Top Feasible Arm Identification

Julian Katz-Samuels, Clayton Scott
; Proceedings of Machine Learning Research, PMLR 89:1593-1601, 2019.

Abstract

We propose a new variant of the top arm identification problem, \emph{top feasible arm identification}, where there are $K$ arms associated with $D$-dimensional distributions and the goal is to find $m$ arms that maximize some known linear function of their means subject to the constraint that their means belong to a given set $P \subset R^D$. This problem has many applications since in many settings, feedback is multi-dimensional and it is of interest to perform \emph{constrained maximization}. We present problem-dependent lower bounds for top feasible arm identification and upper bounds for several algorithms. Our most broadly applicable algorithm, TF-LUCB-B, has an upper bound that is loose by a factor of $O(D \log(K))$. Many problems of practical interest are two-dimensional and, for these, it is loose by a factor of $O(\log(K))$. Finally, we conduct experiments on synthetic and real-world datasets that demonstrate the effectiveness of our algorithms. Our algorithms are superior both in theory and in practice to a naive two-stage algorithm that first identifies the feasible arms and then applies a best arm identification algorithm to the feasible arms.

Cite this Paper


BibTeX
@InProceedings{pmlr-v89-katz-samuels19a, title = {Top Feasible Arm Identification}, author = {Katz-Samuels, Julian and Scott, Clayton}, booktitle = {Proceedings of Machine Learning Research}, pages = {1593--1601}, year = {2019}, editor = {Kamalika Chaudhuri and Masashi Sugiyama}, volume = {89}, series = {Proceedings of Machine Learning Research}, address = {}, month = {16--18 Apr}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v89/katz-samuels19a/katz-samuels19a.pdf}, url = {http://proceedings.mlr.press/v89/katz-samuels19a.html}, abstract = {We propose a new variant of the top arm identification problem, \emph{top feasible arm identification}, where there are $K$ arms associated with $D$-dimensional distributions and the goal is to find $m$ arms that maximize some known linear function of their means subject to the constraint that their means belong to a given set $P \subset R^D$. This problem has many applications since in many settings, feedback is multi-dimensional and it is of interest to perform \emph{constrained maximization}. We present problem-dependent lower bounds for top feasible arm identification and upper bounds for several algorithms. Our most broadly applicable algorithm, TF-LUCB-B, has an upper bound that is loose by a factor of $O(D \log(K))$. Many problems of practical interest are two-dimensional and, for these, it is loose by a factor of $O(\log(K))$. Finally, we conduct experiments on synthetic and real-world datasets that demonstrate the effectiveness of our algorithms. Our algorithms are superior both in theory and in practice to a naive two-stage algorithm that first identifies the feasible arms and then applies a best arm identification algorithm to the feasible arms.} }
Endnote
%0 Conference Paper %T Top Feasible Arm Identification %A Julian Katz-Samuels %A Clayton Scott %B Proceedings of Machine Learning Research %C Proceedings of Machine Learning Research %D 2019 %E Kamalika Chaudhuri %E Masashi Sugiyama %F pmlr-v89-katz-samuels19a %I PMLR %J Proceedings of Machine Learning Research %P 1593--1601 %U http://proceedings.mlr.press %V 89 %W PMLR %X We propose a new variant of the top arm identification problem, \emph{top feasible arm identification}, where there are $K$ arms associated with $D$-dimensional distributions and the goal is to find $m$ arms that maximize some known linear function of their means subject to the constraint that their means belong to a given set $P \subset R^D$. This problem has many applications since in many settings, feedback is multi-dimensional and it is of interest to perform \emph{constrained maximization}. We present problem-dependent lower bounds for top feasible arm identification and upper bounds for several algorithms. Our most broadly applicable algorithm, TF-LUCB-B, has an upper bound that is loose by a factor of $O(D \log(K))$. Many problems of practical interest are two-dimensional and, for these, it is loose by a factor of $O(\log(K))$. Finally, we conduct experiments on synthetic and real-world datasets that demonstrate the effectiveness of our algorithms. Our algorithms are superior both in theory and in practice to a naive two-stage algorithm that first identifies the feasible arms and then applies a best arm identification algorithm to the feasible arms.
APA
Katz-Samuels, J. & Scott, C.. (2019). Top Feasible Arm Identification. Proceedings of Machine Learning Research, in PMLR 89:1593-1601

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