Timezone: »

On the Optimality of Perturbations in Stochastic and Adversarial Multi-armed Bandit Problems
Baekjin Kim · Ambuj Tewari

Tue Dec 10 10:45 AM -- 12:45 PM (PST) @ East Exhibition Hall B + C #24

We investigate the optimality of perturbation based algorithms in the stochastic and adversarial multi-armed bandit problems. For the stochastic case, we provide a unified regret analysis for both sub-Weibull and bounded perturbations when rewards are sub-Gaussian. Our bounds are instance optimal for sub-Weibull perturbations with parameter 2 that also have a matching lower tail bound, and all bounded support perturbations where there is sufficient probability mass at the extremes of the support. For the adversarial setting, we prove rigorous barriers against two natural solution approaches using tools from discrete choice theory and extreme value theory. Our results suggest that the optimal perturbation, if it exists, will be of Frechet-type.

Author Information

Baekjin Kim (University of Michigan)
Ambuj Tewari (University of Michigan)

More from the Same Authors