Hierarchical Online Convex Optimization with Application to Multi-TRP Cooperative Networks

We consider online convex optimization (OCO) over a heterogeneous network with communication delay, where multiple local devices (workers) together with a central coordinator (master) execute a sequence of decisions to minimize the accumulation of time-varying global costs. The local data may not be independent or identically distributed, and the global cost functions may not be locally separable. Due to communication delay, neither the master nor the workers have in-time information about the current global cost function. We propose a new algorithm, termed Hierarchical OCO (HiOCO), which takes full advantage of the network heterogeneity in information timeliness and computation capacity to enable multi-step gradient descent at both the workers and the master. We analyze the impacts of the unique hierarchical architecture, multi-slot delay, and gradient estimation error to derive upper bounds on the dynamic regret of HiOCO, which measures the gap of costs between HiOCO and an offline globally optimal performance benchmark. We further apply HiOCO to an online cooperative precoding design problem in multiple transmission/reception point (TRP) wireless networks with non-ideal backhaul links for 5G New Radio. Simulation results demonstrate substantial performance gain of HiOCO over existing alternatives.