6 papers
Uniform-in-time propagation of chaos for consensus-based minimax algorithm
Erhan Bayraktar, Zhiyan Ding, Ibrahim Ekren +1
We study the large-population convergence of a consensus-based algorithm for the saddle point problem proposed by ArXiv: 2212.12334, establishing the uniform-in-time propagation of…
Viscosity and minimax solutions for path-dependent Hamilton-Jacobi equations in infinite dimensions and related differential games
Erhan Bayraktar, Mikhail Gomoyunov, Christian Keller
We establish new results for path-dependent Hamilton-Jacobi equations with nonlinear monotone, and coercive operators on Hilbert space, which were initially studied in Bayraktar an…
Comparison for semi-continuous viscosity solutions for second order PDEs on the Wasserstein space
Erhan Bayraktar, Ibrahim Ekren, Xihao He +1
In this paper, we prove a comparison result for semi-continuous viscosity solutions of a class of second-order PDEs in the Wasserstein space. This allows us to remove the Lipschitz…
Uniform-in-time weak propagation of chaos for consensus-based optimization
Erhan Bayraktar, Ibrahim Ekren, Hongyi Zhou
We study the uniform-in-time weak propagation of chaos for the consensus-based optimization (CBO) method on a bounded searching domain. We apply the methodology for studying long-t…
Viscosity Solutions of Fully second-order HJB Equations in the Wasserstein Space
Erhan Bayraktar, Hang Cheung, Ibrahim Ekren +3
In this paper, we show that the value functions of mean field control problems with common noise are the unique viscosity solutions to fully second-order Hamilton-Jacobi-Bellman eq…
Sequential optimal contracting in continuous time
Guillermo Alonso Alvarez, Erhan Bayraktar, Ibrahim Ekren +1
In this paper we study a principal-agent problem in continuous time with multiple lump-sum payments (contracts) paid at different deterministic times. We reduce the non-zero sum St…