2020 59th IEEE Conference on Decision and Control (CDC) 2020
DOI: 10.1109/cdc42340.2020.9304223
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Agent independent probabilistic robustness certificates for robust optimization programs with uncertain quadratic cost

Abstract: This paper focuses on a specific class of convex multi-agent programs, prevalent in many practical applications, where agents cooperate to minimize a common cost, expressed as a function of the aggregate decision and affected by uncertainty. We model uncertainty by means of scenarios and use an epigraphic reformulation to transfer the uncertain part of the cost function to the constraints. Then, by exploiting the structure of the program under study and leveraging on existing results in the scenario approach l… Show more

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“…Other problems whose structure shares similarities with our work can be found in [24], [25], [26], though under a purely deterministic and game-theoretic set-up. Following the recent developments in [27] we show based on the notion of the support rank [28], that the obtained probabilistic feasibility certificates are agent independent. This result directly outperforms probabilistic feasibility statements obtained by a direct application of the scenario approach theory [10], and has superior scalability properties as it does not depend on the number of agents involved.…”
Section: Challenges To Be Addressed and Main Contributionsmentioning
confidence: 99%
“…Other problems whose structure shares similarities with our work can be found in [24], [25], [26], though under a purely deterministic and game-theoretic set-up. Following the recent developments in [27] we show based on the notion of the support rank [28], that the obtained probabilistic feasibility certificates are agent independent. This result directly outperforms probabilistic feasibility statements obtained by a direct application of the scenario approach theory [10], and has superior scalability properties as it does not depend on the number of agents involved.…”
Section: Challenges To Be Addressed and Main Contributionsmentioning
confidence: 99%