On Upper-Confidence Bound Policies for Non-Stationary Bandit Problems
| dc.creator | Garivier, Aurélien | |
| dc.creator | Moulines, Eric | |
| dc.date | 2008-05-22 | |
| dc.date.accessioned | 2026-07-07T12:19:10Z | |
| dc.date.available | 2026-07-07T12:19:10Z | |
| dc.description | Multi-armed bandit problems are considered as a paradigm of the trade-off between exploring the environment to find profitable actions and exploiting what is already known. In the stationary case, the distributions of the rewards do not change in time, Upper-Confidence Bound (UCB) policies have been shown to be rate optimal. A challenging variant of the MABP is the non-stationary bandit problem where the gambler must decide which arm to play while facing the possibility of a changing environment. In this paper, we consider the situation where the distributions of rewards remain constant over epochs and change at unknown time instants. We analyze two algorithms: the discounted UCB and the sliding-window UCB. We establish for these two algorithms an upper-bound for the expected regret by upper-bounding the expectation of the number of times a suboptimal arm is played. For that purpose, we derive a 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. | |
| dc.description | 24 pages | |
| dc.identifier | https://arxiv.org/abs/0805.3415 | |
| dc.identifier | http://arxiv.org/abs/0805.3415 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/212661 | |
| dc.subject | Statistics Theory | |
| dc.title | On Upper-Confidence Bound Policies for Non-Stationary Bandit Problems | |
| dc.type | text |