https://hal.science/hal-03792090Abeille, MarcMarcAbeilleCriteo AI Lab - Criteo [Paris]Bouchard, BrunoBrunoBouchardCEREMADE - CEntre de REcherches en MAthématiques de la DEcision - Université Paris Dauphine-PSL - PSL - Université Paris sciences et lettres - CNRS - Centre National de la Recherche ScientifiqueUniversité Paris Dauphine-PSL - PSL - Université Paris sciences et lettresCroissant, LorenzoLorenzoCroissantCEREMADE - CEntre de REcherches en MAthématiques de la DEcision - Université Paris Dauphine-PSL - PSL - Université Paris sciences et lettres - CNRS - Centre National de la Recherche ScientifiqueUniversité Paris Dauphine-PSL - PSL - Université Paris sciences et lettresCriteo AI Lab - Criteo [Paris]Diffusive limit approximation of pure jump optimal ergodic control problemsHAL CCSD2022[MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC]Croissant, Lorenzo2022-09-29 17:45:552022-10-01 03:46:422022-09-30 09:46:47enPreprints, Working Papers, ...https://hal.science/hal-03792090/documentapplication/pdf1Motivated by the design of fast reinforcement learning algorithms, we study the diffusive limit of a class of pure jump ergodic stochastic control problems. We show that, whenever the intensity of jumps is large enough, the approximation error is governed by the Hölder continuity of the Hessian matrix of the solution to the limit ergodic partial differential equation. This extends to this context the results of [1] obtained for finite horizon problems. We also explain how to construct a first order error correction term under appropriate smoothness assumptions. Finally, we quantify the error induced by the use of the Markov control policy constructed from the numerical finite difference scheme associated to the limit diffusive problem, this seems to be new in the literature and of its own interest. This approach permits to reduce very significantly the numerical resolution cost.