Linearly Parameterized Bandits

@article{Rusmevichientong2010LinearlyPB,
  title={Linearly Parameterized Bandits},
  author={Paat Rusmevichientong and John N. Tsitsiklis},
  journal={Math. Oper. Res.},
  year={2010},
  volume={35},
  pages={395-411}
}
We consider bandit problems involving a large (possibly infinite) collection of arms, in which the expected reward of each arm is a linear function of an r-dimensional random vector Z ∈ Rr, where r ≥ 2. The objective is to minimize the cumulative regret and Bayes risk. When the set of arms corresponds to the unit sphere, we prove that the regret and Bayes risk is of order Θ(r √ T ), by establishing a lower bound for an arbitrary policy, and showing that a matching upper bound is obtained… CONTINUE READING
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