4 citations · 15 across the 18 of their papers we have counts for
19 papers
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…
Projected McKean--Vlasov Dynamics for Entropic Weak Optimal Transport
Nathan Sauldubois, Xin Zhang
Unlike classical optimal transport, weak transport costs depend nonlinearly on the conditional law of couplings. This feature is essential in problems involving barycenter, conditi…
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…
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…
Convergence Rate of Particle System for Second-order PDEs On Wasserstein Space
Erhan Bayraktar, Ibrahim Ekren, Xin Zhang
In this paper, we provide a convergence rate for particle approximations of a class of second-order PDEs on Wasserstein space. We show that, up to some error term, the infinite-dim…
Comparison of viscosity solutions for a class of second order PDEs on the Wasserstein space
Erhan Bayraktar, Ibrahim Ekren, Xin Zhang
We prove a comparison result for viscosity solutions of second order parabolic partial differential equations in the Wasserstein space. The comparison is valid for semisolutions th…
Stability and Sample Complexity of Divergence Regularized Optimal Transport
Erhan Bayraktar, Stephan Eckstein, Xin Zhang
We study stability and sample complexity properties of divergence regularized optimal transport (DOT). First, we obtain quantitative stability results for optimizers of DOT measure…
A PDE approach for regret bounds under partial monitoring
Erhan Bayraktar, Ibrahim Ekren, Xin Zhang
In this paper, we study a learning problem in which a forecaster only observes partial information. By properly rescaling the problem, we heuristically derive a limiting PDE on Was…
A smooth variational principle on Wasserstein space
Erhan Bayraktar, Ibrahim Ekren, Xin Zhang
In this note, we provide a smooth variational principle on Wasserstein space by constructing a smooth gauge-type function using the sliced Wasserstein distance. This function is a…
Walsh Spider Diffusions as Time Changed Multi-parameter Processes
Erhan Bayraktar, Jingjie Zhang, Xin Zhang
Inspired by allocation strategies in multi-armed bandit model, we propose a pathwise construction of Walsh spider diffusions. For any infinitesimal generator on a star shaped graph…
Propagation of Chaos of Forward-Backward Stochastic Differential Equations with Graphon Interactions
Erhan Bayraktar, Ruoyu Wu, Xin Zhang
In this paper, we study graphon mean field games using a system of forward-backward stochastic differential equations. We establish the existence and uniqueness of solutions under…
Solvability of Infinite horizon McKean-Vlasov FBSDEs in Mean Field Control Problems and Games
Erhan Bayraktar, Xin Zhang
In this paper, we show existence and uniqueness of solutions of the infinite horizon McKean-Vlasov FBSDEs using two different methods, which lead to two different sets of assumptio…
K-core in percolated dense graph sequences
Erhan Bayraktar, Suman Chakraborty, Xin Zhang
We determine the size of -core in a large class of dense graph sequences. Let be a sequence of undirected, -vertex graphs with edge weights $\{a^n_{i,j}\}_{i,j \in [n]}…
Malicious Experts versus the multiplicative weights algorithm in online prediction
Erhan Bayraktar, H. Vincent Poor, Xin Zhang
We consider a prediction problem with two experts and a forecaster. We assume that one of the experts is honest and makes correct prediction with probability at each round. The…
Finite-Time 4-Expert Prediction Problem
Erhan Bayraktar, Ibrahim Ekren, Xin Zhang
We explicitly solve the nonlinear PDE that is the continuous limit of dynamic programming of \emph{expert prediction problem} in finite horizon setting with experts. The \emp…
On non-uniqueness in mean field games
Erhan Bayraktar, Xin Zhang
We analyze an -player game and the corresponding mean field game with state space . The transition rate of -th player is the sum of his control plus a minimu…
Embedding of Walsh Brownian Motion
Erhan Bayraktar, Xin Zhang
Let be a Walsh Brownian motion with spinning measure . Suppose is a probability measure on . We characterize all the such that is a stopping di…
Transport plans with domain constraints
Erhan Bayraktar, Xin Zhang, Zhou Zhou
This paper focuses on martingale optimal transport problems when the martingales are assumed to have bounded quadratic variation. First, we give a result that characterizes the exi…