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Many black-box optimization tasks arising in high-stakes applications require risk-averse decisions. The standard Bayesian optimization (BO) paradigm, however, optimizes the expected value only. We generalize BO to trade mean and input-dependent variance of the objective, both of which we assume to be unknown a priori. In particular, we propose a novel risk-averse heteroscedastic Bayesian optimization algorithm (RAHBO) that aims to identify a solution with high return and low noise variance, while learning the noise distribution on the fly. To this end, we model both expectation and variance as (unknown) RKHS functions, and propose a novel risk-aware acquisition function. We bound the regret for our approach and provide a robust rule to report the final decision point for applications where only a single solution must be identified. We demonstrate the effectiveness of RAHBO on synthetic benchmark functions and hyperparameter tuning tasks.
Risk-averse Heteroscedastic Bayesian Optimization A. Makarova, I. Usmanova, I. Bogunovic, A. KrauseIn Proc. Neural Information Processing Systems (NeurIPS), 2021
Bibtex Entry:
	author = {Anastasia Makarova and Ilnura Usmanova and Ilija Bogunovic and Andreas Krause},
	booktitle = {Proc. Neural Information Processing Systems (NeurIPS)},
	month = {December},
	title = {Risk-averse Heteroscedastic Bayesian Optimization},
	video = {},
	year = {2021}}