Invited Paper: A Combinatorial Multi-Armed Bandit Approach for Stochastic Facility Allocation Problem.

Combinatorial Multi-Armed Bandit (CMAB) techniques have been widely used to solve many real-world problems. This paper presents a geometric version of a stochastic facility allocation problem and proposes a novel approach using CMAB to solve it. This problem is concerned with optimally locating facilities in a 2-dimensional space with spatially variant population density, where the aim is to maximize the expected attraction of the population to the facility points over multiple rounds. We propose an algorithm based on the Upper Confidence Bound (UCB) principle and leverage Voronoi diagrams to model the attraction of the population to facilities. We consider both the Manhattan and Euclidean distances in the attraction model. The model has a broad range of potential applications, making the solution a feasible approach for similar optimization problems in dynamic and uncertain environments. To the best of our knowledge, this is the first work that applies CMAB models on 2-dimensional spaces with uncertain underlying distributions. Our findings show the potential of machine learning-based solutions, such as the CMAB approach, in advancing the design and implementation of distributed computing systems. Furthermore, we derive the regret bounds of the proposed algorithm. This analysis is complemented by numerical simulations demonstrating the efficiency and effectiveness of our method. The simulation was done on both real-world traces and synthesized data.