估计与控制中的对数凹对偶
Log-Concave Duality in Estimation and Control
摘要：
在本文中，我们推广的估计控制对偶存在于线性二次高斯设置。我们将这种对偶性扩展到系统状态的最大后验估计，其中测量和动力系统噪声是独立的对数凹随机变量。更一般地说，我们表明，一个问题，引起了凸惩罚噪声项将有一个双重控制问题。我们提供的条件强对偶举行，然后证明放松条件的分段线性二次的情况下。这些结果在非光滑密度估计问题中有应用，如对数凹极大似然密度估计问题。最后，我们用一个例子重建最优估计的解决方案的双重控制问题，这两种类型的问题之间的共享解决方案的方法有影响。
英文摘要：
In this paper we generalize the estimation-control duality that exists in the linear-quadratic-Gaussian setting. We extend this duality to maximum a posteriori estimation of the system's state, where the measurement and dynamical system noise are independent log-concave random variables. More generally, we show that a problem which induces a convex penalty on noise terms will have a dual control problem. We provide conditions for strong duality to hold, and then prove relaxed conditions for the piecewise linear-quadratic case. The results have applications in estimation problems with nonsmooth densities, such as log-concave maximum likelihood densities. We conclude with an example reconstructing optimal estimates from solutions to the dual control problem, which has implications for sharing solution methods between the two types of problems.
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