Squeeze All: Novel Estimator and Self-Normalized Bound for Linear Contextual Bandits. (arXiv:2206.05404v2 [stat.ML] UPDATED)

Web: http://arxiv.org/abs/2206.05404

We propose a novel algorithm for linear contextual bandits with $O(\sqrt{dT
\log T})$ regret bound, where $d$ is the dimension of contexts and $T$ is the
time horizon. Our proposed algorithm is equipped with a novel estimator in
which exploration is embedded through explicit randomization. Depending on the
randomization, our proposed estimator takes contribution either from contexts
of all arms or from selected contexts. We establish a self-normalized bound for
our estimator, which allows a novel decomposition of the cumulative …

arxiv linear ml