TY - GEN

T1 - Regret bounds for Gaussian process bandit problems

AU - Grunewalder, S.

AU - Audibert, J.-Y.

AU - Opper, M.

AU - Shawe-Taylor, J.

PY - 2010

Y1 - 2010

N2 - Bandit algorithms are concerned with trading exploration with exploitation where a number of options are available but we can only learn their quality by experimenting with them. We consider the scenario in which the reward distribution for arms is modelled by a Gaussian process and there is no noise in the observed reward. Our main result is to bound the regret experienced by algorithms relative to the a posteriori optimal strategy of playing the best arm throughout based on benign assumptions about the covariance function defining the Gaussian process. We further complement these upper bounds with corresponding lower bounds for particular covariance functions demonstrating that in generalthere is at most a logarithmic looseness in our upper bounds.

AB - Bandit algorithms are concerned with trading exploration with exploitation where a number of options are available but we can only learn their quality by experimenting with them. We consider the scenario in which the reward distribution for arms is modelled by a Gaussian process and there is no noise in the observed reward. Our main result is to bound the regret experienced by algorithms relative to the a posteriori optimal strategy of playing the best arm throughout based on benign assumptions about the covariance function defining the Gaussian process. We further complement these upper bounds with corresponding lower bounds for particular covariance functions demonstrating that in generalthere is at most a logarithmic looseness in our upper bounds.

M3 - Conference contribution/Paper

SP - 273

EP - 280

BT - Artificial Intelligence and Statistics (AISTATS)

ER -