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Poster
Optimizing Conditional Value-At-Risk of Black-Box Functions
Quoc Phong Nguyen · Zhongxiang Dai · Bryan Kian Hsiang Low · Patrick Jaillet

Wed Dec 08 12:30 AM -- 02:00 AM (PST) @ None #None

This paper presents two Bayesian optimization (BO) algorithms with theoretical performance guarantee to maximize the conditional value-at-risk (CVaR) of a black-box function: CV-UCB and CV-TS which are based on the well-established principle of optimism in the face of uncertainty and Thompson sampling, respectively. To achieve this, we develop an upper confidence bound of CVaR and prove the no-regret guarantee of CV-UCB by utilizing an interesting connection between CVaR and value-at-risk (VaR). For CV-TS, though it is straightforwardly performed with Thompson sampling, bounding its Bayesian regret is non-trivial because it requires a tail expectation bound for the distribution of CVaR of a black-box function, which has not been shown in the literature. The performances of both CV-UCB and CV-TS are empirically evaluated in optimizing CVaR of synthetic benchmark functions and simulated real-world optimization problems.

Author Information

Quoc Phong Nguyen (National University of Singapore)
Zhongxiang Dai (National University of Singapore)
Bryan Kian Hsiang Low (National University of Singapore)
Patrick Jaillet (MIT)

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