Contextual Bandit Algorithms with Supervised Learning Guarantees

Notable paper award

Alina Beygelzimer, John Langford, Lihong Li, Lev Reyzin, Robert Schapire; JMLR W&CP 15:19-26, 2011.


We address the problem of competing with any large set of $N$ policies in the non-stochastic bandit setting, where the learner must repeatedly select among $K$ actions but observes only the reward of the chosen action. We present a modification of the Exp4 algorithm of [Auer et al. 2002] called Exp4.P, which with high probability incurs regret at most $O(\sqrt{KT\ln N})$. Such a bound does not hold for Exp4 due to the large variance of the importance-weighted estimates used in the algorithm. The new algorithm is tested empirically in a large-scale, real-world dataset. For the stochastic version of the problem, we can use Exp4.P as a subroutine to compete with a possibly infinite set of policies of VC-dimension $d$ while incurring regret at most $O(\sqrt{Td\ln T})$ with high probability. These guarantees improve on those of all previous algorithms, whether in a stochastic or adversarial environment, and bring us closer to providing guarantees for this setting that are comparable to those in standard supervised learning.


Home Page





Editorial Board



Open Source Software



RSS Feed