A Relative Value Iteration Algorithm for Non-degenerate Controlled Diffusions

Abstract

The ergodic control problem for a non-degenerate controlled diffusion controlled through its drift is considered under a uniform stability condition that ensures the well-posedness of the associated Hamilton-Jacobi-Bellman (HJB) equation. A nonlinear parabolic evolution equation is then proposed as a continuous time continuous state space analog of White's `relative value iteration' algorithm for solving the ergodic dynamic programming equation for the finite state finite action case. Its convergence to the solution of the HJB equation is established using the theory of monotone dynamical systems and also, alternatively, by using the theory of reverse martingales.

17 pages

References in corpus (1)

• Subgeometric ergodicity of strong Markov processes

Cited by in corpus (4)

• On Solutions of Mean Field Games with Ergodic Cost
• Convergence of The Relative Value Iteration for the Ergodic Control Problem of Nondegenerate Diffusions under Near-Monotone Costs
• Relative Value Iteration for Stochastic Differential Games
• Yet again on iteration improvement for averaged expected cost control for 1D ergodic diffusions