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We consider the contextual bandit problem, where a player sequentially makesdecisions based on past observations to maximize the cumulative reward.Although many algorithms have been proposed for contextual bandit, most of themrely on finding the maximum likelihood estimator at each iteration, whichrequires $O(t)$ time at the $t$-th iteration and are memory inefficient. Anatural way to resolve this problem is to apply online stochastic gradientdescent (SGD) so that the per-step time and memory complexity can be reduced toconstant with respect to $t$, but a contextual bandit policy based on onlineSGD updates that balances exploration and exploitation has remained elusive. Inthis work, we show that online SGD can be applied to the generalized linearbandit problem. The proposed SGD-TS algorithm, which uses a single-step SGDupdate to exploit past information and uses Thompson Sampling for exploration,achieves $\tilde{O}(\sqrt{T})$ regret with the total time complexity thatscales linearly in $T$ and $d$, where $T$ is the total number of rounds and $d$is the number of features. Experimental results show that SGD-TS consistentlyoutperforms existing algorithms on both synthetic and real datasets.

An Efficient Algorithm For Generalized Linear Bandit: Online Stochastic Gradient Descent and Thompson Sampling