Langevin Monte Carlo for Contextual Bandits
Abstract
We study the efficiency of Thompson sampling for contextual bandits. Existing Thompson sampling-based algorithms need to construct a Laplace approximation (i.e., a Gaussian distribution) of the posterior distribution, which is inefficient to sample in high dimensional applications for general covariance matrices. Moreover, the Gaussian approximation may not be a good surrogate for the posterior distribution for general reward generating functions. We propose an efficient posterior sampling algorithm, viz., Langevin Monte Carlo Thompson Sampling (LMC-TS), that uses Markov Chain Monte Carlo (MCMC) methods to directly sample from the posterior distribution in contextual bandits. Our method is computationally efficient since it only needs to perform noisy gradient descent updates without constructing the Laplace approximation of the posterior distribution. We prove that the proposed algorithm achieves the same sublinear regret bound as the best Thompson sampling algorithms for a special case of contextual bandits, viz., linear contextual bandits. We conduct experiments on both synthetic data and real-world datasets on different contextual bandit models, which demonstrates that directly sampling from the posterior is both computationally efficient and competitive in performance.
Additional Information
© 2022 by the author(s). The authors would like to thank the anonymous reviewers for their invaluable comments. PX is supported by PIMCO Postdoctoral Fellowship. AA is partially supported by Bren Named Chair Professorship at Caltech.Attached Files
Published - xu22p.pdf
Accepted Version - 2206.11254.pdf
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Additional details
- Eprint ID
- 115574
- Resolver ID
- CaltechAUTHORS:20220714-212437915
- PIMCO
- Bren Professor of Computing and Mathematical Sciences
- Created
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2022-07-15Created from EPrint's datestamp field
- Updated
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2023-06-02Created from EPrint's last_modified field