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 linear optimal controllers. We show that for such linear-quadratic static teams with any log-concave noise, if the length of the noise or data vector becomes large compared to the size of the team and their observations, then linear strategies approach optimality for “most” problems. The quality of the approximation improves as length of the noise vector grows and the class of problems for which the approximation is asymptotically not exact approaches a set of measure zero. We show that if the optimal strategies for problems with log-concave noise converge pointwise, they do so to the (linear) optimal strategy for the problem with Gaussian noise. And we derive an asymptotically tight error bound on the difference between the optimal cost for the non-Gaussian problem and the best cost obtained under linear strategies.

中文翻译：

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具有“大”非高斯噪声的静态团队的线性策略近乎最优

我们研究具有静态信息结构的随机团队问题，其中我们假设控制器具有线性信息和二次成本，但允许噪声来自非高斯类。当噪声为高斯噪声时，众所周知，这些问题允许线性最优控制器。我们表明，对于此类具有任何对数凹面噪声的线性二次静态团队，如果噪声或数据向量的长度与团队规模及其观察结果相比变大，则线性策略接近“大多数”问题的最优性。近似的质量随着噪声向量长度的增加而提高，并且近似不精确的问题类别渐近地接近一组测量值零。我们表明，如果对数凹面噪声问题的最佳策略逐点收敛，他们这样做是针对高斯噪声问题的（线性）最优策略。并且我们在非高斯问题的最佳成本与在线性策略下获得的最佳成本之间的差异上推导出渐近严格的误差界限。