Related papers: The landscape of deterministic and stochastic opti…
In this paper, we consider the problem of optimizing the worst-case behavior of a partially observed system. All uncontrolled disturbances are modeled as finite-valued uncertain variables. Using the theory of cost distributions, we present…
An interior-point algorithm framework is proposed, analyzed, and tested for solving nonlinearly constrained continuous optimization problems. The main setting of interest is when the objective and constraint functions may be nonlinear…
We consider the stochastic optimal control problem for the dynamical system of the stochastic differential equation driven by a local martingale with a spatial parameter. Assuming the convexity of the control domain, we obtain the…
The problem of synthesizing stochastic explicit model predictive control policies is known to be quickly intractable even for systems of modest complexity when using classical control-theoretic methods. To address this challenge, we present…
In this paper, we study numerical approximations for optimal control of a class of stochastic partial differential equations with partial observations. The system state evolves in a Hilbert space, whereas observations are given in…
Planning problems are hard, motion planning, for example, isPSPACE-hard. Such problems are even more difficult in the presence of uncertainty. Although, Markov Decision Processes (MDPs) provide a formal framework for such problems, finding…
Stochastic dual dynamic programming (SDDP) is a state-of-the-art method for solving multi-stage stochastic optimization, widely used for modeling real-world process optimization tasks. Unfortunately, SDDP has a worst-case complexity that…
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…
We consider the stochastic optimal control problem of nonlinear mean-field systems in discrete time. We reformulate the problem into a deterministic control problem with marginal distribution as controlled state variable, and prove that…
Solving general Markov decision processes (MDPs) is a computationally hard problem. Solving finite-horizon MDPs, on the other hand, is highly tractable with well known polynomial-time algorithms. What drives this extreme disparity, and do…
In this paper we consider discrete time stochastic optimal control problems over infinite and finite time horizons. We show that for a large class of such problems the Taylor polynomials of the solutions to the associated Dynamic…
It has recently been shown that the minimum energy solution of the control problem for a linear system produces a control trajectory that is nonlocal. An issue then arises when the dynamics represents a linearization of the underlying…
We introduce a new numerical method to approximate the solution of a finite horizon deterministic optimal control problem. We exploit two Hamilton-Jacobi-Bellman PDE, arising by considering the dynamics in forward and backward time. This…
Growth models with internal habit formation have been studied in various settings under the assumption of deterministic dynamics. The purpose of this paper is to explore a stochastic version of the model in Carroll et al. [1997, 2000], one…
This paper studies the distributed optimization problem with possibly nonidentical local constraints, where its global objective function is composed of $N$ convex functions. The aim is to solve the considered optimization problem in a…
In this paper, we propose an efficient implementation of deep policy gradient method (PGM) for optimal control problems in continuous time. The proposed method has the ability to manage the allocation of computational resources, number of…
In this paper, we present a discretization algorithm for finite horizon risk constrained dynamic programming algorithm in [Chow_Pavone_13]. Although in a theoretical standpoint, Bellman's recursion provides a systematic way to find optimal…
Optimal control deals with optimization problems in which variables steer a dynamical system, and its outcome contributes to the objective function. Two classical approaches to solving these problems are Dynamic Programming and the…
This paper is concerned with the existence of optimal controls for backward stochastic partial differential equations with random coefficients, in which the control systems are represented in an abstract evolution form, i.e. backward…
Diffusion on complex networks is often modeled as a stochastic process. Yet, recent work on strategic diffusion emphasizes the decision power of agents and treats diffusion as a strategic problem. Here we study the computational aspects of…