Exploration versus exploitation trade-off in infinite horizon Pareto multi-armed bandits algorithms

Multi-objective multi-armed bandits (MOMAB) are multi-armed bandits (MAB) extended to reward vectors. We use the Pareto dominance relation to assess the quality of reward vectors, as opposite to scalarization functions. In this paper, we study the exploration vs exploitation trade-off in infinite horizon MOMABs algorithms. Single objective MABs explore the suboptimal arms and exploit a single optimal arm. MOMABs explore the suboptimal arms, but they also need to exploit fairly all optimal arms. We study the exploration vs exploitation trade-off of the Pareto UCB1 algorithm. We extend UCB2 that is another popular infinite horizon MAB algorithm to rewards vectors using the Pareto dominance relation. We analyse the properties of the proposed MOMAB algorithms in terms of upper regret bounds. We experimentally compare the exploration vs exploitation trade-off of the proposed MOMAB algorithms on a bi-objective Bernoulli environment coming from control theory.