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arXiv · 1604.05257

Risk-Averse Multi-Armed Bandit Problems under Mean-Variance Measure

Sattar Vakili·Qing Zhao
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Abstract

The multi-armed bandit problems have been studied mainly under the measure of expected total reward accrued over a horizon of length $T$. In this paper, we address the issue of risk in multi-armed bandit problems and develop parallel results under the measure of mean-variance, a commonly adopted risk measure in economics and mathematical finance. We show that the model-specific regret and the model-independent regret in terms of the mean-variance of the reward process are lower bounded by $\Omega(\log T)$ and $\Omega(T^{2/3})$, respectively. We then show that variations of the UCB policy and the DSEE policy developed for the classic risk-neutral MAB achieve these lower bounds.

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Sattar Vakili, Qing Zhao. 2016-04-18. Risk-Averse Multi-Armed Bandit Problems under Mean-Variance Measure. https://doi.org/10.1109/jstsp.2016.2592622

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