Knowledge gradient for multi-objective multi-armed bandit algorithms

We extend knowledge gradient (KG) policy for the multi-objective, multi-armed bandits problem to efficiently explore the Pareto optimal arms. We consider two partial order relationships to order the mean vectors, i.e. Pareto and scalarized functions. Pareto KG finds the optimal arms using Pareto search, while the scalarizations-KG transform the multi-objective arms into one-objective arm to find the optimal arms. To measure the performance of the proposed algorithms, we propose three regret measures. We compare the performance of knowledge gradient policy with UCB1 on a multi-objective multi-armed bandits problem, where KG outperforms UCB1.