A note on impulsive control of Feller processes with costly information

Dariusz Gątarek

Displaying similar documents to “A note on impulsive control of Feller processes with costly information”

On self-optimizing control of Markov processes

Petr Mandl (1985)

Banach Center Publications

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Estimates of stability of Markov control processes with unbounded costs

Evgueni I. Gordienko, Francisco Salem-Silva (2000)

Kybernetika

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For a discrete-time Markov control process with the transition probability $p$ , we compare the total discounted costs $V_{β}$ $(π_{β})$ and $V_{β} ({\tilde{π}}_{β})$ , when applying the optimal control policy $π_{β}$ and its approximation ${\tilde{π}}_{β}$ . The policy ${\tilde{π}}_{β}$ is optimal for an approximating process with the transition probability $\tilde{p}$ . A cost per stage for considered processes can be unbounded. Under certain ergodicity assumptions we establish the upper bound for the relative stability index $[V_{β} ({\tilde{π}}_{β}) - V_{β} (π_{β})] / V_{β} (π_{β})$ . This bound does not depend...

Ergodic control of partially observed Markov processes with equivalent transition probabilities

Łukasz Stettner (1993)

Applicationes Mathematicae

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Optimal control with long run average cost functional of a partially observed Markov process is considered. Under the assumption that the transition probabilities are equivalent, the existence of the solution to the Bellman equation is shown, with the use of which optimal strategies are constructed.

Adaptive control for discrete-time Markov processes with unbounded costs: Discounted criterion

Evgueni I. Gordienko, J. Adolfo Minjárez-Sosa (1998)

Kybernetika

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We study the adaptive control problem for discrete-time Markov control processes with Borel state and action spaces and possibly unbounded one-stage costs. The processes are given by recurrent equations $x_{t + 1} = F (x_{t}, a_{t}, ξ_{t}), t = 0, 1, ...$ with i.i.d. $ℜ^{k}$ -valued random vectors $ξ_{t}$ whose density $ρ$ is unknown. Assuming observability of $ξ_{t}$ we propose the procedure of statistical estimation of $ρ$ that allows us to prove discounted asymptotic optimality of two types of adaptive policies used early for the processes with bounded...