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	多目的マルコフモデル	Multi-Objective Dynamic Programming
分野	シミュレーション	シミュレーション
系統	Process / pipeline	Process / pipeline
提唱年	2006	1957-1975
提唱者	Chatterjee, K., Majumdar, R., Henzinger, T. A. (formal; survey: Roijers et al.)	Extension of Bellman (1957); formalized by multiple authors from 1970s onward
種類	Stochastic sequential decision model with multiple objectives	Exact optimization — recursive multi-objective decomposition
原典	Roijers, D. M., Vamplew, P., Whiteson, S., & Dazeley, R. (2013). A survey of multi-objective sequential decision-making. Journal of Artificial Intelligence Research, 48, 67–113.	Bellman, R. (1957). Dynamic Programming. Princeton University Press, Princeton, NJ. ISBN: 9780691079516
別名	MOMDP, Multi-objective MDP, Multi-criteria Markov Decision Process, MO-Markov Model	MODP, Multi-criteria dynamic programming, Vector dynamic programming, Pareto dynamic programming
関連	5	5
概要	A Multi-objective Markov Model (MOMDP) extends classical Markov Decision Processes to settings where an agent must optimize several reward signals simultaneously. Instead of a single optimal policy, the model produces a Pareto-optimal set of policies, enabling decision-makers to navigate trade-offs between competing goals such as cost, risk, and throughput over time.	Multi-Objective Dynamic Programming (MODP) extends Bellman's classical dynamic programming to settings where a decision-maker must optimize several competing objectives simultaneously across a sequence of stages. Rather than a single optimal policy, it produces a Pareto-optimal set of policies — each representing a distinct trade-off profile — by propagating vector-valued value functions backward through the state space.