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We study quasi-convex optimization problems, where only a subset of the constraints can be sampled, and yet one would like a probabilistic guarantee on the obtained solution with respect to the initial (unknown) optimization problem. Even…
Data-driven control strategies for dynamical systems with unknown parameters are popular in theory and applications. An essential problem is to prevent stochastic linear systems becoming destabilized, due to the uncertainty of the…
The frequency-domain data of a multivariable system in different operating points is used to design a robust controller with respect to the measurement noise and multimodel uncertainty. The controller is fully parametrized in terms of…
We study control of constrained linear systems with only partial statistical information about the uncertainty affecting the system dynamics and the sensor measurements. Specifically, given a finite collection of disturbance realizations…
The problem of finding a solution to the linear system $Ax = b$ with certain minimization properties arises in numerous scientific and engineering areas. In the era of big data, the stochastic optimization algorithms become increasingly…
Communication is one of the bottlenecks of distributed optimisation and learning. To overcome this bottleneck, we propose a novel quantization method that transforms a vector into a sample of components' indices drawn from a categorical…
This paper presents a novel methodology for tractably solving optimal control and offline reinforcement learning problems for high-dimensional systems. This work is motivated by the ongoing challenges of safety, computation, and optimality…
Experimental design is central to science and engineering. A ubiquitous challenge is how to maximize the value of information obtained from expensive or constrained experimental settings. Bayesian optimal experimental design (OED) provides…
This brief note aims to introduce the recent paradigm of distributional robustness in the field of shape and topology optimization. Acknowledging that the probability law of uncertain physical data is rarely known beyond a rough…
(Stochastic) bilevel optimization is a frequently encountered problem in machine learning with a wide range of applications such as meta-learning, hyper-parameter optimization, and reinforcement learning. Most of the existing studies on…
This work presents a new computational optimization framework for the robust control of parks of Wave Energy Converters (WEC) in irregular waves. The power of WEC parks is maximized with respect to the individual control damping and…
In this paper, we study unconstrained distributed optimization strongly convex problems, in which the exchange of information in the network is captured by a directed graph topology over digital channels that have limited capacity (and…
Two-stage robust unit commitment (RUC) models have been widely used for day-ahead energy and reserve scheduling under high renewable integration. The current state of the art relies on budget-constrained polyhedral uncertainty sets to…
We introduce a distributionally robust maximum likelihood estimation model with a Wasserstein ambiguity set to infer the inverse covariance matrix of a $p$-dimensional Gaussian random vector from $n$ independent samples. The proposed model…
We consider an online two-stage stochastic optimization with long-term constraints over a finite horizon of $T$ periods. At each period, we take the first-stage action, observe a model parameter realization and then take the second-stage…
Hyperparameter tuning is a challenging problem especially when the system itself involves uncertainty. Due to noisy function evaluations, optimization under uncertainty can be computationally expensive. In this paper, we present a novel…
Chance constraints provide a principled framework to mitigate the risk of high-impact extreme events by modifying the controllable properties of a system. The low probability and rare occurrence of such events, however, impose severe…
In this paper we introduce a novel approach to distributionally robust optimal control that supports online learning of the ambiguity set, while guaranteeing recursive feasibility. We introduce conic representable risk, which is useful to…
Optimization over the space of probability measures endowed with the Wasserstein-2 geometry is central to modern machine learning and mean-field modeling. However, traditional methods relying on full Wasserstein gradients often suffer from…
In a given production planning horizon, the demands may only be comfirmed in part of the whole periods, and the others are uncertain. In this paper, we consider a two-stage stochastic lot-sizing problem with chance-constrained condition in…