Related papers: Stochastic Control Methods for Optimization
In this paper, we propose a minimax linear-quadratic control method to address the issue of inaccurate distribution information in practical stochastic systems. To construct a control policy that is robust against errors in an empirical…
The optimal control of problems that are constrained by partial differential equations with uncertainties and with uncertain controls is addressed. The Lagrangian that defines the problem is postulated in terms of stochastic functions, with…
This paper is about operator-theoretic methods for solving nonlinear stochastic optimal control problems to global optimality. These methods leverage on the convex duality between optimally controlled diffusion processes and…
We design receding horizon control strategies for stochastic discrete-time linear systems with additive (possibly) unbounded disturbances, while obeying hard bounds on the control inputs. We pose the problem of selecting an appropriate…
We propose a novel distribution-free scheme to solve optimization problems where the goal is to minimize the expected value of a cost function subject to probabilistic constraints. Unlike standard sampling-based methods, our idea consists…
Randomized optimization is an established tool for control design with modulated robustness. While for uncertain convex programs there exist randomized approaches with efficient sampling, this is not the case for non-convex problems.…
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…
In this paper, we generalize the chance optimization problems and introduce constrained volume optimization where enables us to obtain convex formulation for challenging problems in systems and control. We show that many different problems…
We introduce a stochastic global optimization method based on random walks on Grassmannian manifolds. To minimize a continuous objective $\ell:\mathbb{R}^d\rightarrow\mathbb{R}$, the method repeatedly samples random $k$-dimensional linear…
This paper studies stochastic control problems with the action space taken to be probability measures, with the objective penalised by the relative entropy. We identify suitable metric space on which we construct a gradient flow for the…
In this manuscript, we study optimal control problems for stochastic delay differential equations using the dynamic programming approach in Hilbert spaces via viscosity solutions of the associated Hamilton-Jacobi-Bellman equations. We show…
Controlling the stochastic dynamics of biological populations is a challenge that arises across various biological contexts. However, these dynamics are inherently nonlinear and involve a discrete state space, i.e., the number of molecules,…
We propose a mathematical framework to explain implicit regularization from early stopping during the training of overparametrized neural networks. In the mean-field limit, the parameter distribution evolves according to a gradient flow on…
A numerical study of an optimal control formulation for a shape optimization problem governed by an elliptic variational inequality is performed. The shape optimization problem is reformulated as a boundary control problem in a fixed…
By extending \cite{bensoussan2015control}, we implement the proposal of Lions \cite{lions14} on studying mean field games and their master equations via certain control problems on the Hilbert space of square integrable random variables. In…
We consider fully nonlinear Hamilton-Jacobi-Bellman equations associated to diffusion control problems involving a finite set-valued (or switching) control and possibly a continuum-valued control. We construct a lower complexity…
Motivated by emerging applications in machine learning, we consider an optimization problem in a general form where the gradient of the objective function is available through a biased stochastic oracle. We assume a bias-control parameter…
Computational approaches to PDE-constrained optimization under uncertainty may involve finite-dimensional approximations of control and state spaces, sample average approximations of measures of risk and reliability, smooth approximations…
To tackle the difficulties faced by both stochastic dynamic programming and scenario tree methods, we present some variational approach for numerical solution of stochastic optimal control problems. We consider two different interpretations…
In this paper, we consider a class of stochastic control problems for stochastic differential equations with random coefficients. The control domain need not to be convex but the control process is not allowed to enter in diffusion term.…