Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userMarkov Decision Processes with Incomplete Information and Semi-Uniform Feller Transition Probabilities
107
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
This paper deals with control of partially observable discrete-time stochastic systems. It introduces and studies the class of Markov Decision Processes with Incomplete information and with semi-uniform Feller transition probabilities. The important feature of this class of models is that the classic reduction of such a model with incomplete observation to the completely observable Markov Decision Process with belief states preserves semi-uniform Feller continuity of transition probabilities. Under mild assumptions on cost functions, optimal policies exist, optimality equations hold, and value iterations converge to optimal values for this class of models. In particular, for Partially Observable Markov Decision Processes the results of this paper imply new and generalize several known sufficient conditions on transition and observation probabilities for the existence of optimal policies, validity of optimality equations, and convergence of value iterations.
rate research
Read More
This paper studies average-cost Markov decision processes with semi-uniform Feller transition probabilities. This class of MDPs was recently introduced by the authors to study MDPs with incomplete information. This paper studies the validity of optimality inequalities, the existence of optimal policies, and the approximations of optimal policies by policies optimizing total discounted costs.
This work considers two-player zero-sum semi-Markov games with incomplete information on one side and perfect observation. At the beginning, the system selects a game type according to a given probability distribution and informs to Player 1 only. After each stage, the actions chosen are observed by both players before proceeding to the next stage. Firstly, we show the existence of the value function under the expected discount criterion and the optimality equation. Secondly, the existence and iterative algorithm of the optimal policy for Player 1 are introduced through the optimality equation of value function. Moreove, About the optimal policy for the uninformed Player 2, we define the auxiliary dual games and construct a new optimality equation for the value function in the dual games, which implies the existence of the optimal policy for Player 2 in the dual game. Finally, the existence and iterative algorithm of the optimal policy for Player 2 in the original game is given by the results of the dual game.
We study a two-player, zero-sum, stochastic game with incomplete information on one side in which the players are allowed to play more and more frequently. The informed player observes the realization of a Markov chain on which the payoffs depend, while the non-informed player only observes his opponents actions. We show the existence of a limit value as the time span between two consecutive stages vanishes; this value is characterized through an auxiliary optimization problem and as the solution of an Hamilton-Jacobi equation.
This paper studies transition probabilities from a Borel subset of a Polish space to a product of two Borel subsets of Polish spaces. For such transition probabilities it introduces and studies semi-uniform Feller continuity and a weaker property called WTV-continuity. This paper provides several equivalent definitions of semi-uniform Feller continuity and describes the preservation property of WTV-continuity under integration. The motivation for this study came from the theory of Markov decision processes with incomplete information, and this paper provides fundamental results useful for this theory.
We study discrete-time discounted constrained Markov decision processes (CMDPs) on Borel spaces with unbounded reward functions. In our approach the transition probability functions are weakly or set-wise continuous. The reward functions are upper semicontinuous in state-action pairs or semicontinuous in actions. Our aim is to study models with unbounded reward functions, which are often encountered in applications, e.g., in consumption/investment problems. We provide some general assumptions under which the optimization problems in CMDPs are solvable in the class of stationary randomized policies. Then, we indicate that if the initial distribution and transition probabilities are non-atomic, then using a general purification result of Feinberg and Piunovskiy, stationary optimal policies can be deterministic. Our main results are illustrated by five examples.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
