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We propose a hybrid algorithmic strategy for complex stochastic optimization problems, which combines the use of scenario trees from multistage stochastic programming with machine learning techniques for learning a policy in the form of a…

The aim of this notes is to give a concise introduction to control theory for systems governed by stochastic partial differential equations. We shall mainly focus on controllability and optimal control problems for these systems. For the…

Trajectory following is one of the complicated control problems when its dynamics are nonlinear, stochastic and include a large number of parameters. The problem has significant difficulties including a large number of trials required for…

We consider partially observable Markov decision processes (POMDPs) with a set of target states and positive integer costs associated with every transition. The traditional optimization objective (stochastic shortest path) asks to minimize…

Markov Decision Processes (MDPs) offer a fairly generic and powerful framework to discuss the notion of optimal policies for dynamic systems, in particular when the dynamics are stochastic. However, computing the optimal policy of an MDP…

This paper is concerned with impulse approximate controllability for stochastic evolution equations with impulse controls. As direct applications, we formulate captivating minimal norm and time optimal control problems; The minimal norm…

Optimization problems in engineering and applied mathematics are typically solved in an iterative fashion, by systematically adjusting the variables of interest until an adequate solution is found. The iterative algorithms that govern these…

Stochastic optimization problems often involve the expectation in its objective. When risk is incorporated in the problem description as well, then risk measures have to be involved in addition to quantify the acceptable risk, often in the…

We present a reformulation of stochastic global optimization as a filtering problem. The motivation behind this reformulation comes from the fact that for many optimization problems we cannot evaluate exactly the objective function to be…

We consider a stochastic linear system and address the design of a finite horizon control policy that is optimal according to some average cost criterion and accounts also for probabilistic constraints on both the input and state variables.…

We characterize the optimal control for a class of singular stochastic control problems as the unique solution to a related Skorokhod reflection problem. The considered optimization problems concern the minimization of a discounted cost…

The paper is devoted to deriving necessary optimality conditions in a general optimal control problem for dynamical systems governed by controlled sweeping processes with hard-constrained control actions entering both polyhedral moving sets…

In this paper, we present long-awaited algorithmic advances toward the efficient construction of near-optimal replenishment policies for a true inventory management classic, the economic warehouse lot scheduling problem. While this paradigm…

Stochastic dynamical systems are fundamental in state estimation, system identification and control. System models are often provided in continuous time, while a major part of the applied theory is developed for discrete-time systems.…

Inventory management problems with periodic and controllable resets occur in the context of managing water storage in the developing world and retailing limited-time availability products. In this paper, we consider a set of sequential…

We study a new two-time-scale stochastic gradient method for solving optimization problems, where the gradients are computed with the aid of an auxiliary variable under samples generated by time-varying MDPs controlled by the underlying…

Sample average approximation--based stochastic dynamic programming (SDP) and model predictive control (MPC) are two different methods for approaching multistage stochastic optimization. In this paper we investigate the conditions under…

We study the effect of stochasticity in on-policy policy optimization, and make the following four contributions. First, we show that the preferability of optimization methods depends critically on whether stochastic versus exact gradients…

Stochastic maximum principle of nonlinear controlled forward-backward systems, where the set of strict (classical) controls need not be convex and the diffusion coefficient depends explicitly on the variable control, is an open problem…

We introduce a continuous policy-value iteration algorithm where the approximations of the value function of a stochastic control problem and the optimal control are simultaneously updated through Langevin-type dynamics. This framework…