10 papers
Kullback-Leibler Mirror-Prox for Measure-Valued Variational Inequalities and Mean-Field Equilibria
Erhan Bayraktar, Ibrahim Ekren, Lu Vy +1
We study the computation of static mean-field equilibria on a compact state space by formulating the equilibrium condition as a variational inequality over probability measures. We…
Quantitative Particle Approximation for Controlled Nonlinear Filtering
Erhan Bayraktar, Ibrahim Ekren, Xihao He +1
We estimate convergence rates of value functions for particle approximations of a controlled nonlinear filtering problem. The state is a McKean--Vlasov diffusion on the flat torus,…
A comparison principle for Wasserstein PDEs with state- and law-dependent common noise
Erhan Bayraktar, Ibrahim Ekren, Xihao He +1
We prove a comparison principle for a class of second-order Hamilton--Jacobi--Bellman equations on the Wasserstein space whose second-order term is generated by a general common-no…
Contracting a crowd of heterogeneous agents
Guillermo Alonso Alvarez, Erhan Bayraktar, Ibrahim Ekren
We study optimal contract design for large populations of heterogeneous agents whose actions generate network spillovers represented by an interaction function. In a linear-quadrat…
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…
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…