Time Consistency Issue in Multi-Objective Optimization†
Time Consistency Issue in Multi-Objective Optimization†
复制标题
多目标优化中的时间一致性问题†
DOI：
10.1002/mcda.480
复制
发表时间：
2011
期刊：
影响因子：
--
通讯作者：
Shushang Zhu
中科院分区：
文献类型：
--
作者：
Duan Li;Xiangyu Cui;Shushang Zhu
当应用Bellman最优性原理的条件成立时，在初始时刻由动态规划得到的预承诺最优策略是时间一致的，即对于以后阶段产生的任何状态，该策略仍然是最优的。在具有一般可分结构的多目标优化问题中，由多目标动态规划得到的预承诺最优策略在效率上是时间一致的，即初始时刻得到的策略对以后的任何可能状态都是有效的，尽管一般情况下不是时间一致的.然而，当多目标动态优化问题在多目标动态规划意义下不可分离时，所得到的预承诺策略在效率上不具有时间一致性，如本文所研究的多期均值-方差投资组合选择问题，从而导致一些非理性的决策行为.这一现象的揭示认识到时间一致性问题的重要性，并呼吁我们的注意力，以建立更合适的多目标优化的决策准则。版权所有© 2011约翰威利父子有限公司.
When the conditions for applying Bellman's principle of optimality hold, the pre-committed optimal policy derived by dynamic programming at initial time is time consistent, that is, the policy remains to be optimal for any state resulted in at later stages. In multi-objective optimization with a general separable structure, the pre-committed optimal policy derived by multi-objective dynamic programming is time-consistent in efficiency, that is, the policy derived at initial time remains to be efficient for any possible state at later stages, albeit not time-consistent in general. However, when a multi-objective dynamic optimization problem is not separable in the sense of multi-objective dynamic programming, the derived pre-committed policy is not time-consistent in efficiency, as witnessed in the multi-period mean-variance portfolio selection problem studied in this paper, thus leading to some irrational decision behaviours. This revealed phenomenon recognizes the importance of the time consistency issue and calls our attentions to construct more suitable decision criteria in multi-objective optimization. Copyright © 2011 John Wiley & Sons, Ltd.