Representation Results and Error Estimates for Differential Games with Applications Using Neural Networks

Olivier Bokanowski () and Xavier Warin ()
Additional contact information
Olivier Bokanowski: Université Paris Cité
Xavier Warin: EDF R&D & FiME

Dynamic Games and Applications, 2025, vol. 15, issue 2, No 5, 417-453

Abstract: Abstract We study deterministic optimal control problems for differential games with finite horizon. We propose new approximations of the strategies in feedback form and show error estimates and a convergence result of the value in some weak sense for one of the formulations. This result applies in particular to neural network approximations. This work follows some ideas introduced in Bokanowski, Prost and Warin (PDEA, 2023) for deterministic optimal control problems, yet with a simplified approach for the error estimates, which allows to consider a global optimization scheme instead of a time-marching scheme. We also give a new approximation result between the continuous and the semi-discrete optimal control value in the game setting, improving the classical convergence order $$O({\Delta t}^{1/2})$$ O ( Δ t 1 / 2 ) to $$O({\Delta t})$$ O ( Δ t ) , under some assumptions on the dynamical system. Numerical examples are performed on elementary academic problems related to backward reachability, with exact analytic solutions given, as well as a two-player game in the presence of state constraints, using stochastic gradient-type algorithms to deal with the minimax problem.

Keywords: Differential games; Two-player games; Neural networks; Deterministic optimal control; Dynamic programming principle; Hamilton Jacobi Isaacs equation; Front propagation; Level sets; Non-anticipative strategies (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s13235-024-00597-0 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:dyngam:v:15:y:2025:i:2:d:10.1007_s13235-024-00597-0

Ordering information: This journal article can be ordered from
http://www.springer.com/economics/journal/13235

DOI: 10.1007/s13235-024-00597-0

Access Statistics for this article

Dynamic Games and Applications is currently edited by Georges Zaccour

More articles in Dynamic Games and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().