Title: Robust Contextual Bandit via the Capped-$\ell_{2}$ norm,
Abstract: This paper considers the actor-critic contextual bandit for the mobile health
(mHealth) intervention. The state-of-the-art decision-making methods in mHealth
generally assume that the noise in the dynamic system follows the Gaussian
distribution. Those methods use the least-square-based algorithm to estimate
the expected reward, which is prone to the existence of outliers. To deal with
the issue of outliers, we propose a novel robust actor-critic contextual bandit
method for the mHealth intervention. In the critic updating, the
capped-$\ell_{2}$ norm is used to measure the approximation error, which
prevents outliers from dominating our objective. A set of weights could be
achieved from the critic updating. Considering them gives a weighted objective
for the actor updating. It provides the badly noised sample in the critic
updating with zero weights for the actor updating. As a result, the robustness
of both actor-critic updating is enhanced. There is a key parameter in the
capped-$\ell_{2}$ norm. We provide a reliable method to properly set it by
making use of one of the most fundamental definitions of outliers in
statistics. Extensive experiment results demonstrate that our method can
achieve almost identical results compared with the state-of-the-art methods on
the dataset without outliers and dramatically outperform them on the datasets
noised by outliers.