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We study stochastic team problems with static information structure where weassume controllers have linear information and quadratic cost but allow thenoise to be from a non-Gaussian class. When the noise is Gaussian, it is wellknown that these problems admit linear optimal controllers. We show that forsuch linear-quadratic static teams with any log-concave noise, if the length ofthe noise or data vector becomes large compared to the size of the team andtheir observations, then linear strategies approach optimality for `most'problems. The quality of the approximation improves as length of the noisevector grows and the class of problems for which the approximation isasymptotically not exact approaches a set of measure zero. We show that if theoptimal strategies for problems with log-concave noise converge pointwise, theydo so to the (linear) optimal strategy for the problem with Gaussian noise. Andwe derive an asymptotically tight error bound on the difference between theoptimal cost for the non-Gaussian problem and the best cost obtained underlinear strategies.

Near-Optimality of Linear Strategies for Static Teams with `Big' Non-Gaussian Noise