HyperPrism: An Adaptive Non-linear Aggregation Framework for Distributed Machine Learning over non-IID Data and Time-varying Communication Links

While Distributed Machine Learning (DML) has been widely used to achieve decent performance, it is still challenging to take full advantage of data and devices distributed at multiple vantage points to adapt and learn; this is because the current linear aggregation paradigm cannot solve inter-model divergence caused by (1) heterogeneous learning data at different devices (i.e., non-IID data) and (2) in the case of time-varying communication links, the limited ability for devices to reconcile model divergence. In this paper, we present a non-linear class aggregation framework HyperPrism that leverages Kolmogorov Means to conduct distributed mirror descent with the averaging occurring within the mirror descent dual space; HyperPrism selects the degree for a Weighted Power Mean (WPM), a subset of the Kolmogorov Means, each round. Moreover, HyperPrism can adaptively choose different mapping for different layers of the local model with a dedicated hypernetwork per device, achieving automatic optimization of DML in high divergence settings. We perform rigorous analysis and experimental evaluations to demonstrate the effectiveness of adaptive, mirror-mapping DML. In particular, we extend the generalizability of existing related works and position them as special cases within HyperPrism. For practitioners, the strength of HyperPrism is in making feasible the possibility of distributed asynchronous training with minimal communication. Our experimental results show HyperPrism can improve the convergence speed up to 98.63% and scale well to more devices compared with the state-of-the-art, all with little additional computation overhead compared to traditional linear aggregation.