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Learning Optimal Control via Forward and Backward Stochastic Differential Equations
[article]
2016
arXiv
pre-print
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In this paper we present a novel sampling-based numerical scheme designed to solve a certain class of stochastic optimal control problems, utilizing forward and backward stochastic differential equations ...
The modified scheme is capable of learning the optimal control without requiring an initial guess. ...
The latter, being a linear PDE, enables the use of the linear Feynman-Kac formula, which relates certain linear backward PDEs to forward stochastic differential equations (SDEs). ...
arXiv:1509.02195v2
fatcat:hvscxhazbjaxbmmzeqtc7yctxa
Neural Differential Equations as a Basis for Scientific Machine Learning (SciML)
[article]
2020
figshare.com
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Problems such as optimal control and automated learning of differential equation models will be reduced to training problems on neural differential equations. ...
Additionally, deep learning embedded within backwards stochastic differential equations has been shown to be an effective tool for solving high-dimensional partial differential equations, like the Hamilton-Jacobian-Bellman ...
Learn the unknown function via neural network. ALLOW FOR AUTOMATICALLY LEARNING MODELS, USING KNOWN EQUATIONS AS A PRIOR SOLVE OPTIMAL CONTROL PROBLEMS ACCELERATE THE SOLUTION OF PDES SOLVE PDES ...
doi:10.6084/m9.figshare.12751955.v1
fatcat:zhwjvt23tfhmjljetsfobsv5q4
Differentiable Implicit Soft-Body Physics
[article]
2021
arXiv
pre-print
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We demonstrate the effectiveness of our differentiable simulator in policy optimization for locomotion tasks and show that it achieves better sample efficiency than model-free reinforcement learning. ...
these derivatives automatically and in a matrix-free fashion via reverse-mode automatic differentiation. ...
Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation. ...
arXiv:2102.05791v3
fatcat:uxmj5ukfvjaajkznqvlszu4x6a
NOVAS: Non-convex Optimization via Adaptive Stochastic Search for End-to-End Learning and Control
[article]
2021
arXiv
pre-print
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2020 pre-print arXiv:2006.11992v2 fatcat:g6socas65zbh7mfzsjz3fiasxeOther Versions
optimal control applications. ...
This operation is differentiable and does not obstruct the passing of gradients during backpropagation, thus enabling us to incorporate it as a component in end-to-end learning. ...
The transition from a PDE formulation to a trainable neural network is done via the concept of a system of Forward-Backward Stochastic Differential Equations (FBSDEs). ...
arXiv:2006.11992v3
fatcat:r4tgjunt7nhznbpncjocvvxmk4
Scalable Gradients for Stochastic Differential Equations
[article]
2020
arXiv
pre-print
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We generalize this method to stochastic differential equations, allowing time-efficient and constant-memory computation of gradients with high-order adaptive solvers. ...
Specifically, we derive a stochastic differential equation whose solution is the gradient, a memory-efficient algorithm for caching noise, and conditions under which numerical solutions converge. ...
We also thank Guodong Zhang, Kevin Swersky, Chris Rackauckas, and members of the Vector Institute for helpful comments on an early draft of this paper. ...
arXiv:2001.01328v6
fatcat:k6q44v5w5zg4jkrdn2wm32mrdi
Table of Contents
2021
IEEE Transactions on Automatic Control
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of a Probability Measure by Forward-Backward Stochastic Differential Equation Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...
Hadjicostis and A. D. Domínguez-García 5637 Hamilton-Jacobi-Bellman Equation for Control Systems With Friction . . . . . . . . . . . . . . . . . . . F. Tedone and M. ...
doi:10.1109/tac.2021.3127403
fatcat:gd2yja5fynclpbtib4wjosstlu
Mean field stochastic games: Convergence, Q/H-learning and optimality
2011
Proceedings of the 2011 American Control Conference
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Using multidimensional diffusion processes, a general mean field convergence to coupled stochastic differential equation is given. ...
We characterize the mean field payoff optimality by solutions of a coupled system of backwardforward equations. ...
ACKNOWLEDGMENTS The author would like to thank three anonymous reviewers, the seminar audience at GERAD, UIUC and INRIA Hipercom and RAP for their interesting comments on a preliminary version of this ...
doi:10.1109/acc.2011.5991087
fatcat:66c4ox62dvhtdjfzjlqfhvyfb4
Deep ℒ^1 Stochastic Optimal Control Policies for Planetary Soft-landing
[article]
2021
arXiv
pre-print
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This is achieved by building off of recent work on deep Forward-Backward Stochastic Differential Equations (FBSDEs) and differentiable non-convex optimization neural-network layers based on stochastic ...
In this paper, we introduce a novel deep learning based solution to the Powered-Descent Guidance (PDG) problem, grounded in principles of nonlinear Stochastic Optimal Control (SOC) and Feynman-Kac theory ...
Solution using Forward and Backward Stochastic Differential Equations In this section, we describe our methodology to solve the L 1 stochastic optimal control problem described in equation (10) . ...
arXiv:2109.00183v1
fatcat:3wrtmixvnzbjhbbilh2bh3ucd4
A Neural Network Approach for Stochastic Optimal Control
[article]
2024
arXiv
pre-print
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2022 pre-print arXiv:2209.13104v1 fatcat:pr62v25qcffsbpcurzvh23iilyOther Versions
Our approach leverages insights from optimal control theory and the fundamental relation between semi-linear parabolic partial differential equations and forward-backward stochastic differential equations ...
To focus the sampling on relevant states during neural network training, we use the stochastic Pontryagin maximum principle (PMP) to obtain the optimal controls for the current value function estimate. ...
This can be achieved by using a nonlinear version of the Feynman-Kac lemma and replacing the HJB equation by a system of Forward-Backward Stochastic Differential Equations (FBSDEs); see, for example, ...
arXiv:2209.13104v3
fatcat:2ln7tybxuzf3pdtdgtkmtx6uiu
Neural Network Architectures for Stochastic Control using the Nonlinear Feynman-Kac Lemma
[article]
2019
arXiv
pre-print
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Our work is grounded on the nonlinear Feynman-Kac lemma and the fundamental connection between backward nonlinear partial differential equations and forward-backward stochastic differential equations. ...
Using these connections and results from our prior work on importance sampling for forward-backward stochastic differential equations, we develop a control framework that is scalable and applicable to ...
An alternative approach to solve SOC problems is to transform the HJB into a system of Forward-Backward Stochastic Differential Equations (FBSDEs) using the nonlinear version of the Feynman-Kac lemma ...
arXiv:1902.03986v2
fatcat:tzyraoxnk5gnzmwh5qwmepx5ru
Risk-Sensitive Stochastic Optimal Control as Rao-Blackwellized Markovian Score Climbing
[article]
2023
arXiv
pre-print
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Stochastic optimal control of dynamical systems is a crucial challenge in sequential decision-making. ...
Our approach, while purely inference-centric, provides asymptotically unbiased estimates for gradient-based policy optimization with optimal importance weighting and no explicit value function learning ...
Acknowledgements The authors express their gratitude to Joe Watson for his insightful early comments and valuable literature references. ...
arXiv:2312.14000v1
fatcat:qv4cy6w3pbc3hi6qw6ccpu2s5i
Physics-informed neural networks via stochastic Hamiltonian dynamics learning
[article]
2024
arXiv
pre-print
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2024 pre-print arXiv:2111.08108v2 fatcat:bammw2xeerfr3b2kzjaqiarpsaOther Versions
In this paper, we propose novel learning frameworks to tackle optimal control problems by applying the Pontryagin maximum principle and then solving for a Hamiltonian dynamical system. ...
Applying the Pontryagin maximum principle to the original optimal control problem shifts the learning focus to reduced Hamiltonian dynamics and corresponding adjoint variables. ...
The backpropagation of NeuralODE is based on the adjoint method with a backward ordinary differential equation on the adjoint states a(t) = dL dh(t) . ...
arXiv:2111.08108v3
fatcat:6qgfbyp5krcdjmpmgxcdzrsua4
Solving Coupled Nonlinear Forward-backward Stochastic Differential Equations: An Optimization Perspective with Backward Measurability Loss
[article]
2023
arXiv
pre-print
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We interpret BML from the fixed-point iteration perspective and show that optimizing BML is equivalent to minimizing the distance between two consecutive trial solutions in a fixed-point iteration. ...
Thus, this paper provides a theoretical foundation for an optimization-based approach to solving FBSDEs. We also empirically evaluate the method through four numerical experiments. ...
Introduction Forward-backward stochastic differential equations (FBSDEs) are a class of coupled stochastic differential equation systems consisting of forward stochastic differential equations (SDEs) and ...
arXiv:2310.13562v2
fatcat:inid3hboo5aa7ln436p7mtgxqe
Semilinear Feynman-Kac Formulae for B-Continuous Viscosity Solutions
[article]
2023
arXiv
pre-print
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Our approach also yields a stochastic representation formula for the solution in terms of a scalar-valued backward stochastic differential equation. ...
We prove the existence of a B-continuous viscosity solution for a class of infinite dimensional semilinear partial differential equations (PDEs) using probabilistic methods. ...
Wu, Fully coupled forward-backward stochastic differential equations and applications to optimal control, SIAM J. Control Optim., ( ), -. [ ] H. ...
arXiv:2303.10038v1
fatcat:prfcry2fofddjayanfkpvba2wi
A deep learning method for solving stochastic optimal control problems driven by fully-coupled FBSDEs
[article]
2022
arXiv
pre-print
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In this paper, we mainly focus on the numerical solution of high-dimensional stochastic optimal control problem driven by fully-coupled forward-backward stochastic differential equations (FBSDEs in short ...
We first transform the problem into a stochastic Stackelberg differential game(leader-follower problem), then a cross-optimization method (CO method) is developed where the leader's cost functional and ...
When a BSDE is coupled with a (forward) stochastic differential equation (SDE in short), the system is usually called a forward-backward stochastic differential equation (FBSDE in short). ...
arXiv:2204.05796v1
fatcat:yymniqoqizcv3fixyis6acnn5u
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