[Paper Review] Practical Bayesian Optimization for Model Fitting with Bayesian Adaptive Direct Search

Luigi Acerbi, Wei Ji|arXiv (Cornell University)|May 11, 2017

Advanced Bandit Algorithms Research156 citations

TL;DR

The paper introduces Bayesian Adaptive Direct Search (BADS), a hybrid Bayesian optimization algorithm combining MADS and a local Gaussian process surrogate, and shows it outperforms many non-Bayesian optimizers and vanilla BO on model-fitting problems in neuroscience.

ABSTRACT

Computational models in fields such as computational neuroscience are often evaluated via stochastic simulation or numerical approximation. Fitting these models implies a difficult optimization problem over complex, possibly noisy parameter landscapes. Bayesian optimization (BO) has been successfully applied to solving expensive black-box problems in engineering and machine learning. Here we explore whether BO can be applied as a general tool for model fitting. First, we present a novel hybrid BO algorithm, Bayesian adaptive direct search (BADS), that achieves competitive performance with an affordable computational overhead for the running time of typical models. We then perform an extensive benchmark of BADS vs. many common and state-of-the-art nonconvex, derivative-free optimizers, on a set of model-fitting problems with real data and models from six studies in behavioral, cognitive, and computational neuroscience. With default settings, BADS consistently finds comparable or better solutions than other methods, including `vanilla' BO, showing great promise for advanced BO techniques, and BADS in particular, as a general model-fitting tool.

Motivation & Objective

• Motivate the use of Bayesian optimization for fitting complex, noisy computational neuroscience models where gradients may be unavailable.
• Develop a practical, low-overhead BO-enabled tool (BADS) that can be used out-of-the-box for model fitting.
• Benchmark BADS against common and state-of-the-art derivative-free optimizers on artificial and real data?models, assessing performance under deterministic and stochastic evaluations.

Proposed method

• Propose Bayesian Adaptive Direct Search (BADS), a hybrid of Mesh Adaptive Direct Search (MADS) and local Gaussian process surrogate optimization.
• Use a local GP with ARD Rational Quadratic kernel to model the objective and an LCB (lower confidence bound) acquisition function during search.
• Integrate GP-based search within the MADS search stage, and use a GP-informed poll stage to ensure convergence and robustness.
• Maintain a local GP training set (cache) around the incumbent, with reweighting by distance and a radius-based inclusion rule for efficiency.
• Handle uncertainty by using GP quantiles in the presence of noise, and by maintaining an active incumbent set evaluated via a GP-based quantile function.
• Provide default hyperparameters and an empirical Bayes prior for GP hyperparameters; refit periodically to adapt to local landscape.

Experimental results

Research questions

• RQ1 Can a hybrid optimization framework that blends Bayesian optimization with a direct-search mesh achieve competitive performance on model-fitting tasks with moderate computational cost?
• RQ2 Does BADS offer robust performance across deterministic and noisy (stochastic) objective evaluations compared to common nonlinear optimizers and vanilla BO?
• RQ3 Is BADS practical for real-world neuroscience model-fitting problems in terms of overhead and user-friendliness (out-of-the-box use with no tuning)?

Key findings

• BADS consistently matches or outperforms other optimizers, including vanilla BO, across artificial and real model-fitting problems.
• BADS remains competitive on noiseless bbob09 functions and shows robustness to heteroskedastic noise where other methods struggle.
• On real ccn17 model-fitting problems, BADS achieves favorable efficiency with overheads largely due to GP hyperparameter fitting, yet still often beats CMA-ES and fmincon variants.
• Vanilla Bayesian optimization (bayesopt) substantially underperforms compared to BADS and other methods on the tested model-fitting problems.
• The authors provide BADS as an open MATLAB package with default settings, enabling out-of-the-box use for researchers.