  Decentralized stochastic control problems with local information involve
problems where multiple agents and subsystems which are coupled via dynamics
and/or cost are present. Typically, however, the dynamics of such couplings is
complex and difficult to precisely model, leading to questions on robustness in
control design. Additionally, when such a coupling can be modeled, the problem
arrived at is typically challenging and non-convex, due to decentralization of
information. In this paper, we develop a robustness framework for optimal
decentralized control of interacting agents, where we show that a decentralized
control problem with interacting agents can be robustly designed by considering
a risk-sensitive version of non-interacting agents/particles. This leads to a
tractable robust formulation where we give a bound on the value of the cost
function in terms of the risk-sensitive cost function for the non-interacting
case plus a term involving the ``strength" of the interaction as measured by
relative entropy. We will build on Gaussian measure theory and an associated
variational equality. A particular application includes mean-field models
consisting of (a generally large number of) interacting agents which are often
hard to solve for the case with small or moderate numbers of agents, leading to
an interest in effective approximations and robustness. By adapting a
risk-sensitivity parameter, we also robustly control a non-symmetrically
interacting problem with mean-field cost by one which is symmetric with a
risk-sensitive criterion, and in the limit of small interactions, show the
stability of optimal solutions to perturbations.
