Structure Adaptive Algorithms for Stochastic Bandits

Rémy Degenne, Han Shao, Wouter Koolen
Proceedings of the 37th International Conference on Machine Learning, PMLR 119:2443-2452, 2020.

Abstract

We study reward maximisation in a wide class of structured stochastic multi-armed bandit problems, where the mean rewards of arms satisfy some given structural constraints, e.g. linear, unimodal, sparse, etc. Our aim is to develop methods that are \emph{flexible} (in that they easily adapt to different structures), \emph{powerful} (in that they perform well empirically and/or provably match instance-dependent lower bounds) and \emph{efficient} in that the per-round computational burden is small. We develop asymptotically optimal algorithms from instance-dependent lower-bounds using iterative saddle-point solvers. Our approach generalises recent iterative methods for pure exploration to reward maximisation, where a major challenge arises from the estimation of the sub-optimality gaps and their reciprocals. Still we manage to achieve all the above desiderata. Notably, our technique avoids the computational cost of the full-blown saddle point oracle employed by previous work, while at the same time enabling finite-time regret bounds. Our experiments reveal that our method successfully leverages the structural assumptions, while its regret is at worst comparable to that of vanilla UCB.

Cite this Paper


BibTeX
@InProceedings{pmlr-v119-degenne20b, title = {Structure Adaptive Algorithms for Stochastic Bandits}, author = {Degenne, R{\'e}my and Shao, Han and Koolen, Wouter}, booktitle = {Proceedings of the 37th International Conference on Machine Learning}, pages = {2443--2452}, year = {2020}, editor = {Hal Daumé III and Aarti Singh}, volume = {119}, series = {Proceedings of Machine Learning Research}, month = {13--18 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v119/degenne20b/degenne20b.pdf}, url = { http://proceedings.mlr.press/v119/degenne20b.html }, abstract = {We study reward maximisation in a wide class of structured stochastic multi-armed bandit problems, where the mean rewards of arms satisfy some given structural constraints, e.g. linear, unimodal, sparse, etc. Our aim is to develop methods that are \emph{flexible} (in that they easily adapt to different structures), \emph{powerful} (in that they perform well empirically and/or provably match instance-dependent lower bounds) and \emph{efficient} in that the per-round computational burden is small. We develop asymptotically optimal algorithms from instance-dependent lower-bounds using iterative saddle-point solvers. Our approach generalises recent iterative methods for pure exploration to reward maximisation, where a major challenge arises from the estimation of the sub-optimality gaps and their reciprocals. Still we manage to achieve all the above desiderata. Notably, our technique avoids the computational cost of the full-blown saddle point oracle employed by previous work, while at the same time enabling finite-time regret bounds. Our experiments reveal that our method successfully leverages the structural assumptions, while its regret is at worst comparable to that of vanilla UCB.} }
Endnote
%0 Conference Paper %T Structure Adaptive Algorithms for Stochastic Bandits %A Rémy Degenne %A Han Shao %A Wouter Koolen %B Proceedings of the 37th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2020 %E Hal Daumé III %E Aarti Singh %F pmlr-v119-degenne20b %I PMLR %P 2443--2452 %U http://proceedings.mlr.press/v119/degenne20b.html %V 119 %X We study reward maximisation in a wide class of structured stochastic multi-armed bandit problems, where the mean rewards of arms satisfy some given structural constraints, e.g. linear, unimodal, sparse, etc. Our aim is to develop methods that are \emph{flexible} (in that they easily adapt to different structures), \emph{powerful} (in that they perform well empirically and/or provably match instance-dependent lower bounds) and \emph{efficient} in that the per-round computational burden is small. We develop asymptotically optimal algorithms from instance-dependent lower-bounds using iterative saddle-point solvers. Our approach generalises recent iterative methods for pure exploration to reward maximisation, where a major challenge arises from the estimation of the sub-optimality gaps and their reciprocals. Still we manage to achieve all the above desiderata. Notably, our technique avoids the computational cost of the full-blown saddle point oracle employed by previous work, while at the same time enabling finite-time regret bounds. Our experiments reveal that our method successfully leverages the structural assumptions, while its regret is at worst comparable to that of vanilla UCB.
APA
Degenne, R., Shao, H. & Koolen, W.. (2020). Structure Adaptive Algorithms for Stochastic Bandits. Proceedings of the 37th International Conference on Machine Learning, in Proceedings of Machine Learning Research 119:2443-2452 Available from http://proceedings.mlr.press/v119/degenne20b.html .

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