Related papers: A quasi-Monte Carlo Method for an Optimal Control …
Recent low-thrust space missions have highlighted the importance of designing trajectories that are robust against uncertainties. In its complete form, this process is formulated as a nonlinear constrained stochastic optimal control…
This article presents a constrained policy optimization approach for the optimal control of systems under nonstationary uncertainties. We introduce an assumption that we call Markov embeddability that allows us to cast the stochastic…
Least squares Monte Carlo methods are a popular numerical approximation method for solving stochastic control problems. Based on dynamic programming, their key feature is the approximation of the conditional expectation of future rewards by…
This work considers the stability of nonlinear stochastic receding horizon control when the optimal controller is only computed approximately. A number of general classes of controller approximation error are analysed including…
Deep learning methods have achieved great success in solving partial differential equations (PDEs), where the loss is often defined as an integral. The accuracy and efficiency of these algorithms depend greatly on the quadrature method. We…
Quasi-Monte Carlo (QMC) integration of output functionals of solutions of the diffusion problem with a log-normal random coefficient is considered. The random coefficient is assumed to be given by an exponential of a Gaussian random field…
We investigate Monte Carlo based algorithms for solving stochastic control problems with probabilistic constraints. Our motivation comes from microgrid management, where the controller tries to optimally dispatch a diesel generator while…
Quasi-Monte Carlo sampling can attain far better accuracy than plain Monte Carlo sampling. However, with plain Monte Carlo sampling it is much easier to estimate the attained accuracy. This article describes methods old and new to quantify…
A local convergence rate is established for an orthogonal collocation method based on Radau quadrature applied to an unconstrained optimal control problem. If the continuous problem has a sufficiently smooth solution and the Hamiltonian…
Driven by several successful applications such as in stochastic gradient descent or in Bayesian computation, control variates have become a major tool for Monte Carlo integration. However, standard methods do not allow the distribution of…
We investigate the numerical approximation of an elliptic optimal control problem which involves a nonconvex local regularization of the $L^q$-quasinorm penalization (with $q\in(0,1)$) in the cost function. Our approach is based on the…
Multifidelity Monte Carlo methods rely on a hierarchy of possibly less accurate but statistically correlated simplified or reduced models, in order to accelerate the estimation of statistics of high-fidelity models without compromising the…
A method is developed to numerically solve chance constrained optimal control problems. The chance constraints are reformulated as nonlinear constraints that retain the probability properties of the original constraint. The reformulation…
In this study, we give an extension of Montanaro's arXiv/archive:1504.06987 quantum Monte Carlo method, tailored for computing expected values of random variables that exhibit infinite variance. This addresses a challenge in analyzing…
Dynamic Programming (DP) suffers from the well-known ``curse of dimensionality'', further exacerbated by the need to compute expectations over process noise in stochastic models. This paper presents a Monte Carlo-based sampling approach for…
Quasi-Monte Carlo methods are used for numerically integrating multivariate functions. However, the error bounds for these methods typically rely on a priori knowledge of some semi-norm of the integrand, not on the sampled function values.…
We study the numerical solution of nonlinear partially observed optimal stopping problems. The system state is taken to be a multi-dimensional diffusion and drives the drift of the observation process, which is another multi-dimensional…
We consider the numerical solution of scalar, nonlinear degenerate convection-diffusion problems with random diffusion coefficient and with random flux functions. Building on recent results on the existence, uniqueness and continuous…
Stochastic PDE eigenvalue problems often arise in the field of uncertainty quantification, whereby one seeks to quantify the uncertainty in an eigenvalue, or its eigenfunction. In this paper we present an efficient multilevel quasi-Monte…
Distributionally robust control is a well-studied framework for optimal decision making under uncertainty, with the objective of minimizing an expected cost function over control actions, assuming the most adverse probability distribution…