Maximum likelihood estimation of discrete control processes
Maximum likelihood estimation of discrete control processes
复制标题
离散控制过程的最大似然估计
DOI：
10.1137/0326056
复制
发表时间：
1988
影响因子：
2.2
通讯作者：
John Rust
中科院分区：
文献类型：
--
作者：
John Rust
考虑下面的“逆随机控制”问题。一个统计学家观察一个受控随机过程$\{ d_t，x_t \} $的实现，该过程由一系列状态$x_t$和一个智能体在时间$t = 1，\cdots，T$的决策$d_t$组成。零假设是代理的行为是从马尔可夫决策问题的解决方案中产生的。逆问题是使用数据$\{ d_t，x_t \} $来回溯并“揭示”主体的目标函数U，以及他对状态变量p的运动规律的信念。这个问题由于统计学家通常只观察主体观察到的状态变量$（x_t，\eta _t）$的子集$x_t$而变得复杂。本文制定的逆问题作为一个问题的统计推断，明确占未观察到的状态变量$\eta _t $，以产生一个非退化和内部一致的统计模型。具体地说，函数U和p被假定依赖于u的向量。
Consider the following “inverse stochastic control” problem. A statistician observes a realization of a controlled stochastic process $\{ d_t ,x_t \} $ consisting of the sequence of states $x_t$, and decisions $d_t$ of an agent at times $t = 1, \cdots ,T$. The null hypothesis is that the agent’s behavior is generated from the solution to a Markovian decision problem. The inverse problem is to use the data $\{ d_t ,x_t \} $ to go backward and “uncover” the agent's objective function U, and his beliefs about the law of motion of the state variables p. The problem is complicated by the fact that the statistician generally only observes a subset $x_t$ of the state variables $(x_t ,\eta _t )$ observed by the agent. This paper formulates the inverse problem as a problem of statistical inference, explicitly accounting for unobserved state variables$\eta _t $, in order to produce a nondegenerate and internally consistent statistical model. Specifically, the functions U and p are assumed to depend on a vector of u...