Related papers: Relationship between General MP and DPP for the St…
Motion planning and control problems are embedded and essential in almost all robotics applications. These problems are often formulated as stochastic optimal control problems and solved using dynamic programming algorithms. Unfortunately,…
In this paper we study the stochastic control problem of partially observed (multi-dimensional) stochastic system driven by both Brownian motions and fractional Brownian motions. In the absence of the powerful tool of Girsanov…
This paper presents three versions of maximum principle for a stochastic optimal control problem of Markov regime-switching forward-backward stochastic differential equations with jumps (FBSDEJs). A general sufficient maximum principle for…
We study an optimal control problem of generalized mean-field dynamics with open-loop controls, where the coefficients depend not only on the state processes and controls, but also on the joint law of them. The value function $V$ defined in…
We consider a general type of non-Markovian impulse control problems under adverse non-linear expectation or, more specifically, the zero-sum game problem where the adversary player decides the probability measure. We show that the upper…
We study the optimal control of mean-field systems with heterogeneous and asymmetric interactions. This leads to considering a family of controlled Brownian diffusion processes with dynamics depending on the whole collection of marginal…
In this paper, we introduce a model-based deep-learning approach to solve finite-horizon continuous-time stochastic control problems with jumps. We iteratively train two neural networks: one to represent the optimal policy and the other to…
The dynamic programming approach for the control of a 3D flow governed by the stochastic Navier-Stokes equations for incompressible fluid in a bounded domain is studied. By a compactness argument, existence of solutions for the associated…
In this paper, we study a stochastic optimal control problem under degenerate G-expectation. By using implied partition method, we show that the approximation result for admissible controls still hold. Based on this result, we prove that…
We study stochastic motion planning problems which involve a controlled process, with possibly discontinuous sample paths, visiting certain subsets of the state-space while avoiding others in a sequential fashion. For this purpose, we first…
In this paper, we study a kind of optimal control problem for forward-backward stochastic differential equations (FBSDEs for short) of McKean--Vlasov type via the dynamic programming principle (DPP for short) motivated by studying the…
This paper studies the dynamic programming principle using the measurable selection method for stochastic control of continuous processes. The novelty of this work is to incorporate intermediate expectation constraints on the canonical…
In this paper the connection between stochastic optimal control and reinforcement learning is investigated. Our main motivation is to apply importance sampling to sampling rare events which can be reformulated as an optimal control problem.…
This article proposes an improved trajectory optimization approach for stochastic optimal control of dynamical systems affected by measurement noise by combining optimal control with maximum likelihood techniques to improve the reduction of…
We present a neural network approach for approximating the value function of high-dimensional stochastic control problems. Our training process simultaneously updates our value function estimate and identifies the part of the state space…
We prove the dynamic programming principle (DPP) in a class of problems where an agent controls a $d$-dimensional diffusive dynamics via both classical and singular controls and, moreover, is able to terminate the optimisation at a time of…
In this paper, we aim to develop the theory of optimal stochastic control for branching diffusion processes where both the movement and the reproduction of the particles depend on the control. More precisely, we study the problem of…
In this paper, we investigate the optimal control problems for stochastic differential equations (SDEs in short) of mean-field type with jump processes. The control variable is allowed to enter into both diffusion and jump terms. This…
In this paper, we study the generalized mean-field stochastic control problem when the usual stochastic maximum principle (SMP) is not applicable due to the singularity of the Hamiltonian function. In this case, we derive a second order…
In this paper, we investigate a sparse optimal control of continuous-time stochastic systems. We adopt the dynamic programming approach and analyze the optimal control via the value function. Due to the non-smoothness of the $L^0$ cost…