Risk-averse Heteroscedastic Bayesian Optimization
This addresses the need for risk-averse decisions in black-box optimization for high-stakes applications, representing a novel method for a known bottleneck.
The paper tackles the problem of risk-averse optimization in high-stakes applications by generalizing Bayesian optimization to trade off mean and input-dependent variance, proposing the RAHBO algorithm that learns noise distribution on the fly and demonstrates effectiveness on synthetic benchmarks and hyperparameter tuning tasks.
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.