Sequential Randomized Algorithms for Convex Optimization in the Presence of Uncertainty

Chamanbaz, Mohammadreza; Dabbene, Fabrizio; Tempo, Roberto; Venkataramanan, V.; Wang, Qingguo

doi:10.1109/tac.2015.2494875

Cited by 46 publications

(57 citation statements)

References 21 publications

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“…The approach and the results in [8], however, are distinctively different from the ones proposed here. In [8], the scenario problems are solved using a number N k of scenarios that grows with the iteration count k, up to the value N plain that corresponds to the plain, one-shot, scenario design. The major shortcoming of the approach and analysis in [8] is that the number of iterations is not bounded a-priori, either in a deterministic or in a probabilistic sense, and no tradeoff curve is proposed for the choice of N k in function of the expected running time of the algorithm.…”

Section: Repetitive Scenario Designcontrasting

confidence: 68%

“…In [8], the scenario problems are solved using a number N k of scenarios that grows with the iteration count k, up to the value N plain that corresponds to the plain, one-shot, scenario design. The major shortcoming of the approach and analysis in [8] is that the number of iterations is not bounded a-priori, either in a deterministic or in a probabilistic sense, and no tradeoff curve is proposed for the choice of N k in function of the expected running time of the algorithm. As a result, there is no a-priori guarantee that the algorithm does not reach the final iteration, in which N k equals N plain , hence the worst-case complexity of the algorithm in [8] can be worse than the one of the plain scenario design method, and an actual reduction of the number of design samples is not theoretically guaranteed.…”

Section: Repetitive Scenario Designmentioning

confidence: 99%

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Repetitive Scenario Design

Calafiore

2016

2016 IEEE 55th Conference on Decision and Control (CDC)

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Repetitive Scenario Design (RSD) is a randomized approach to robust design based on iterating two phases: a standard scenario design phase that uses N scenarios (design samples), followed by randomized feasibility phase that uses N o test samples on the scenario solution. We give a full and exact probabilistic characterization of the number of iterations required by the RSD approach for returning a solution, as a function of N , N o , and of the desired levels of probabilistic robustness in the solution. This novel approach broadens the applicability of the scenario technology, since the user is now presented with a clear tradeoff between the number N of design samples and the ensuing expected number of repetitions required by the RSD algorithm. The plain (one-shot) scenario design becomes just one of the possibilities, sitting at one extreme of the tradeoff curve, in which one insists in finding a solution in a single repetition: this comes at the cost of possibly high N . Other possibilities along the tradeoff curve use lower N values, but possibly require more than one repetition. KeywordsScenario design, probabilistic robustness, randomized algorithms, random convex programs.

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Section: Repetitive Scenario Designcontrasting

confidence: 68%

Section: Repetitive Scenario Designmentioning

confidence: 99%

Repetitive Scenario Design

Calafiore

2016

2016 IEEE 55th Conference on Decision and Control (CDC)

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“…In particular, in Alamo et al (2013), the general class of sequential probabilistic validation (SPV) algorithms has been introduced. A specific SPV algorithm tailored to scenario problems, providing a sequential scheme for dealing with the optimization problem, has been recently studied in Chamanbaz et al (2013).…”

Section: Discussionmentioning

confidence: 99%

Randomized Methods for Control of Uncertain Systems

Dabbene¹,

Tempo²

2014

Encyclopedia of Systems and Control

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In this article, we study the tools and methodologies for the analysis and design of control systems in the presence of random uncertainty. For analysis, the methods are largely based on the Monte Carlo simulation approach, while for design new randomized algorithms have been developed. These methods have been successfully employed in various application areas, which include systems biology; aerospace control; control of hard disk drives; high-speed networks; quantized, embedded, and electric circuits; structural design; and automotive and driver assistance. PreliminariesRandomized methods for control deal with the design of uncertain and complex systems. They have been originally developed for linear systems affected by structured uncertainty, usually expressed in the so-called M configuration. A similar approach may be followed when dealing with uncertainty in other contexts, such as uncertainty in the environment (random disturbances) or even when there is no uncertainty in the problem formulation, but the complexity of the problem is such that randomized methods may be the best approach, since these methods are known to break the curse of dimensionality, see Tempo et al. (2013) for details.For the sake of simplicity, we consider here an uncertain plant transfer function P .s; q/ affected by parametric uncertainty q D OEq 1 : : : q` T bounded in a set Q R`. The objective is to design the parameters Â 2 R n of a controller transfer function C.s; Â/ so to guarantee robustly some desired performance. This is reformulated as the problem of finding a design satisfying some uncertain constraints of the form f .Â; q/ Ä for all q 2 Q:In other words, the goal is to design a robust controller which satisfies the uncertain constraints. Specific examples of these constraints include an H 1 or H 2 norm bound on the closed-loop sensitivity function or time-domain specifications.

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“…Along this direction, sequential randomized algorithms were developed for convex scenario optimization problems [180], and fell into the framework of Sequential Probabilistic Validation (SPV) [181]. The motivation behind these sequential algorithms is that validating a given solution with a large number of samples is less computational expensive than solving the corresponding scenario optimization problem.…”

Section: Scenario Optimization Approach For Chance Constrained Programsmentioning

confidence: 99%

Optimization under uncertainty in the era of big data and deep learning: When machine learning meets mathematical programming

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You

2019

Computers & Chemical Engineering

240

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This paper reviews recent advances in the field of optimization under uncertainty via a modern data lens, highlights key research challenges and promise of data-driven optimization that organically integrates machine learning and mathematical programming for decision-making under uncertainty, and identifies potential research opportunities. A brief review of classical mathematical programming techniques for hedging against uncertainty is first presented, along with their wide spectrum of applications in Process Systems Engineering. A comprehensive review and classification of the relevant publications on data-driven distributionally robust optimization, data-driven chance constrained program, data-driven robust optimization, and data-driven scenario-based optimization is then presented. This paper also identifies fertile avenues for future research that focuses on a closed-loop data-driven optimization framework, which allows the feedback from mathematical programming to machine learning, as well as scenario-based optimization leveraging the power of deep learning techniques. Perspectives on online learningbased data-driven multistage optimization with a learning-while-optimizing scheme is presented.

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Sequential Randomized Algorithms for Convex Optimization in the Presence of Uncertainty

Cited by 46 publications

References 21 publications

Repetitive Scenario Design

Repetitive Scenario Design

Randomized Methods for Control of Uncertain Systems

Optimization under uncertainty in the era of big data and deep learning: When machine learning meets mathematical programming

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