Adaptive Algorithms for Relaxed Pareto Set Identification
This work addresses the challenge of efficiently finding optimal strategies in multi-criteria decision-making problems, such as public health interventions, though it is incremental by building on existing relaxations for Pareto set identification.
The paper tackles the problem of identifying Pareto optimal sets in multi-objective multi-armed bandits by proposing adaptive algorithms that allow relaxations, such as outputting a subset of arms, to reduce sample complexity, with results including quantified reductions when seeking at most k arms and demonstrated practical performance in a Covid-19 vaccination scenario.
In this paper we revisit the fixed-confidence identification of the Pareto optimal set in a multi-objective multi-armed bandit model. As the sample complexity to identify the exact Pareto set can be very large, a relaxation allowing to output some additional near-optimal arms has been studied. In this work we also tackle alternative relaxations that allow instead to identify a relevant subset of the Pareto set. Notably, we propose a single sampling strategy, called Adaptive Pareto Exploration, that can be used in conjunction with different stopping rules to take into account different relaxations of the Pareto Set Identification problem. We analyze the sample complexity of these different combinations, quantifying in particular the reduction in sample complexity that occurs when one seeks to identify at most $k$ Pareto optimal arms. We showcase the good practical performance of Adaptive Pareto Exploration on a real-world scenario, in which we adaptively explore several vaccination strategies against Covid-19 in order to find the optimal ones when multiple immunogenicity criteria are taken into account.