Brian Swenson

Brian Swenson, Soummya Kar, H. Vincent Poor et al.

The paper proves convergence to global optima for a class of distributed algorithms for nonconvex optimization in network-based multi-agent settings. Agents are permitted to communicate over a time-varying undirected graph. Each agent is assumed to possess a local objective function (assumed to be smooth, but possibly nonconvex). The paper considers algorithms for optimizing the sum function. A distributed algorithm of the consensus+innovations type is proposed which relies on first-order information at the agent level. Under appropriate conditions on network connectivity and the cost objective, convergence to the set of global optima is achieved by an annealing-type approach, with decaying Gaussian noise independently added into each agent's update step. It is shown that the proposed algorithm converges in probability to the set of global minima of the sum function.

Soummya Kar, Brian Swenson

We consider $K$-means clustering in networked environments (e.g., internet of things (IoT) and sensor networks) where data is inherently distributed across nodes and processing power at each node may be limited. We consider a clustering algorithm referred to as networked $K$-means, or $NK$-means, which relies only on local neighborhood information exchange. Information exchange is limited to low-dimensional statistics and not raw data at the agents. The proposed approach develops a parametric family of multi-agent clustering objectives (parameterized by $ρ$) and associated distributed $NK$-means algorithms (also parameterized by $ρ$). The $NK$-means algorithm with parameter $ρ$ converges to a set of fixed points relative to the associated multi-agent objective (designated as `generalized minima'). By appropriate choice of $ρ$, the set of generalized minima may be brought arbitrarily close to the set of Lloyd's minima. Thus, the $NK$-means algorithm may be used to compute Lloyd's minima of the collective dataset up to arbitrary accuracy.