Approximately optimal linear strategies for static teams with ‘big’ non-Gaussian noise

We study stochastic team problems with static information structure where we assume controllers have linear information and quadratic cost but allow the noise to be from a non-Gaussian class. When the noise is Gaussian, it is well known that these problems admit a linear optimal controller. We show that if the noise has a log-concave density, then for `most' problems of this kind, linear strategies are approximately optimal. The quality of the approximation improves as length of the noise vector grows. We show that if the optimal strategies for problems with log-concave noise converge pointwise, they converge to the (linear) optimal strategy for the problem with Gaussian noise. And we derive an error bound on the difference between the optimal cost for the non-Gaussian problem and the best cost obtained under linear strategies.