Related papers: Multistage Stochastic Optimization via Kernels

Multi-stage decision-making under uncertainty, where decisions are taken under sequentially revealing uncertain problem parameters, is often essential to faithfully model managerial problems. Given the significant computational challenges…

We present a data-driven algorithm for efficiently computing stochastic control policies for general joint chance constrained optimal control problems. Our approach leverages the theory of kernel distribution embeddings, which allows…

Variable selection is central to high-dimensional data analysis, and various algorithms have been developed. Ideally, a variable selection algorithm shall be flexible, scalable, and with theoretical guarantee, yet most existing algorithms…

Two-stage stochastic programming is a popular framework for optimization under uncertainty, where decision variables are split between first-stage decisions, and second-stage (or recourse) decisions, with the latter being adjusted after…

In this paper, we introduce a framework for solving finite-horizon multistage optimization problems under uncertainty in the presence of auxiliary data. We assume the joint distribution of the uncertain quantities is unknown, but noisy…

This paper presents a novel operator-theoretic approach for optimal control of nonlinear stochastic systems within reproducing kernel Hilbert spaces. Our learning framework leverages data samples of system dynamics and stage cost functions,…

In this paper, sparsification techniques aided online prediction algorithms in a reproducing kernel Hilbert space are studied for nonstationary time series. The online prediction algorithms as usual consist of the selection of kernel…

We propose a (seemingly) new computationally tractable model for multi-stage decision making under stochastic uncertainty.

Optimization problems involving sequential decisions in a stochastic environment were studied in Stochastic Programming (SP), Stochastic Optimal Control (SOC) and Markov Decision Processes (MDP). In this paper we mainly concentrate on SP…

Contextual stochastic optimization is an advanced methodology to model uncertainty in the presence of contextual information during decision planning processes. Although classical methodologies focus on minimizing the expectation of a…

The application of Gaussian processes (GPs) to large data sets is limited due to heavy memory and computational requirements. A variety of methods has been proposed to enable scalability, one of which is to exploit structure in the kernel…

We develop a novel framework for sparse multiscale kernel approximation of large scattered data problems based on a samplet representation. Samplets form a multiresolution analysis of localized discrete signed measures and enable…

Stochastic simulation models are generative models that mimic complex systems to help with decision-making. The reliability of these models heavily depends on well-calibrated input model parameters. However, in many practical scenarios,…

We present a multilevel stochastic gradient descent method for the optimal control of systems governed by partial differential equations under uncertain input data. The gradient descent method used to find the optimal control leverages a…

We provide a functional view of distributional robustness motivated by robust statistics and functional analysis. This results in two practical computational approaches for approximate distributionally robust nonlinear optimization based on…

This paper concerns models and convergence principles for dealing with stochasticity in a wide range of algorithms arising in nonlinear analysis and optimization in Hilbert spaces. It proposes a flexible geometric framework within which…

Multi-stage stochastic programming is a well-established framework for sequential decision making under uncertainty by seeking policies that are fully adapted to the uncertainty. Often such flexible policies are not desirable, and the…

We study two-stage stochastic optimization problems with random recourse, where the adaptive decisions are multiplied with the uncertain parameters in both the objective function and the constraints. To mitigate the computational…

Production planning must account for uncertainty in a production system, arising from fluctuating demand forecasts. Therefore, this article focuses on the integration of updated customer demand into the rolling horizon planning cycle. We…

In most adaptive signal processing applications, system linearity is assumed and adaptive linear filters are thus used. The traditional class of supervised adaptive filters rely on error-correction learning for their adaptive capability.…