Adaptive Kernel Learning in Heterogeneous Networks

We consider learning in decentralized heterogeneous networks: agents seek to minimize a convex functional that aggregates data across the network, while only having access their local streams. focus on case where estimate regression function belongs reproducing kernel Hilbert space (RKHS). To incentivize coordination respecting network heterogeneity, we impose nonlinear proximity constraints. The resulting constrained stochastic optimization problem is solved using variant of primal-dual (Arrow-Hurwicz) method which yields algorithm. In order avoid model complexity from growing linearly over time, project primal iterates onto subspaces greedily constructed evaluations agents' observations. scheme, dubbed Heterogeneous Adaptive Learning with Kernels (HALK), allows us, for first characterize precise trade-off between optimality gap, constraint violation, and complexity. particular, proposed algorithm can be tuned achieve zero an gap O (T -1/2 +?) after T iterations, number elements retained dictionary determined by 1/?. Simulations correlated spatio-temporal field estimation validate our theoretical results, are corroborated practice networked oceanic sensing buoys estimating temperature salinity depth measurements.