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The purpose of this paper is to describe the numerical solution of the Hamilton-Jacobi-Bellman (HJB) for an optimal control problem for quantum spin systems. This HJB equation is a first order nonlinear partial differential equation defined…
We determine the optimal robust investment strategy of an individual who targets at a given rate of consumption and seeks to minimize the probability of lifetime ruin when she does not have perfect confidence in the drift of the risky…
Autonomous systems have witnessed a rapid increase in their capabilities, but it remains a challenge for them to perform tasks both effectively and safely. The fact that performance and safety can sometimes be competing objectives renders…
We consider stochastic dynamic programming problems with high-dimensional, discrete state-spaces and finite, discrete-time horizons that prohibit direct computation of the value function from a given Bellman equation for all states and time…
The Hamilton Jacobi Bellman Equation (HJB) provides the globally optimal solution to large classes of control problems. Unfortunately, this generality comes at a price, the calculation of such solutions is typically intractible for systems…
We consider a kind of stochastic exit time optimal control problems, in which the cost function is defined through a nonlinear backward stochastic differential equation. We study the regularity of the value function for such a control…
Dynamic programming on tree decompositions is a frequently used approach to solve otherwise intractable problems on instances of small treewidth. In recent work by Bodlaender et al., it was shown that for many connectivity problems, there…
This work investigates the optimal control problem for reflected McKean-Vlasov SDEs and the viscosity solutions to Hamilton-Jacobi-Bellman(HJB) equations on the Wasserstein space in terms of intrinsic derivative. It follows from the flow…
We consider an infinite horizon control problem for dynamics constrained to remain on a multidimensional junction with entry costs. We derive the associated system of Hamilton-Jacobi equations (HJ), prove the comparison principle and that…
The problem of learning forest-structured discrete graphical models from i.i.d. samples is considered. An algorithm based on pruning of the Chow-Liu tree through adaptive thresholding is proposed. It is shown that this algorithm is both…
In several applications of automatic diagnosis and active learning a central problem is the evaluation of a discrete function by adaptively querying the values of its variables until the values read uniquely determine the value of the…
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's dynamic programming principle, corresponding also to some…
Structural learning, a method to estimate the parameters for discrete energy minimization, has been proven to be effective in solving computer vision problems, especially in 3D scene parsing. As the complexity of the models increases,…
We extend the stochastic Perron method to analyze the framework of stochastic target games, in which one player tries to find a strategy such that the state process almost surely reaches a given target no matter which action is chosen by…
We study optimal control problems for interacting branching diffusion processes, a class of measure-valued dynamics capturing both spatial motion and branching mechanisms. From the perspective of the dynamic programming principle, we…
We discuss a class of time-dependent Hamilton-Jacobi equations, where an unknown function of time is intended to keep the maximum of the solution to the constant value 0. Our main result is that the full problem has a unique viscosity…
We investigate feedback control for infinite horizon optimal control problems for partial differential equations. The method is based on the coupling between Hamilton-Jacobi-Bellman (HJB) equations and model reduction techniques. It is…
In this paper, we are concerned with the classical solvability of a class of second-order Hamilton-Jacobi-Bellman equations (HJB equations) arising from stochastic optimal control problems with linear dynamics and uniformly convex cost…
In this paper, we study backward doubly stochastic recursive optimal control problem where the cost function is described by the solution of a backward doubly stochastic differential equation. We give the dynamical programming principle for…