Timezone: »

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) @

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)

More from the Same Authors