Gradient Convergence in Gradient methods with Errors
SIAM Journal on Optimization
IEEE/ACM Transactions on Networking (TON) - Special issue on networking and information theory
Geographic Gossip: Efficient Averaging for Sensor Networks
IEEE Transactions on Signal Processing
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We consider a distributed multi-agent network system where the goal is to minimize an objective function that can be written as the sum of component functions, each of which is known (with stochastic errors) to a specific network agent. We propose an asynchronous algorithm that is motivated by a random gossip scheme where each agent has a local Poisson clock. At each tick of its local clock, the agent averages its estimate with a randomly chosen neighbor and adjusts the average using the gradient of its local function that is computed with stochastic errors.We investigate the convergence properties of the algorithm for two different classes of functions: differentiable but not necessarily convex and convex but not necessarily differentiable.