Fetching the paper…
Reading the bibliography…
We propose a new algorithm for solving parabolic partial differential equations (PDEs) and backward stochastic differential equations (BSDEs) in high dimension, by making an analogy between the BSDE and reinforcement learning with the gradient of the solution playing the role of the policy function, and the loss function given by the error between the prescribed terminal condition and the solution of the BSDE.
Dynamic programming
Bellman, R · 1957
Earlier work this paper cites.
Adapted solution of a backward stochastic differential equation
Pardoux, É., and Peng, S. G · 1990
Earlier work this paper cites.
Probabilistic interpretation for systems of quasilinear parabolic partial differential equations
Peng, S. G · 1991
Earlier work this paper cites.
Backward stochastic differential equations and quasilinear parabolic partial differential equations
Pardoux, É., and Peng, S · 1992
Earlier work this paper cites.
Option pricing with differential interest rates
Bergman, Y. Z · 1995
Earlier work this paper cites.
Forward-backward stochastic differential equations and quasilinear parabolic PDEs
Pardoux, E., and Tang, S · 1999
Earlier work this paper cites.
A regression-based Monte Carlo method to solve backward stochastic differential equations
Gobet, E., Lemor, J.-P., and Warin, X · 2005
Earlier work this paper cites.
A forward scheme for backward SDEs
Bender, C., and Denk, R · 2007
Earlier work this paper cites.
Solving backward stochastic differential equations using the cubature method: Application to nonlinear pricing
Crisan, D., and Manolarakis, K · 2012
Earlier work this paper cites.
Nonlinear partial differential equations for scientists and engineers
Debnath, L · 2012
Earlier work this paper cites.
Counterparty risk valuation: a marked branching diffusion approach
Henry-Labordère, P · 2012
Cited alongside, same era.
Deep neural networks for acoustic modeling in speech recognition
Hinton, G. E., Deng, L., Yu, D., Dahl, G., Mohamed, A., Jaitly, N., Senior, A., Vanhoucke, V., Nguyen, P., Sainath, T., and Kingsbury, B · 2012
Cited alongside, same era.
Imagenet classification with deep convolutional neural networks
Krizhevsky, A., Sutskever, I., and Hinton, G. E · 2012
Cited alongside, same era.
A primal-dual algorithm for BSDEs
Bender, C., Schweizer, N., and Zhuo, J · 2014
Cited alongside, same era.
Simulation of BSDEs by Wiener chaos expansion
Briand, P., and Labart, C · 2014
Cited alongside, same era.
Deep learning
LeCun, Y., Bengio, Y., and Hinton, G · 2015
Later among the works it cites.
Numerical simulation of quadratic BSDEs
Chassagneux, J.-F., and Richou, A · 2016
Later among the works it cites.
Algorithms for overcoming the curse of dimensionality for certain Hamilton-Jacobi equations arising in control theory and elsewhere
Darbon, J., and Osher, S · 2016
Later among the works it cites.
Linear regression MDP scheme for discrete backward stochastic differential equations under general conditions
Gobet, E., and Turkedjiev, P · 2016
Later among the works it cites.
Deep Learning
Goodfellow, I., Bengio, Y., and Courville, A · 2016
Later among the works it cites.
Deep Learning Approximation for Stochastic Control Problems
Han, J., and E, W · 2016
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
Chassagneux, J.-F · 2014
Cited alongside, same era.
A numerical algorithm for a class of BSDEs via the branching process
Henry-Labordère, P., Tan, X., and Touzi, N · 2014
Cited alongside, same era.
Batch normalization: accelerating deep network training by reducing internal covariate shift
Ioffe, S., and Szegedy, C · 2015
Cited alongside, same era.
Adam: a method for stochastic optimization
Kingma, D., and Ba, J · 2015
Cited alongside, same era.
Later among the works it cites.
Branching diffusion representation of semilinear PDEs and Monte Carlo approximation
Henry-Labordère, P., Oudjane, N., Tan, X., Touzi, N., and Warin, X · 2016
Later among the works it cites.
E, W., Hutzenthaler, M., Jentzen, A., and Kruse, T · 2017
Closest in time.
Adaptive importance sampling in least-squares Monte Carlo algorithms for backward stochastic differential equations
Gobet, E., and Turkedjiev, P · 2017
Closest in time.