Decomposable Submodular Maximization in Federated Setting
This addresses privacy and scalability issues in machine learning and recommendation systems for applications like welfare maximization, though it is incremental as it adapts existing methods to a federated setting.
The paper tackles the computational and privacy challenges of optimizing decomposable submodular functions with millions of private component functions by proposing a federated optimization setting, where a federated continuous greedy algorithm with subsampling and intermittent aggregation achieves a good approximate solution while reducing communication costs.
Submodular functions, as well as the sub-class of decomposable submodular functions, and their optimization appear in a wide range of applications in machine learning, recommendation systems, and welfare maximization. However, optimization of decomposable submodular functions with millions of component functions is computationally prohibitive. Furthermore, the component functions may be private (they might represent user preference function, for example) and cannot be widely shared. To address these issues, we propose a {\em federated optimization} setting for decomposable submodular optimization. In this setting, clients have their own preference functions, and a weighted sum of these preferences needs to be maximized. We implement the popular {\em continuous greedy} algorithm in this setting where clients take parallel small local steps towards the local solution and then the local changes are aggregated at a central server. To address the large number of clients, the aggregation is performed only on a subsampled set. Further, the aggregation is performed only intermittently between stretches of parallel local steps, which reduces communication cost significantly. We show that our federated algorithm is guaranteed to provide a good approximate solution, even in the presence of above cost-cutting measures. Finally, we show how the federated setting can be incorporated in solving fundamental discrete submodular optimization problems such as Maximum Coverage and Facility Location.