Online Calibrated and Conformal Prediction Improves Bayesian Optimization
This work addresses the need for reliable uncertainty estimates in sequential decision-making for practitioners in fields like hyperparameter optimization, though it is incremental as it builds on existing calibration and Bayesian optimization methods.
The paper tackles the problem of imperfect uncertainty estimates in Bayesian optimization due to model assumptions and non-stationary data, proposing online learning algorithms to maintain calibration, which results in convergence to better optima in fewer steps, as demonstrated on benchmark functions and hyperparameter optimization tasks.
Accurate uncertainty estimates are important in sequential model-based decision-making tasks such as Bayesian optimization. However, these estimates can be imperfect if the data violates assumptions made by the model (e.g., Gaussianity). This paper studies which uncertainties are needed in model-based decision-making and in Bayesian optimization, and argues that uncertainties can benefit from calibration -- i.e., an 80% predictive interval should contain the true outcome 80% of the time. Maintaining calibration, however, can be challenging when the data is non-stationary and depends on our actions. We propose using simple algorithms based on online learning to provably maintain calibration on non-i.i.d. data, and we show how to integrate these algorithms in Bayesian optimization with minimal overhead. Empirically, we find that calibrated Bayesian optimization converges to better optima in fewer steps, and we demonstrate improved performance on standard benchmark functions and hyperparameter optimization tasks.