TY - GEN
T1 - Maximizing and Satisficing in Multi-armed Bandits with Graph Information
AU - Thaker, Parth K.
AU - Rao, Nikhil
AU - Malu, Mohit
AU - Dasarathy, Gautam
N1 - Funding Information:
∗This work was supported in part by the National Science Foundation through the awards CCF-2048223, CNS-2003111, CCF-2029044, and OAC-1934766. This work was also supported partly by the ASU SenSIP Center
Publisher Copyright:
© 2022 Neural information processing systems foundation. All rights reserved.
PY - 2022
Y1 - 2022
N2 - Pure exploration in multi-armed bandits has emerged as an important framework for modeling decision making and search under uncertainty. In modern applications however, one is often faced with a tremendously large number of options and even obtaining one observation per option may be too costly rendering traditional pure exploration algorithms ineffective. Fortunately, one often has access to similarity relationships amongst the options that can be leveraged. In this paper, we consider the pure exploration problem in stochastic multi-armed bandits where the similarities between the arms is captured by a graph and the rewards may be represented as a smooth signal on this graph. In particular, we consider the problem of finding the arm with the maximum reward (i.e., the maximizing problem) or one that has sufficiently high reward (i.e., the satisficing problem) under this model. We propose novel algorithms GRUB (GRaph based UcB) and ζ-GRUB for these problems and provide theoretical characterization of their performance which specifically elicits the benefit of the graph side information. We also prove a lower bound on the data requirement that shows a large class of problems where these algorithms are near-optimal. We complement our theory with experimental results that show the benefit of capitalizing on such side information.
AB - Pure exploration in multi-armed bandits has emerged as an important framework for modeling decision making and search under uncertainty. In modern applications however, one is often faced with a tremendously large number of options and even obtaining one observation per option may be too costly rendering traditional pure exploration algorithms ineffective. Fortunately, one often has access to similarity relationships amongst the options that can be leveraged. In this paper, we consider the pure exploration problem in stochastic multi-armed bandits where the similarities between the arms is captured by a graph and the rewards may be represented as a smooth signal on this graph. In particular, we consider the problem of finding the arm with the maximum reward (i.e., the maximizing problem) or one that has sufficiently high reward (i.e., the satisficing problem) under this model. We propose novel algorithms GRUB (GRaph based UcB) and ζ-GRUB for these problems and provide theoretical characterization of their performance which specifically elicits the benefit of the graph side information. We also prove a lower bound on the data requirement that shows a large class of problems where these algorithms are near-optimal. We complement our theory with experimental results that show the benefit of capitalizing on such side information.
UR - http://www.scopus.com/inward/record.url?scp=85163197689&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85163197689&partnerID=8YFLogxK
M3 - Conference contribution
AN - SCOPUS:85163197689
T3 - Advances in Neural Information Processing Systems
BT - Advances in Neural Information Processing Systems 35 - 36th Conference on Neural Information Processing Systems, NeurIPS 2022
A2 - Koyejo, S.
A2 - Mohamed, S.
A2 - Agarwal, A.
A2 - Belgrave, D.
A2 - Cho, K.
A2 - Oh, A.
PB - Neural information processing systems foundation
T2 - 36th Conference on Neural Information Processing Systems, NeurIPS 2022
Y2 - 28 November 2022 through 9 December 2022
ER -