7 papers · 1 filter
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,…
Analytical Approach to Continuous-Time Causal Optimal Transport
Julio Backhoff, Erhan Bayraktar, Ibrahim Ekren +1
We study causal optimal transport in continuous time, with Markovian cost, between a finite-state Markov source and a diffusion target. By replacing the source with its conditional…
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…
Neural Operators Can Play Dynamic Stackelberg Games
Guillermo Alvarez, Ibrahim Ekren, Anastasis Kratsios +1
Dynamic Stackelberg games are a broad class of two-player games in which the leader acts first, and the follower chooses a response strategy to the leader's strategy. Unfortunately…