用生成函数判定MDP的矩最优策略

Use the Generating Function to Determinate the Moments—Optimality for the MDP

本文引入了策略的生成函数,利用此函数来判定一个策略是否是矩最优策略。证明了π是矩最优策略的充分必要条件是它的生成函数M(π,x)等于M~*(x),特别是得出了π是矩最优策略的充分条件是M(π,x)等于(?)~*(x)。后一结论对于判定矩最优策略有较大的实用价值。

In this paper we establish a generating function of a policy to determinate the oments—optimality of a policy. We have proved that a policy is of moments—optimality if only f its generating function M(π, x) is equal to the funtion M~*(x)and that a policy is of oments—optimality when its generating function M(π, x) is equal to the function (?)~*(x). In special he later result is more useful to determinate the moments—optimality of a policy.