We study the problem of online multi-task learning where the tasks are performed within similar but not necessarily identical multi-armed bandit environments. In particular, we study how a learner can improve its overall performance across multiple related tasks through robust transfer of knowledge. While an upper confidence bound (UCB)-based algorithm has recently been shown to achieve nearly-optimal performance guarantees in a setting where all tasks are solved concurrently, it remains unclear whether Thompson sampling (TS) algorithms, which have superior empirical performance in general, share similar theoretical properties. In this work, we present a TS-type algorithm for a more general online multi-task learning protocol, which extends the concurrent setting. We provide its frequentist analysis and prove that it is also nearly-optimal using a novel concentration inequality for multi-task data aggregation at random stopping times. Finally, we evaluate the algorithm on synthetic data and show that the TS-type algorithm enjoys superior empirical performance in comparison with the UCB-based algorithm and a baseline algorithm that performs TS for each individual task without transfer.
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An efficient algorithm for generalized linear bandit: Online stochastic gradient descent and thompson sampling
We consider the contextual bandit problem, where a player sequentially makes decisions based on past observations to maximize the cumulative reward. Although many algorithms have been proposed for contextual bandit, most of them rely on finding the maximum likelihood estimator at each iteration, which requires π(π‘) time at the π‘-th iteration and are memory inefficient. A natural way to resolve this problem is to apply online stochastic gradient descent (SGD) so that the per-step time and memory complexity can be reduced to constant with respect to π‘, but a contextual bandit policy based on online SGD updates that balances exploration and exploitation has remained elusive. In this work, we show that online SGD can be applied to the generalized linear bandit problem. The proposed SGD-TS algorithm, which uses a single-step SGD update to exploit past information and uses Thompson Sampling for exploration, achieves πΜ (πβΎβΎβ) regret with the total time complexity that scales linearly in π and π, where π is the total number of rounds and π is the number of features. Experimental results show that SGD-TS consistently outperforms existing algorithms on both synthetic and real datasets.
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- Award ID(s):
- 1712996
- NSF-PAR ID:
- 10402485
- Editor(s):
- Banerjee, Arindam; Fukumizu, Kenji
- Date Published:
- Journal Name:
- Proceedings of Machine Learning Research
- Volume:
- 130
- ISSN:
- 2640-3498
- Page Range / eLocation ID:
- 1585-1593
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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