## Markovian Decision Processes with Uncertain Transition Matrices Or/and Probabilistic Observation of States |

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arguments similar assumed asymptotically Bayes Bayesian formulation Coefficient of optimism considered continuous function contraction mapping convex criteria decision maker decision problem decision tree denote described Discount factor distribution dynamic programming expected discounted return expected immediate reward expected return finite number form of analysis game theoretic formulation Hence horizon problem implicit enumeration algorithm jeS2 linear program lower bounds MARKOVIAN DECISION PROCESSES Markovian sequential decision max-max policy max-min maximize mixed strategy Number of decisions optimal policy optimum decision partitioned policy iteration algorithm probabilistic observation probability density probability vector problem procedure Proof pure strategy selected sequence of decisions set of feasible similar to Prop solve stationary policy stochastic game stochastic matrix strategy strict inequality holds suboptimal policies successive approximation tion total expected discounted transition matrix uncertainty transition probability rows upper and lower upperbound