17 citations · 30 across the 11 of their papers we have counts for
12 papers
Neural feedback approximation for stochastic control with degenerate diffusions: error estimates and numerical analysis
Olivier Bokanowski, Jean-François Chassagneux, Marco Scaratti +1
We study finite-horizon stochastic optimal control problems and approximate the resulting time-discrete formulation by a direct policy-learning problem over neural-network feedback…
Numerical Approximation for Path-Dependent McKean-Vlasov Control with Non-Asymptotic Error Estimates
Olivier Bokanowski, Jean-Francois Chassagneux, Xinyu Li +1
Path-dependent McKean--Vlasov (MKV) control models large interacting populations with history-dependent dynamics and costs. This paper develops a unified approximation-and-learning…
Solving Hamilton-Jacobi equations by residual minimization of monotone finite-difference discretizations
Olivier Bokanowski, Carlos Esteve-Yagüe, Richard Tsai
We introduce a method for solving Hamilton--Jacobi equations, both inviscid and viscous, by minimizing the squared residuals of monotone finite-difference discretizations on grids…
Representation results and error estimates for differential games with applications using neural networks
Olivier Bokanowski, Xavier Warin
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 estimat…
Neural networks for first order HJB equations and application to front propagation with obstacle terms
Olivier Bokanowski, Xavier Warin, Averil Prost
We consider a deterministic optimal control problem with a maximum running cost functional, in a finite horizon context, and propose deep neural network approximations for Bellman'…
Computation of avoidance regions for driver assistance systems by using a Hamilton-Jacobi approach
Ilaria Xausa, Robert Baier, Olivier Bokanowski +1
We consider the problem of computing safety regions, modeled as nonconvex backward reachable sets, for a nonlinear car collision avoidance model with time-dependent obstacles. The…
Stability and convergence of second order backward differentiation schemes for parabolic Hamilton-Jacobi-Bellman equations
Olivier Bokanowski, Athena Picarelli, Christoph Reisinger
We study a second order BDF (Backward Differentiation Formula) scheme for the numerical approximation of parabolic HJB (Hamilton-Jacobi-Bellman) equations. The scheme under conside…
Backward Differentiation Formula finite difference schemes for diffusion equations with an obstacle term
Olivier Bokanowski, Kristian Debrabant
Finite difference schemes, using Backward Differentiation Formula (BDF), are studied for the approximation of one-dimensional diffusion equations with an obstacle term, of the form…
High-order filtered schemes for time-dependent second order HJB equations
Olivier Bokanowski, Athena Picarelli, Christoph Reisinger
In this paper, we present and analyse a class of "filtered" numerical schemes for second order Hamilton-Jacobi-Bellman equations. Our approach follows the ideas introduced in B.D.…
Semi-Lagrangian discontinuous Galerkin schemes for some first and second-order partial differential equations
Olivier Bokanowski, Giorevinus Simarmata
Explicit, unconditionally stable, high-order schemes for the approximation of some first- andsecond-order linear, time-dependent partial differential equations (PDEs) are proposed.…
An efficient filtered scheme for some first order Hamilton-Jacobi-Bellman equations
Olivier Bokanowski, Maurizio Falcone, Smita Sahu
We introduce a new class of "filtered" schemes for some first order non-linear Hamilton-Jacobi-Bellman equations. The work follows recent ideas of Froese and Oberman (SIAM J. Numer…
Convergence of discontinuous Galerkin schemes for front propagation with obstacles
Olivier Bokanowski, Yingda Cheng, Chi-Wang Shu
We study semi-Lagrangian discontinuous Galerkin (SLDG) and Runge-Kutta discontinuous Galerkin (RKDG) schemes for some front propagation problems in the presence of an obstacle term…