TY - JOUR
T1 - Extended mean field control problems
T2 - Stochastic maximum principle and transport perspective
AU - Acciaio, Beatrice
AU - Backhoff-Veraguas, Julio
AU - Carmona, René
N1 - Funding Information:
The third author was partially supported by National Science Foundation grant DMS-1716673 and by Army Research Ofce grant W911NF-17-1-0578.
Publisher Copyright:
© 2019 Society for Industrial and Applied Mathematics
PY - 2019
Y1 - 2019
N2 - We study mean feld stochastic control problems where the cost function and the state dynamics depend upon the joint distribution of the controlled state and the control process. We prove suitable versions of the Pontryagin stochastic maximum principle, both in necessary and in sufcient forms, which extend the known conditions to this general framework. We suggest a variational approach for a weak formulation of these control problems. We show a natural connection between this weak formulation and optimal transport on path space, which inspires a novel discretization scheme.
AB - We study mean feld stochastic control problems where the cost function and the state dynamics depend upon the joint distribution of the controlled state and the control process. We prove suitable versions of the Pontryagin stochastic maximum principle, both in necessary and in sufcient forms, which extend the known conditions to this general framework. We suggest a variational approach for a weak formulation of these control problems. We show a natural connection between this weak formulation and optimal transport on path space, which inspires a novel discretization scheme.
KW - Casual transport plans
KW - Controlled McKean-Vlasov SDEs
KW - Mean-feld interaction
KW - Pontryagin principle
UR - http://www.scopus.com/inward/record.url?scp=85077121759&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85077121759&partnerID=8YFLogxK
U2 - 10.1137/18M1196479
DO - 10.1137/18M1196479
M3 - Article
AN - SCOPUS:85077121759
VL - 57
SP - 3666
EP - 3693
JO - SIAM Journal on Control and Optimization
JF - SIAM Journal on Control and Optimization
SN - 0363-0129
IS - 6
ER -