Multi-Information Source Optimization

Abstract: We consider Bayesian optimization of an expensive-to-evaluate black-box objective function, where we also have access to cheaper approximations of the objective. In general, such approximations arise in applications such as reinforcement learning, engineering, and the natural sciences, and are subject to an inherent, unknown bias. This model discrepancy is caused by an inadequate internal model that deviates from reality and can vary over the domain, making the utilization of these approximations a non-trivial task. We present a novel algorithm that provides a rigorous mathematical treatment of the uncertainties arising from model discrepancies and noisy observations. Its optimization decisions rely on a value of information analysis that extends the Knowledge Gradient factor to the setting of multiple information sources that vary in cost: each sampling decision maximizes the predicted benefit per unit cost. We conduct an experimental evaluation that demonstrates that the method consistently outperforms other state-of-the-art techniques: it finds designs of considerably higher objective value and additionally inflicts less cost in the exploration process.

• The paper introduces a novel Bayesian framework that unifies multiple biased information sources to efficiently balance evaluation cost and uncertainty.
• It extends the traditional Knowledge Gradient factor to a cost-sensitive setting, achieving rapid convergence and improved decision-making.
• Extensive experiments show superior performance in both synthetic benchmarks and hyper-parameter tuning applications.

Overview of Multi-Information Source Optimization

This paper presents an innovative approach to optimizing expensive-to-evaluate black-box objective functions, utilizing multiple, less costly information sources that provide varying levels of approximation. The authors illuminate the complexities associated with model discrepancies and propose a novel algorithm that extends the Knowledge Gradient (KG) factor to embrace a multi-information source setting. This tackles the challenges of balancing cost and uncertainty in data acquisition, offering a compelling solution for various fields including reinforcement learning and engineering applications.

Key Contributions

The primary contribution is a robust algorithm that incorporates a Bayesian optimization framework for managing multiple biased information sources efficiently. This method is particularly adept at dealing with the inherent model discrepancy — the deviation of surrogate models from the actual objective — which is often encountered in practical scenarios.

1. Unified Statistical Model: The paper introduces a uniform Bayesian treatment, consolidating the objective function and its surrogates within a single statistical framework. This integration surpasses existing methodologies by fully exploiting inter-source correlations to refine estimates and reduce uncertainties across all information sources more effectively.
2. Cost-Sensitive Knowledge Gradient: The algorithm uses a cost-sensitive KG factor to determine the next query point. This factor is adjusted to account for the expense of each potential information source, optimizing the acquisition process by maximizing the benefit per unit cost. This method demonstrates improved decision-making capability by efficiently utilizing available budget for sample collection.
3. Innovative Handling of Correlated Model Discrepancies: Extending the single-process Gaussian prior model, the paper addresses scenarios where biases among information sources are interrelated, such as in simulations with common model approximations. This flexibility enhances the algorithm's capacity to tackle complex real-world problems where information sources do not operate in isolation.

Experimental Evaluation

The algorithm's efficacy is corroborated through extensive experimental evaluations against state-of-the-art methods such as MTBO+ and misoEI across benchmarks like the Rosenbrock function and hyper-parameter optimization in image classification tasks. These experiments underscore the proposed method's superior performance in terms of attaining higher objective values with lower expenditure.

• On synthetic benchmark problems like the Rosenbrock test function, the proposed method achieves rapid convergence and superior gains per cost ratio compared to traditional methods, efficiently navigating through the bias and noise.
• In a practical application for hyper-parameter optimization, the proposed method demonstrates its capability in significantly reducing the time and cost needed to tune machine learning models by leveraging cost-effective but biased information sources.

Implications and Future Directions

The advent of this algorithm is pivotal for fields necessitating optimized parameter selection under stringent resource constraints. By addressing both noise and model discrepancy, the proposed method provides a more realistic approach to multifidelity optimization problems often encountered in engineering and machine learning contexts.

Future research could investigate adaptive strategies for dynamically altering the fidelity of information sources based on real-time feedback and results, further enhancing the cost-effectiveness and reliability of optimization processes. Additionally, the exploration of integrating this approach with other domains such as active learning and automated experimentation could yield new paradigms in data-driven inferential techniques.

In conclusion, this paper lays a substantial foundation for advancing optimization techniques that judiciously utilize information sources, potentially impacting a wide range of scientific and industrial applications.