Conventional algorithms for solving Markov decision processes (MDPs) become intractable a large finite state and action spaces. Several studies have been devoted to this issue, but most of them only treat infinite-horizon MDPs. This paper is one the first works deal with non-stationary finite-horizon MDPs by proposing new decomposition approach, which consists in partitioning problem into small...

We develop the dynamic programming approach for a family of infinite horizon boundary control problems with linear state equation and convex cost. We prove that the value function of the problem is the unique regular solution of the associated stationary Hamilton–Jacobi–Bellman equation and use this to prove existence and uniqueness of feedback controls. The idea of studying this kind of proble...

curvature at the horizon away from the Hawking temperature O. B. Zaslavskii Department of Physics, Kharkov State University, Svobody Sq.4, Kharkov 310077, Ukraine E-mail: [email protected] It is shown that static solutions with a finite curvature at the horizon may exist in dilaton gravity at temperatures T 6= TH (including T = 0) where TH is the Hawking one. Hawking radiation is absent and the s...