Contextual bandits are widely used in Internet services from news recommendation to advertising, and to Web search. Generalized linear models (logistical regression in particular) have demonstrated stronger performance than linear models in many applications where rewards are binary. However, most theoretical analyses on contextual bandits so far are on linear bandits. In this work, we propose an upper confidence bound based algorithm for generalized linear contextual bandits, which achieves an ~O(sqrt{dT}) regret over T rounds with d dimensional feature vectors. This regret matches the minimax lower bound, up to logarithmic terms, and improves on the best previous result by a sqrt{d} factor, assuming the number of arms is fixed. A key component in our analysis is to establish a new, sharp finite-sample confidence bound for maximum likelihood estimates in generalized linear models, which may be of independent interest. We also analyze a simpler upper confidence bound algorithm, which is useful in practice, and prove it to have optimal regret for certain cases.
Summary/Notes »Author Information
Lihong Li (Microsoft Research)
Yu Lu (Yale University)
Dengyong Zhou (Microsoft Research)
Related Events (a corresponding poster, oral, or spotlight)
-
2017 Talk: Provably Optimal Algorithms for Generalized Linear Contextual Bandits »
Mon Aug 7th 04:06 -- 04:24 PM Room C4.1
More from the Same Authors
-
2019 Workshop: Reinforcement Learning for Real Life »
Yuxi Li · Alborz Geramifard · Lihong Li · Csaba Szepesvari · Tao Wang -
2019 Poster: Policy Certificates: Towards Accountable Reinforcement Learning »
Christoph Dann · Lihong Li · Wei Wei · Emma Brunskill -
2019 Oral: Policy Certificates: Towards Accountable Reinforcement Learning »
Christoph Dann · Lihong Li · Wei Wei · Emma Brunskill -
2018 Poster: Scalable Bilinear Pi Learning Using State and Action Features »
Yichen Chen · Lihong Li · Mengdi Wang -
2018 Poster: SBEED: Convergent Reinforcement Learning with Nonlinear Function Approximation »
Bo Dai · Albert Shaw · Lihong Li · Lin Xiao · Niao He · Zhen Liu · Jianshu Chen · Le Song -
2018 Oral: Scalable Bilinear Pi Learning Using State and Action Features »
Yichen Chen · Lihong Li · Mengdi Wang -
2018 Oral: SBEED: Convergent Reinforcement Learning with Nonlinear Function Approximation »
Bo Dai · Albert Shaw · Lihong Li · Lin Xiao · Niao He · Zhen Liu · Jianshu Chen · Le Song -
2017 Poster: Sequence Modeling via Segmentations »
Chong Wang · Yining Wang · Po-Sen Huang · Abdelrahman Mohammad · Dengyong Zhou · Li Deng -
2017 Poster: Stochastic Variance Reduction Methods for Policy Evaluation »
Simon Du · Jianshu Chen · Lihong Li · Lin Xiao · Dengyong Zhou -
2017 Talk: Sequence Modeling via Segmentations »
Chong Wang · Yining Wang · Po-Sen Huang · Abdelrahman Mohammad · Dengyong Zhou · Li Deng -
2017 Talk: Stochastic Variance Reduction Methods for Policy Evaluation »
Simon Du · Jianshu Chen · Lihong Li · Lin Xiao · Dengyong Zhou
