Distributed Learning for Cooperative Inference
This work addresses distributed parameter estimation in multi-agent systems, offering incremental improvements in convergence guarantees and computational efficiency for specific observation models.
The paper tackles cooperative inference among networked agents with unknown topology and private observations by proposing a new distributed learning algorithm based on a variational interpretation of Bayesian posterior and stochastic mirror descent. It shows that beliefs concentrate around the true parameter exponentially fast with explicit non-asymptotic convergence bounds and provides efficient algorithms for exponential family models.
We study the problem of cooperative inference where a group of agents interact over a network and seek to estimate a joint parameter that best explains a set of observations. Agents do not know the network topology or the observations of other agents. We explore a variational interpretation of the Bayesian posterior density, and its relation to the stochastic mirror descent algorithm, to propose a new distributed learning algorithm. We show that, under appropriate assumptions, the beliefs generated by the proposed algorithm concentrate around the true parameter exponentially fast. We provide explicit non-asymptotic bounds for the convergence rate. Moreover, we develop explicit and computationally efficient algorithms for observation models belonging to exponential families.