED - David Blei ID - pmlr-v37-wen15 PB - PMLR DP - Proceedings of Machine Learning Research VL - 37 SP - 1113 EP - 1122 L1 - http://proceedings.mlr.press/v37/wen15.pdf UR - http://proceedings.mlr.press/v37/wen15.html AB - A stochastic combinatorial semi-bandit is an online learning problem where at each step a learning agent chooses a subset of ground items subject to combinatorial constraints, and then observes stochastic weights of these items and receives their sum as a payoff. In this paper, we consider efficient learning in large-scale combinatorial semi-bandits with linear generalization, and as a solution, propose two learning algorithms called Combinatorial Linear Thompson Sampling (CombLinTS) and Combinatorial Linear UCB (CombLinUCB). Both algorithms are computationally efficient as long as the offline version of the combinatorial problem can be solved efficiently. We establish that CombLinTS and CombLinUCB are also provably statistically efficient under reasonable assumptions, by developing regret bounds that are independent of the problem scale (number of items) and sublinear in time. We also evaluate CombLinTS on a variety of problems with thousands of items. Our experiment results demonstrate that CombLinTS is scalable, robust to the choice of algorithm parameters, and significantly outperforms the best of our baselines. ER -
APA
Wen, Z., Kveton, B. & Ashkan, A.. (2015). Efficient Learning in Large-Scale Combinatorial Semi-Bandits. Proceedings of the 32nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 37:1113-1122 Available from http://proceedings.mlr.press/v37/wen15.html .

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