Related papers: On Semi-Stochastic Model for Multi-Stage Decision …

This paper introduces a multi-timescale stochastic programming framework designed to address decision-making challenges in power systems, particularly those with high renewable energy penetration. The framework models interactions across…

Real-world decision-making problems often involve decision-dependent uncertainty, where the probability distribution of the random vector depends on the model decisions. Few studies focus on two-stage stochastic programs with this type of…

Stochastic simulation is widely used to study complex systems composed of various interconnected subprocesses, such as input processes, routing and control logic, optimization routines, and data-driven decision modules. In practice, these…

We address the design and synthesis of optimal control strategies for high-dimensional stochastic dynamical systems. Such systems may be deterministic nonlinear systems evolving from random initial states, or systems driven by random…

We present a numerical method for learning unknown nonautonomous stochastic dynamical system, i.e., stochastic system subject to time dependent excitation or control signals. Our basic assumption is that the governing equations for the…

In this article we propose a qualitative (ordinal) counterpart for the Partially Observable Markov Decision Processes model (POMDP) in which the uncertainty, as well as the preferences of the agent, are modeled by possibility distributions.…

We consider two-stage robust optimization problems, which can be seen as games between a decision maker and an adversary. After the decision maker fixes part of the solution, the adversary chooses a scenario from a specified uncertainty…

We consider a risk-averse stochastic capacity planning problem under uncertain demand in each period. Using a scenario tree representation of the uncertainty, we formulate a multistage stochastic integer program to adjust the capacity…

This paper deals with uncertain dynamical systems in which predictions about the future state of a system are assessed by so called pseudomeasures. Two special cases are stochastic dynamical systems, where the pseudomeasure is the…

In networks, there are often more than one source of capacity. The capacities can be permanently or temporarily owned by the decision maker. Depending on the nature of sources, we identify the permanent capacity, spot market capacity and…

Transmission expansion planning (TEP) plays a critical role in ensuring power system reliability and facilitating the integration of renewable energy resources. However, this process requires planners to constantly deal with significant…

Due to the penetration of renewable energy resources and load deviation, uncertainty handling is one of the main challenges for power system; therefore the need for accurate decision-making in a power system under the penetration of…

We introduce temporal multimodal multivariate learning, a new family of decision making models that can indirectly learn and transfer online information from simultaneous observations of a probability distribution with more than one peak or…

In this paper we study a family of nonlinear (conditional) expectations that can be understood as a stochastic process with uncertain parameters. We develop a general framework which can be seen as a version of the martingale problem method…

The vast majority of stochastic simulation models are imperfect in that they fail to exactly emulate real system dynamics. The inexactness of the simulation model, or model discrepancy, can impact the predictive accuracy and usefulness of…

A multiscale numerical method is proposed for the solution of semi-linear elliptic stochastic partial differential equations with localized uncertainties and non-linearities, the uncertainties being modeled by a set of random parameters. It…

We present a numerical method for learning the dynamics of slow components of unknown multiscale stochastic dynamical systems. While the governing equations of the systems are unknown, bursts of observation data of the slow variables are…

Influence diagrams are widely employed to represent multi-stage decision problems in which each decision is a choice from a discrete set of alternatives, uncertain chance events have discrete outcomes, and prior decisions may influence the…

When optimizing problems with uncertain parameter values in a linear objective, decision-focused learning enables end-to-end learning of these values. We are interested in a stochastic scheduling problem, in which processing times are…

Bilevel optimization is a powerful tool for modeling hierarchical decision making processes. However, the resulting problems are challenging to solve - both in theory and practice. Fortunately, there have been significant algorithmic…