Related papers: Time Consistency for Multistage Stochastic Optimiz…

In this paper we deal with stochastic optimization problems where the data distributions change in response to the decision variables. Traditionally, the study of optimization problems with decision-dependent distributions has assumed…

In this contribution we develop an efficient reduced order model for solving parametrized linear-quadratic optimal control problems with linear time-varying state system. The fully reduced model combines reduced basis approximations of the…

We introduce the class of multistage stochastic optimization problems with a random number of stages. For such problems, we show how to write dynamic programming equations and detail the Stochastic Dual Dynamic Programming algorithm to…

We consider stochastic optimization problems where data is drawn from a Markov chain. Existing methods for this setting crucially rely on knowing the mixing time of the chain, which in real-world applications is usually unknown. We propose…

In this paper, we consider a multistage expected utility maximization problem where the decision maker's utility function at each stage depends on historical data and the information on the true utility function is incomplete. To mitigate…

This paper considers time-average stochastic optimization, where a time average decision vector, an average of decision vectors chosen in every time step from a time-varying (possibly non-convex) set, minimizes a convex objective function…

This paper considers data-driven chance-constrained stochastic optimization problems in a Bayesian framework. Bayesian posteriors afford a principled mechanism to incorporate data and prior knowledge into stochastic optimization problems.…

Optimization problems with continuous data appear in, e.g., robust machine learning, functional data analysis, and variational inference. Here, the target function is given as an integral over a family of (continuously) indexed target…

Efficiently computing the optimal control policy concerning a complicated future with stochastic disturbance has always been a challenge. The predicted stochastic future disturbance can be represented by a scenario tree, but solving the…

We extend the Longstaff-Schwartz algorithm for approximately solving optimal stopping problems on high-dimensional state spaces. We reformulate the optimal stopping problem for Markov processes in discrete time as a generalized statistical…

Bellman formulated a vague principle for optimization over time, which characterizes optimal policies by stating that a decision maker should not regret previous decisions retrospectively. This paper addresses time consistency in stochastic…

We investigate constrained optimal control problems for linear stochastic dynamical systems evolving in discrete time. We consider minimization of an expected value cost over a finite horizon. Hard constraints are introduced first, and then…

This paper presents a method to approximately solve stochastic optimal control problems in which the cost function and the system dynamics are polynomial. For stochastic systems with polynomial dynamics, the moments of the state can be…

This work addresses the optimal covariance control problem for stochastic discrete-time linear time-varying systems subject to chance constraints. Covariance steering is a stochastic control problem to steer the system state Gaussian…

Consider the problem of minimizing the expected value of a (possibly nonconvex) cost function parameterized by a random (vector) variable, when the expectation cannot be computed accurately (e.g., because the statistics of the random…

Multistage stochastic programming is a powerful tool allowing decision-makers to revise their decisions at each stage based on the realized uncertainty. However, in practice, organizations are not able to be fully flexible, as decisions…

We study a stochastic optimization problem in which the sampling distribution depends on the decision variable, and the available samples are generated through an iterate-dependent Markov chain. Such settings arise naturally in problems…

We prove a general existence result in stochastic optimal control in discrete time where controls take values in conditional metric spaces, and depend on the current state and the information of past decisions through the evolution of a…

Trajectory optimization is a fundamental stochastic optimal control problem. This paper deals with a trajectory optimization approach for dynamical systems subject to measurement noise that can be fitted into linear time-varying stochastic…

Stochastic optimization problems often involve data distributions that change in reaction to the decision variables. This is the case for example when members of the population respond to a deployed classifier by manipulating their features…