B²-Bandit: Budgeted Pricing With Blocking Constraints for Metaverse Crowdsensing Under Uncertainty

Metaverse has been viewed as the next generation of human-computer interaction, which requires collecting information from both the physical and virtual world. One potential way is to employ virtual service providers (VSPs) to finish collection tasks by designing posted-pricing mechanisms via the crowdsensing platform. As VSPs’ costs and values are usually unknown, learning the optimal posted-pricing policy under uncertainty is undoubtedly critical to utilize the budget efficiently. However, existing posted-pricing learning algorithms assume that agents provide services without blocking and agents’ attributes follow an independent identical distribution, both of which are unrealistic in Metaverse, e.g., VSPs should continuously sense the physical world to make provided services realistic, which makes the long working VSP unavailable/blocked for a certain period of time. In this paper, we address the budgeted pricing problem under uncertainty by considering blocking constraints and unknown non-identical VSPs’ attributes. The problem is modeled as a Budgeted-pricing Blocking Bandit (B2-bandit) problem, which remains unaddressed even for the oracle case with known VSPs’ information. We thus first propose a pricing policy for the oracle case with an instance-dependent approximation ratio to the global optimum. For the general B2-bandit problem with unknown information, we propose an online learning algorithm satisfying blocking constraints and incurring an accumulated regret up to $O(MK\log B)$ as compared to the oracle approximation algorithm, where $M,K,B$ are the number of VSPs, candidate prices and the budget, respectively. Experiments on real datasets validate that the proposed algorithm improves more than 172% accumulated value compared to baseline pricing algorithms.