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Multistage stochastic optimization problems are oftentimes formulated informally in a pathwise way. These are correct in a discrete setting and suitable when addressing computational challenges, for example. But the pathwise problem…
Decision rules offer a rich and tractable framework for solving certain classes of multistage adaptive optimization problems. Recent literature has shown the promise of using linear and nonlinear decision rules in which wait-and-see…
We study the problem of computing deterministic optimal policies for constrained Markov decision processes (MDPs) with continuous state and action spaces, which are widely encountered in constrained dynamical systems. Designing…
Constrained Markov Decision Processes (CMDPs) are critical in many high-stakes applications, where decisions must optimize cumulative rewards while strictly adhering to complex nonlinear constraints. In domains such as power systems,…
The linear programming (LP) approach has a long history in the theory of approximate dynamic programming. When it comes to computation, however, the LP approach often suffers from poor scalability. In this work, we introduce a relaxed…
There has been widespread interest in the use of grid-level storage to handle the variability from increasing penetrations of wind and solar energy. This problem setting requires optimizing energy storage and release decisions for anywhere…
Benders decomposition is widely used to solve large mixed-integer problems. This paper takes advantage of machine learning and proposes enhanced variants of Benders decomposition for solving two-stage stochastic security-constrained unit…
We consider a multiperiod stochastic capacitated facility location problem under uncertain demand and budget in each period. Using a scenario tree representation of the uncertainties, we formulate a multistage stochastic integer program to…
In this paper, we have studied a decomposition method for solving a class of nonconvex two-stage stochastic programs, where both the objective and constraints of the second-stage problem are nonlinearly parameterized by the first-stage…
We propose a novel Two-Stage framework for Structured Pruning (\textsc{2SSP}) for pruning Large Language Models (LLMs), which combines two different strategies of pruning, namely Width and Depth Pruning. The first stage (Width Pruning)…
We investigate the problem of stochastic network optimization in the presence of imperfect state prediction and non-stationarity. Based on a novel distribution-accuracy curve prediction model, we develop the predictive learning-aided…
We provide performance guarantees for a variant of simulation-based policy iteration for controlling Markov decision processes that involves the use of stochastic approximation algorithms along with state-of-the-art techniques that are…
We consider a generic convex optimization problem associated with regularized empirical risk minimization of linear predictors. The problem structure allows us to reformulate it as a convex-concave saddle point problem. We propose a…
We introduce an inexact variant of Stochastic Mirror Descent (SMD), called Inexact Stochastic Mirror Descent (ISMD), to solve nonlinear two-stage stochastic programs where the second stage problem has linear and nonlinear coupling…
Machine learning (ML) primarily evolved to solve "prediction problems." The first stage of two-stage least squares (2SLS) is a prediction problem, suggesting potential gains from ML first-stage assistance. However, little guidance exists on…
We study two classic variants of block-structured integer programming. Two-stage stochastic programs are integer programs of the form $\{A_i \mathbf{x} + D_i \mathbf{y}_i = \mathbf{b}_i\textrm{ for all }i=1,\ldots,n\}$, where $A_i$ and…
Numerical resolution of high-dimensional nonlinear PDEs remains a huge challenge due to the curse of dimensionality. Starting from the weak formulation of the Lawson-Euler scheme, this paper proposes a stochastic particle method (SPM) by…
Multistage stochastic programs can be approximated by restricting policies to follow decision rules. Directly applying this idea to problems with integer decisions is difficult because of the need for decision rules that lead to integral…
We develop multi-stage linear decision rules (LDRs) for dynamic power system generation and energy storage investment planning under uncertainty and propose their chance-constrained optimization with performance guarantees. First, the…
The (R, s, S) is a stochastic inventory control policy widely used by practitioners. In an inventory system managed according to this policy, the inventory is reviewed at instant R; if the observed inventory position is lower than the…