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Optimistic Bayesian sampling in contextual-bandit problems

Research output: Contribution to journalJournal article

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<mark>Journal publication date</mark>06/2012
<mark>Journal</mark>Journal of Machine Learning Research
Volume13
Number of pages37
Pages (from-to)2069-2106
Publication statusPublished
Original languageEnglish

Abstract

In sequential decision problems in an unknown environment, the decision maker often faces a dilemma over whether to explore to discover more about the environment, or to exploit current knowledge. We address the exploration-exploitation dilemma in a general setting encompassing both standard and contextualised bandit problems. The contextual bandit problem has recently resurfaced in attempts to maximise click-through rates in web based applications, a task with significant commercial interest.
In this article we consider an approach of Thompson (1933) which makes use of samples from the posterior distributions for the instantaneous value of each action. We extend the approach by introducing a new algorithm, Optimistic Bayesian Sampling (OBS), in which the probability of playing an action increases with the uncertainty in the estimate of the action value. This results in better directed exploratory behaviour.
We prove that, under unrestrictive assumptions, both approaches result in optimal behaviour with respect to the average reward criterion of Yang and Zhu (2002). We implement OBS and measure its performance in simulated Bernoulli bandit and linear regression domains, and also when tested with the task of personalised news article recommendation on a Yahoo! Front Page Today Module data set. We find that OBS performs competitively when compared to recently proposed benchmark algorithms and outperforms Thompson's method throughout.

Bibliographic note

This research was undertaken as part of the ALADDIN (Autonomous Learning Agents for Decentralised Data and Information Networks) project and is jointly funded by a BAE Systems and EPRSC (Engineering and Physical Sciences Research Council) strategic partnership (EP/C548051/1).