HAL will be down for maintenance from Friday, June 10 at 4pm through Monday, June 13 at 9am. More information
Skip to Main content Skip to Navigation
Other publications

Use of variance estimation in the multi-armed bandit problem

Jean-Yves Audibert 1 Rémi Munos 2 Csaba Szepesvari 3
2 SEQUEL - Sequential Learning
LIFL - Laboratoire d'Informatique Fondamentale de Lille, Inria Lille - Nord Europe, LAGIS - Laboratoire d'Automatique, Génie Informatique et Signal
Abstract : An important aspect of most decision making problems concerns the appropriate balance between exploitation (acting optimally according to the partial knowledge acquired so far) and exploration of the environment (acting sub-optimally in order to refine the current knowledge and improve future decisions). A typical example of this so-called exploration versus exploitation dilemma is the multi-armed bandit problem, for which many strategies have been developed. Here we investigate policies based the choice of the arm having the highest upper-confidence bound, where the bound takes into account the empirical variance of the different arms. Such an algorithm was found earlier to outperform its peers in a series of numerical experiments. The main contribution of this paper is the theoretical investigation of this algorithm. Our contribution here is twofold. First, we prove that with probability at least $1-\beta$, the regret after $n$ plays of a variant of the UCB algorithm (called $\beta$-UCB) is upper-bounded by a constant, that scales linearly with $\log(1/\beta)$, but which is independent from $n$. We also analyse a variant which is closer to the algorithm suggested earlier. We prove a logarithmic bound on the expected regret of this algorithm and argue that the bound scales favourably with the variance of the suboptimal arms.
Document type :
Other publications
Complete list of metadata

Cited literature [3 references]  Display  Hide  Download

https://hal.inria.fr/inria-00203496
Contributor : Rémi Munos Connect in order to contact the contributor
Submitted on : Thursday, January 10, 2008 - 12:11:52 PM
Last modification on : Thursday, January 20, 2022 - 4:12:33 PM
Long-term archiving on: : Tuesday, April 13, 2010 - 4:56:00 PM

File

ucbtuned.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : inria-00203496, version 1

Collections

Citation

Jean-Yves Audibert, Rémi Munos, Csaba Szepesvari. Use of variance estimation in the multi-armed bandit problem. 2006. ⟨inria-00203496⟩

Share

Metrics

Record views

243

Files downloads

231