Bayesian Optimization for minimizing CVaR under performance constraints
Abstract: Optimal portfolio allocation can often be formulated as to a constrained risk problem, where one aims to minimize a risk measure subject to some performance constraints. This paper presents new Bayesian Optimization (BO) algorithms for such constrained minimization problems, seeking to minimize the conditional value-at-risk a computationally intensive risk measure, under a minimum expected return constraint. The proposed algorithms utilize a new acquisition function, which drives sampling towards the optimal region. Additionally, a new two-stage procedure is developed, which significantly reduces the number of evalua- tions of the expensive-to-evaluate objective function. The proposed algorithm’s competitive performance is demonstrated through practical examples.
Submission Length: Long submission (more than 12 pages of main content)
Changes Since Last Submission: Title and abstract have been changed according to the reviewers' suggestions.
Futher discussion regarding the limitation of the method, especially when the theoretical assumption is not satisfied.
Notations have been modified and so that they are unified thoughrout the work.
Discussion on the contextual BO is added.
Discussion on the acquisition function is added.
Other changes to address the reviewers' comments as outlined in the responses.
Assigned Action Editor: ~Mohammad_Ghavamzadeh1
Submission Number: 2268
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