Correlated Gaussian Multi-Objective Multi-Armed Bandit Across Arms Algorithm

Stochastic multi-objective multi-armed bandit problem, (MOMAB), is a stochastic multi-armed problem where each arm generates a vector of rewards instead of a single scalar reward. The goal of (MOMAB) is to minimize the regret of playing suboptimal arms while playing fairly the Pareto optimal arms. In this paper, we consider Gaussian correlation across arms in (MOMAB), meaning that the generated reward vector of an arm gives us information not only about that arm itself but also on all the available arms. We call this framework the correlated-MOMAB problem. We extended Gittins index policy to correlated (MOMAB) because Gittins index has been used before to model the correlation between arms. We empirically compared Gittins index policy with multi-objective upper confidence bound policy on a test suite of correlated-MOMAB problems. We conclude that the performance of these policies depend on the number of arms and objectives.