The scenario approach: A tool at the service of data-driven decision making

Campi, Marco C.; Carè, Algo; Garatti, Simone

doi:10.1016/j.arcontrol.2021.10.004

Cited by 42 publications

(36 citation statements)

References 89 publications

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“…In the framework of the scenario approach (also called scenario optimization) [8], [9], [11], the solution of the robust optimization problem in (1) is approximated with a finite number of samples. More precisely, we randomly generate N ∈ Z + samples, denoted by (δ 1 , δ 2 , • • • , δ N ) ∈ ∆ N , from some probability measure with the support ∆, and formulate the following scenario convex program (SCP)…”

Section: Preliminariesmentioning

confidence: 99%

“…The next lemma states the equivalence between the RCP in (1) and the max-min formulation as defined in (11).…”

Section: B Max-min Reformulationmentioning

confidence: 99%

“…Lemma 2: Consider Problems ( 1) and ( 11) for any N ∈ Z + with the optimal values J ⋆ and g * N respectively. Suppose Assumptions 1 -3 hold, then it holds that J ⋆ = g * N for any N ≥ d; Proof: From the definitions in ( 1) and (11), it holds that g N (ω) ≤ J ⋆ for any ω ∈ ∆ N , which implies that g * N ≤ J ⋆ for any N ∈ Z + . As {g * N } N ∈Z + is a monotonically increasing sequence, bounded from above by J ⋆ , we only need to show that g * d = J ⋆ .…”

Section: B Max-min Reformulationmentioning

confidence: 99%

“…An alternative approach for handling uncertainties is called the scenario approach or scenario optimization, which is somehow at the intersection of stochastic optimization and robust optimization as it is able to provide solutions to robust optimization and chance-constrained stochastic optimization problems in a probabilistic sense, see, e.g., some early works [8], [9]. We refer to [10], [11] for a comprehensive view on this subject.…”

Section: Introductionmentioning

confidence: 99%

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Probabilistic guarantees on the objective value for the scenario approach via sensitivity analysis

Wang¹,

Jungers²

2022

Preprint

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This paper is concerned with objective value performance of the scenario approach for robust convex optimization. A novel method is proposed to derive probabilistic bounds for the objective value from scenario programs with a finite number of samples. This method relies on a maxmin reformulation and the concept of complexity of robust optimization problems. With additional continuity and regularity conditions, via sensitivity analysis, we also provide explicit bounds which outperform an existing result in the literature. To illustrate the improvements of our results, we also provide a numerical example.

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Section: Preliminariesmentioning

confidence: 99%

“…The next lemma states the equivalence between the RCP in (1) and the max-min formulation as defined in (11).…”

Section: B Max-min Reformulationmentioning

confidence: 99%

Section: B Max-min Reformulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Probabilistic guarantees on the objective value for the scenario approach via sensitivity analysis

Wang¹,

Jungers²

2022

Preprint

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“…We solve the problem using a sampling-based approach. Starting with a set of solution vectors, we use techniques from scenario optimization, a data-driven methodology for solving stochastic optimization problems [17,20]. As such, we construct the prediction region from the solution to an optimization problem.…”

Section: Introductionmentioning

confidence: 99%

Sampling-Based Verification of CTMCs with Uncertain Rates

Badings,

Jansen,

Junges

et al. 2022

Preprint

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We employ uncertain parametric CTMCs with parametric transition rates and a prior on the parameter values. The prior encodes uncertainty about the actual transition rates, while the parameters allow dependencies between transition rates. Sampling the parameter values from the prior distribution then yields a standard CTMC, for which we may compute relevant reachability probabilities. We provide a principled solution, based on a technique called scenario-optimization, to the following problem: From a finite set of parameter samples and a user-specified confidence level, compute prediction regions on the reachability probabilities. The prediction regions should (with high probability) contain the reachability probabilities of a CTMC induced by any additional sample. To boost the scalability of the approach, we employ standard abstraction techniques and adapt our methodology to support approximate reachability probabilities. Experiments with various well-known benchmarks show the applicability of the approach.

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The Scenario Quality Assessment Method: A New Technique for Verifying the Quality of Scenarios

Curnin,

Brooks,

Brooks

2024

Futures & Foresight Science

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In a modern world faced by increasing uncertainty and crises, the importance of scenarios to inform the strategic decision‐making processes of governments and corporations has become paramount. This necessitates that those scenarios are rigorous and of high quality. A challenge is that research articulating how to classify and ensure the quality of a scenario is not prolific. This paper addresses this challenge by developing a framework of criteria for assessing scenario quality based on the futures and foresight literature and then using this to offer a new method for specifically assessing the quality of scenarios in the context of crisis management. The Scenario Quality Assessment Method infuses both the critical thinking and creativity required to develop quality scenarios. The method was empirically verified with scholars and practitioners in the industry to determine inter‐rater reliability before its intended use in the analysis of a data set for a scenario planning research project in the context of crisis management. This paper contributes theoretically to future and foresight research by including the concept of creativity when assessing the quality of scenarios and offers practitioners in crisis management an effective technique to assess the quality of their own scenarios.

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The scenario approach: A tool at the service of data-driven decision making

Cited by 42 publications

References 89 publications

Probabilistic guarantees on the objective value for the scenario approach via sensitivity analysis

Probabilistic guarantees on the objective value for the scenario approach via sensitivity analysis

Sampling-Based Verification of CTMCs with Uncertain Rates

The Scenario Quality Assessment Method: A New Technique for Verifying the Quality of Scenarios

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