Decentralized online optimization with heterogeneous data sources
We consider stochastic optimization problems in decentralized settings, where a network of agents aims to learn decision variables which are optimal in terms of a global objective which depends on possibly heterogeneous streaming observations received at each node. Consensus optimization techniques implicitly operate on the hypothesis that each node aims to learn a common parameter vector, which is inappropriate for this context. Motivated by this observation, we formulate a problem where each agent minimizes a global objective while enforcing network proximity constraints that may encode correlation structures among the observations at each node. To solve this problem, we propose a decentralized stochastic saddle point algorithm inspired by Arrow and Hurwicz. We establish that under a constant step size regime the time average suboptimality and constraint violation are contained in a neighborhood whose radius vanishes with the iteration index. Further, the time average primal vectors converge to the optimal objective while satisfying the network proximity constraints. We apply this method to an online source localization problem and show it outperforms consensus based schemes.
2016 IEEE Global Conference on Signal and Information Processing (GlobalSIP)