Private Learning on Networks: Part II

This paper considers a distributed multi-agent optimization problem, with the global objective consisting of the sum of local objective functions of the agents. The agents solve the optimization problem using local computation and communication between adjacent agents in the network. We present two randomized iterative algorithms for distributed optimization. To improve privacy, our algorithms add "structured" randomization to the information exchanged between the agents. We prove deterministic correctness (in every execution) of the proposed algorithms despite the information being perturbed by noise with non-zero mean. We prove that a special case of a proposed algorithm (called function sharing) preserves privacy of individual polynomial objective functions under a suitable connectivity condition on the network topology.

Distributed Optimization for Client-Server Architecture with Negative Gradient Weights

Availability of both massive datasets and computing resources have made machine learning and predictive analytics extremely pervasive. In this work we present a synchronous algorithm and architecture for distributed optimization motivated by privacy requirements posed by applications in machine learning. We present an algorithm for the recently proposed multi-parameter-server architecture. We consider a group of parameter servers that learn a model based on randomized gradients received from clients. Clients are computational entities with private datasets (inducing a private objective function), that evaluate and upload randomized gradients to the parameter servers. The parameter servers perform model updates based on received gradients and share the model parameters with other servers. We prove that the proposed algorithm can optimize the overall objective function for a very general architecture involving $C$ clients connected to $S$ parameter servers in an arbitrary time varying topology and the parameter servers forming a connected network.

Private Learning on Networks

Continual data collection and widespread deployment of machine learning algorithms, particularly the distributed variants, have raised new privacy challenges. In a distributed machine learning scenario, the dataset is stored among several machines and they solve a distributed optimization problem to collectively learn the underlying model. We present a secure multi-party computation inspired privacy preserving distributed algorithm for optimizing a convex function consisting of several possibly non-convex functions. Each individual objective function is privately stored with an agent while the agents communicate model parameters with neighbor machines connected in a network. We show that our algorithm can correctly optimize the overall objective function and learn the underlying model accurately. We further prove that under a vertex connectivity condition on the topology, our algorithm preserves privacy of individual objective functions. We establish limits on the what a coalition of adversaries can learn by observing the messages and states shared over a network.

Distributed Optimization of Convex Sum of Non-Convex Functions

We present a distributed solution to optimizing a convex function composed of several non-convex functions. Each non-convex function is privately stored with an agent while the agents communicate with neighbors to form a network. We show that coupled consensus and projected gradient descent algorithm proposed in [1] can optimize convex sum of non-convex functions under an additional assumption on gradient Lipschitzness. We further discuss the applications of this analysis in improving privacy in distributed optimization.