  The Metaverse has received much attention recently. Metaverse applications
via mobile augmented reality (MAR) require rapid and accurate object detection
to mix digital data with the real world. Federated learning (FL) is an
intriguing distributed machine learning approach due to its privacy-preserving
characteristics. Due to privacy concerns and the limited computation resources
on mobile devices, we incorporate FL into MAR systems of the Metaverse to train
a model cooperatively. Besides, to balance the trade-off between energy,
execution latency and model accuracy, thereby accommodating different demands
and application scenarios, we formulate an optimization problem to minimize a
weighted combination of total energy consumption, completion time and model
accuracy. Through decomposing the non-convex optimization problem into two
subproblems, we devise a resource allocation algorithm to determine the
bandwidth allocation, transmission power, CPU frequency and video frame
resolution for each participating device. We further present the convergence
analysis and computational complexity of the proposed algorithm. Numerical
results show that our proposed algorithm has better performance (in terms of
energy consumption, completion time and model accuracy) under different weight
parameters compared to existing benchmarks.
