Abstract
Many problems, such as cognitive radio, parameter control of a scanning tunnelling microscope or internet advertisement, can be modelled as non-stationary bandit problems where the distributions of rewards changes abruptly at unknown time instants. In this paper, we analyze two algorithms designed for solving this issue: discounted UCB (D-UCB) and sliding-window UCB (SW-UCB). We establish an upper-bound for the expected regret by upper-bounding the expectation of the number of times suboptimal arms are played. The proof relies on an interesting Hoeffding type inequality for self normalized deviations with a random number of summands. We establish a lower-bound for the regret in presence of abrupt changes in the arms reward distributions. We show that the discounted UCB and the sliding-window UCB both match the lower-bound up to a logarithmic factor. Numerical simulations show that D-UCB and SW-UCB perform significantly better than existing soft-max methods like EXP3.S.
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Garivier, A., Moulines, E. (2011). On Upper-Confidence Bound Policies for Switching Bandit Problems. In: Kivinen, J., Szepesvári, C., Ukkonen, E., Zeugmann, T. (eds) Algorithmic Learning Theory. ALT 2011. Lecture Notes in Computer Science(), vol 6925. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24412-4_16
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DOI: https://doi.org/10.1007/978-3-642-24412-4_16
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