依赖于历史的折扣半马氏决策规划

Semi-Markov Decision Process with Discount Factors Depend on History

研究无界报酬折扣半马氏决策规划问题．证明了： 策略π·＝（π１·，π２·，…πｎ·，π·ｎ＋１，…）是最优策略，则π１·（∞）及（π１·，π２·，…，πｎ·）（∞）对同一折扣因子函数也是最优的，对任给的整数ｎ≥１，在一定的条件下，πｎ·（∞）也是最优的；证明了若最优策略存在，必存在最优平稳策略；证明了ε最优平稳策略的存在性。

This paper discusses the semi-markov decision processes with discount factors depend on history. We show: If the strategy π*= (π·1, π2·, ...,πn·,...) is optimal, then π1·(∞)and (π1·, π2·,...,πn·)(∞) are optimal for any n≥1. Under certain conditions, if π·= (π1,π2,..., πn, ...) is optimal, then π·n(∞) is optimal for any n≥1. There are ε-optimal stationary strategies.