[Paper Review] Incorporating Expert Prior Knowledge into Experimental Design via Posterior Sampling

Cheng Li, Sunil Gupta+4 more|arXiv (Cornell University)|Feb 26, 2020

Advanced Multi-Objective Optimization Algorithms25 references5 citations

TL;DR

This paper proposes a Bayesian optimization framework that incorporates expert prior knowledge about the global optimum's location via a prior distribution on the optimum, using posterior sampling to guide efficient experimental design. By modeling expert intuition as a vague prior over the optimum and updating it with observations, the method accelerates convergence in expensive black-box optimization, demonstrating significant gains in synthetic, hyperparameter tuning, and real-world polymer fiber experiments.

ABSTRACT

Scientific experiments are usually expensive due to complex experimental preparation and processing. Experimental design is therefore involved with the task of finding the optimal experimental input that results in the desirable output by using as few experiments as possible. Experimenters can often acquire the knowledge about the location of the global optimum. However, they do not know how to exploit this knowledge to accelerate experimental design. In this paper, we adopt the technique of Bayesian optimization for experimental design since Bayesian optimization has established itself as an efficient tool for optimizing expensive black-box functions. Again, it is unknown how to incorporate the expert prior knowledge about the global optimum into Bayesian optimization process. To address it, we represent the expert knowledge about the global optimum via placing a prior distribution on it and we then derive its posterior distribution. An efficient Bayesian optimization approach has been proposed via posterior sampling on the posterior distribution of the global optimum. We theoretically analyze the convergence of the proposed algorithm and discuss the robustness of incorporating expert prior. We evaluate the efficiency of our algorithm by optimizing synthetic functions and tuning hyperparameters of classifiers along with a real-world experiment on the synthesis of short polymer fiber. The results clearly demonstrate the advantages of our proposed method.

Motivation & Objective

• To address the challenge of incorporating expert prior knowledge about the location of the global optimum into Bayesian optimization for experimental design.
• To develop a tractable method for representing and updating expert beliefs about the optimum using a prior distribution on the optimum location.
• To improve the efficiency of experimental design by accelerating convergence in expensive optimization tasks through informed sampling.
• To validate the method on synthetic functions, machine learning hyperparameter tuning, and a real-world polymer fiber synthesis experiment.

Proposed method

• Represent expert knowledge about the global optimum as a prior distribution π(x*) on the optimum location x*.
• Use a Gaussian process (GP) to model the unknown function f(x), with a standard non-informative prior on f.
• Derive the posterior distribution p(x* | D_n, π(x*)) by combining the GP posterior with the expert prior π(x*) on the optimum.
• Sample from the joint posterior p(x* | D_n, π(x*)) to guide the next evaluation point via posterior sampling.
• Apply Thompson sampling on the posterior of the optimum to balance exploration and exploitation in sequential experiments.
• Update the posterior iteratively with new observations D_n to refine the estimate of the optimum location.

Experimental results

Research questions

• RQ1 How can expert prior knowledge about the location of the global optimum be formally represented in a Bayesian optimization framework?
• RQ2 What is the theoretical impact of incorporating such prior knowledge on the convergence of experimental design algorithms?
• RQ3 How does the proposed method compare to standard Bayesian optimization in terms of convergence speed and sample efficiency?
• RQ4 Can the method effectively handle weak or imprecise expert priors without degrading performance?
• RQ5 How does the method perform in real-world experimental design scenarios with expensive function evaluations?

Key findings

• The proposed posterior sampling method with expert prior on the optimum significantly accelerates convergence in synthetic function optimization compared to standard Bayesian optimization.
• In hyperparameter tuning for random forest and XGBoost, the method achieved higher performance with fewer evaluations, particularly when the expert prior was aligned with the true optimum.
• In a real-world polymer fiber synthesis experiment, the method identified the optimal configuration with fewer trials, achieving a maximal percentage of desirable fibers (50–150 microns) faster than baseline methods.
• The algorithm remained robust even when the expert prior was weak or slightly inaccurate, showing stable performance across multiple runs.
• The posterior sampling approach with expert-informed priors outperformed random search and standard BO in both synthetic and real-world settings, demonstrating practical utility.
• The method effectively leveraged expert intuition without requiring strong assumptions about the underlying function, making it suitable for real experimental domains.