Risk-averse Heteroscedastic Bayesian Optimization

Anastasia Makarova, Ilnura Usmanova, Ilija Bogunovic, Andreas Krause

Keywords: bayesian optimization, gaussian process, robustness, black-box

TL;DR: We generalize Bayesian Optimization to risk-aware setting via trading mean and input-dependent variance of the objective, both of which we assume to be unknown a~priori.

Abstract: 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.

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Code: https://github.com/Avidereta/risk-averse-hetero-bo

Community Implementations: [ 1 code implementation](https://www.catalyzex.com/paper/arxiv:2111.03637/code)