When the optimal policy is independent of the initial state

A Markov decision process (MDP) is a popular model of sequential decision making, but its standard objective of minimizing cumulative cost is often inadequate, for example, to avoid the possibility of large loss. Risk-sensitive objective functions and constraints have thus been proposed for MDPs. Unlike the standard MDP, however, the optimal policy for some of these MDPs can depend on the initial states, so that the optimal policy can change over time. We show that an agent can surely incur larger cumulative cost by following the latest optimal policy at every state than by following other policies. We then establish sufficient conditions on the objective function and on the constraints for the optimal policies to be consistent between the initial states. We also show when the sufficient conditions are necessary. We discuss implications of our results to the MDPs that have been studied in the literature, stating whether their optimal policies depend on the initial states.

By: Takayuki Osogami and Tetsuro Morimura

Published in: RT0966 in 2015


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