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Bayesian optimization (BO) has well-documented merits for optimizing black-box functions with an expensive evaluation cost. Such functions emerge in applications as diverse as hyperparameter tuning, drug discovery, and robotics. BO hinges on a Bayesian surrogate model to sequentially select query points so as to balance exploration with exploitation of the search space. Most existing works rely on a single Gaussian process (GP) based surrogate model, where the kernel function form is typically preselected using domain knowledge. To bypass such a design process, this paper leverages an ensemble (E) of GPs to adaptively select the surrogate model fit on-the-fly, yielding a GP mixture posterior with enhanced expressiveness for the sought function. Acquisition of the next evaluation input using this EGP-based function posterior is then enabled by Thompson sampling (TS) that requires no additional design parameters. To endow function sampling with scalability, random feature-based kernel approximation is leveraged per GP model. The novel EGP-TS readily accommodates parallel operation. To further establish convergence of the proposed EGP-TS to the global optimum, analysis is conducted based on the notion of Bayesian regret for both sequential and parallel settings. Tests on synthetic functions and real-world applications showcase the merits of the proposed method.
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Uncertainty quantification using martingales for misspecified Gaussian processes
We address uncertainty quantification for Gaussian processes (GPs) under misspecified priors, with an eye towards Bayesian Optimization (BO). GPs are widely used in BO because they easily enable exploration based on posterior uncertainty bands. However, this convenience comes at the cost of robustness: a typical function encountered in practice is unlikely to have been drawn from the data scientist’s prior, in which case uncertainty estimates can be misleading, and the resulting exploration can be suboptimal. We present a frequentist approach to GP/BO uncertainty quantification. We utilize the GP framework as a working model, but do not assume correctness of the prior. We instead construct a \emph{confidence sequence} (CS) for the unknown function using martingale techniques. There is a necessary cost to achieving robustness: if the prior was correct, posterior GP bands are narrower than our CS. Nevertheless, when the prior is wrong, our CS is statistically valid and empirically outperforms standard GP methods, in terms of both coverage and utility for BO. Additionally, we demonstrate that powered likelihoods provide robustness against model misspecification.
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- Award ID(s):
- 1916320
- PAR ID:
- 10251948
- Publisher / Repository:
- PMLR (JMLR W&CP)
- Date Published:
- Journal Name:
- Proceedings of Machine Learning Research
- Volume:
- 132
- ISSN:
- 2640-3498
- Page Range / eLocation ID:
- 963-982
- Format(s):
- Medium: X
- Location:
- Algorithmic Learning Theory
- Sponsoring Org:
- National Science Foundation
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Accepted Manuscript
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- The DOI is not currently available.
