Online Experimental Design for Network Tomography

How to efficiently perform network tomography is a fundamental problem in network management and monitoring. A network tomography task usually consists of applying multiple probing experiments, e.g., across different paths or via different casts (including unicast and multicast). We study how to optimize the network tomography process through online sequential decision-making. From the methodology perspective, we introduce an online probe allocation algorithm that dynamically performs network tomography based on the principles of optimal experimental design and the maximum likelihood estimation. We rigorously analyze the regret of the algorithm under the conditions that i) the optimal allocation is Lipschitz continuous in the parameters being estimated and ii) the parameter estimators satisfy a concentration property. From the application perspective, we present two case studies: a) the classical lossy packet-switched network and b) the quantum bit-flip network. We show that both cases fulfill the two theoretical conditions and provide their corresponding regrets when deploying our proposed online probe allocation algorithm. Besides these two case studies with theoretical guarantees, we also conduct simulations to compare our proposed algorithm with existing methods and demonstrate our algorithm's effectiveness in a broader range of scenarios.