Conservative Multi-agent Online Kernel Learning in Heterogeneous Networks

In this paper, we consider a decentralized heterogeneous network of agents that seek to cooperatively estimate a function belonging to reproducing kernel Hilbert space (RKHS), motivated by supervised learning. Since the network is assumed to be heterogeneous, imposing consensus constraints fails to allow agents to retain their local differences in their estimates, which motivates the use of nonlinear constraints to incentivize coordination. We develop a decentralized functional stochastic variant of the primal-dual (Arrow-Hurwicz) method. We use a dynamically regularized Lagrangian relaxation to derive convergence in expectation of this scheme to a optimality gap of O(√(T)) with zero constraint violation when used with a constant step-size, where T is the final iteration index. Further, the decentralized algorithms performance is validated on real world data set for estimating temperature and salinity from depth measurements of the Gulf of Mexico.