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Age-of-Information (AoI) is a critical metric for network applications.Existing works mostly address optimization with homogeneous AoI requirements,which is different from practice. In this work, we optimize uplink schedulingfor an access point (AP) over multiple unknown channels with heterogeneous AoIrequirements defined by AoI-dependent costs. The AP serves $N$ users by using$M$ channels without the channel state information. Each channel serves onlyone user in each decision epoch. The optimization objective is to minimize thetime-averaged AoI-dependent costs plus additional communication transmissioncosts over an infinite horizon. This decision-making problem can be formulatedas a Markov decision process, but it is computationally intractable because thesize of the state space grows exponentially with respect to the number ofusers. To alleviate the challenge, we reformulate the problem as a variant ofthe restless multi-armed bandit (RMAB) problem and leverage Whittle's indextheory to design an index-based scheduling policy algorithm. We derive ananalytic formula for the indices, which reduces the computational overhead andfacilitates online adaptation. Our numerical examples show that our index-basedscheduling policy achieves comparable performance to the optimal policy andoutperforms several other heuristics.

Towards Efficient Dynamic Uplink Scheduling over Multiple Unknown Channels