Federated learning (FL) is a viable technique to train a shared machine learning model without sharing data. Hierarchical FL (HFL) system has yet to be studied regrading its multiple levels of energy, computation, communication, and client scheduling, especially when it comes to clients relying on energy harvesting to power their operations. This paper presents a new two-phase deep deterministic policy gradient (DDPG) framework, referred to as ``TP-DDPG'', to balance online the learning delay and model accuracy of an FL process in an energy harvesting-powered HFL system. The key idea is that we divide optimization decisions into two groups, and employ DDPG to learn one group in the first phase, while interpreting the other group as part of the environment to provide rewards for training the DDPG in the second phase. Specifically, the DDPG learns the selection of participating clients, and their CPU configurations and the transmission powers. A new straggler-aware client association and bandwidth allocation (SCABA) algorithm efficiently optimizes the other decisions and evaluates the reward for the DDPG. Experiments demonstrate that with substantially reduced number of learnable parameters, the TP-DDPG can quickly converge to effective polices that can shorten the training time of HFL by 39.4% compared to its benchmarks, when the required test accuracy of HFL is 0.9.

Federated Learning (FL) has been considered as an appealing framework to tackle data privacy issues of mobile devices compared to conventional Machine Learning (ML). Using Edge Servers (ESs) as intermediaries to perform model aggregation in proximity can reduce the transmission overhead, and it enables great potentials in low-latency FL, where the hierarchical architecture of FL (HFL) has been attracted more attention. Designing a proper client selection policy can significantly improve training performance, and it has been extensively used in FL studies. However, to the best of our knowledge, there are no studies focusing on HFL. In addition, client selection for HFL faces more challenges than conventional FL, e.g., the time-varying connection of client-ES pairs and the limited budget of the Network Operator (NO). In this paper, we investigate a client selection problem for HFL, where the NO learns the number of successful participating clients to improve the training performance (i.e., select as many clients in each round) as well as under the limited budget on each ES. An online policy, called Context-aware Online Client Selection (COCS), is developed based on Contextual Combinatorial Multi-Armed Bandit (CC-MAB). COCS observes the side-information (context) of local computing and transmission of client-ES pairs and makes client selection decisions to maximize NO's utility given a limited budget. Theoretically, COCS achieves a sublinear regret compared to an Oracle policy on both strongly convex and non-convex HFL. Simulation results also support the efficiency of the proposed COCS policy on real-world datasets. Z. Qu, R. Duan and Z. Lu are with the Department of Electrical Engineering, University of South Florida, Tampa, FL, 33620 USA.