We consider the problem of estimating a probability distribution that
maximizes the entropy while satisfying a finite number of moment constraints,
possibly corrupted by noise. Based on duality of convex programming, we present
a novel approximation scheme using a smoothed fast gradient method that is
equipped with explicit bounds on the approximation error. We further
demonstrate how the presented scheme can be used for approximating the chemical
master equation through the zero-information moment closure method, and for an
approximate dynamic programming approach in the context of constrained Markov
decision processes with uncountable state and action spaces.

本文提出了一个基于凸规划对偶性的新的近似方案，使用平滑的快速梯度方法来估计最大化熵的概率分布，同时满足一定数量的被噪声污染的时刻约束，进一步阐述了如何通过该方案来近似化学主方程和解决具有无穷状态和动作空间的约束马尔可夫决策过程的问题。

广义最大熵估计

Generalized maximum entropy estimation

We use the method of Maximum (relative) Entropy to process information in the
form of observed data and moment constraints. The generic "canonical" form of
the posterior distribution for the problem of simultaneous updating with data
and moments is obtained. We discuss the general problem of non-commuting
constraints, when they should be processed sequentially and when
simultaneously. As an illustration, the multinomial example of die tosses is
solved in detail for two superficially similar but actually very different
problems.

利用最大熵方法处理观测数据和矩约束，得到了同步更新问题的后验分布的通用 “规范” 形式，并讨论了非交换约束的一般问题，以及两个外表相似但实际上非常不同的问题的多项式实例的示例详细解法。