Gaussian multi-armed bandit problems with multiple objectives

Motivated by the goal of formally integrating human designers into computational systems for engineering design optimization, I study decision making under uncertainty with multiple objectives in the context of the multi-armed bandit problem. A key aspect of multi-objective optimization is the need for scalarization, i.e., a way to combine the various objectives into a single well-defined scalar objective function. I study the case where the multi-objective rewards are Gaussian distributed and the scalarization is linear and develop an algorithm that achieves optimal performance, i.e., converges to selecting the best arm at the highest possible rate.