Exploration Through Reward Biasing: Reward-Biased Maximum Likelihood Estimation for Stochastic Multi-Armed Bandits
Xi Liu, Ping-Chun Hsieh, Yu Heng Hung, Anirban Bhattacharya, P. Kumar
Abstract
Inspired by the Reward-Biased Maximum Likelihood Estimate method of adaptive control, we propose RBMLE – a novel family of learning algorithms for stochastic multi-armed bandits (SMABs). For a broad range of SMABs including both the parametric Exponential Family as well as the non-parametric sub-Gaussian/Exponential family, we show that RBMLE yields an index policy. To choose the bias-growth rate $\alpha(t)$ in RBMLE, we reveal the nontrivial interplay between $\alpha(t)$ and the regret bound that generally applies in both the Exponential Family as well as the sub-Gaussian/Exponential family bandits. To quantify the finite-time performance, we prove that RBMLE attains order-optimality by adaptively estimating the unknown constants in the expression of $\alpha(t)$ for Gaussian and sub-Gaussian bandits. Extensive experiments demonstrate that the proposed RBMLE achieves empirical regret performance competitive with the state-of-the-art methods, while being more computationally efficient and scalable in comparison to the best-performing ones among them.
BibTeX
@InProceedings{pmlr-v119-liu20g,
title = {Exploration Through Reward Biasing: Reward-Biased Maximum Likelihood Estimation for Stochastic Multi-Armed Bandits},
author = {Liu, Xi and Hsieh, Ping-Chun and Hung, Yu Heng and Bhattacharya, Anirban and Kumar, P.},
booktitle = {Proceedings of the 37th International Conference on Machine Learning},
pages = {6248--6258},
year = {2020},
editor = {III, Hal Daumé and Singh, Aarti},
volume = {119},
series = {Proceedings of Machine Learning Research},
month = {13--18 Jul},
publisher = {PMLR},
pdf = {http://proceedings.mlr.press/v119/liu20g/liu20g.pdf},
url = {https://proceedings.mlr.press/v119/liu20g.html},
abstract = {Inspired by the Reward-Biased Maximum Likelihood Estimate method of adaptive control, we propose RBMLE – a novel family of learning algorithms for stochastic multi-armed bandits (SMABs). For a broad range of SMABs including both the parametric Exponential Family as well as the non-parametric sub-Gaussian/Exponential family, we show that RBMLE yields an index policy. To choose the bias-growth rate $\alpha(t)$ in RBMLE, we reveal the nontrivial interplay between $\alpha(t)$ and the regret bound that generally applies in both the Exponential Family as well as the sub-Gaussian/Exponential family bandits. To quantify the finite-time performance, we prove that RBMLE attains order-optimality by adaptively estimating the unknown constants in the expression of $\alpha(t)$ for Gaussian and sub-Gaussian bandits. Extensive experiments demonstrate that the proposed RBMLE achieves empirical regret performance competitive with the state-of-the-art methods, while being more computationally efficient and scalable in comparison to the best-performing ones among them.}
}