2 research outputs found
Distributed Learning with Infinitely Many Hypotheses
We consider a distributed learning setup where a network of agents
sequentially access realizations of a set of random variables with unknown
distributions. The network objective is to find a parametrized distribution
that best describes their joint observations in the sense of the
Kullback-Leibler divergence. Apart from recent efforts in the literature, we
analyze the case of countably many hypotheses and the case of a continuum of
hypotheses. We provide non-asymptotic bounds for the concentration rate of the
agents' beliefs around the correct hypothesis in terms of the number of agents,
the network parameters, and the learning abilities of the agents. Additionally,
we provide a novel motivation for a general set of distributed Non-Bayesian
update rules as instances of the distributed stochastic mirror descent
algorithm.Comment: Submitted to CDC201
Nonasymptotic Convergence Rates for Cooperative Learning Over Time-Varying Directed Graphs
We study the problem of distributed hypothesis testing with a network of
agents where some agents repeatedly gain access to information about the
correct hypothesis. The group objective is to globally agree on a joint
hypothesis that best describes the observed data at all the nodes. We assume
that the agents can interact with their neighbors in an unknown sequence of
time-varying directed graphs. Following the pioneering work of Jadbabaie,
Molavi, Sandroni, and Tahbaz-Salehi, we propose local learning dynamics which
combine Bayesian updates at each node with a local aggregation rule of private
agent signals. We show that these learning dynamics drive all agents to the set
of hypotheses which best explain the data collected at all nodes as long as the
sequence of interconnection graphs is uniformly strongly connected. Our main
result establishes a non-asymptotic, explicit, geometric convergence rate for
the learning dynamic