Fast Bayesian Optimization of Needle-in-a-Haystack Problems using Zooming Memory-Based Initialization (ZoMBI) (2208.13771v2)

Abstract: Needle-in-a-Haystack problems exist across a wide range of applications including rare disease prediction, ecological resource management, fraud detection, and material property optimization. A Needle-in-a-Haystack problem arises when there is an extreme imbalance of optimum conditions relative to the size of the dataset. For example, only $0.82\%$ out of $146$k total materials in the open-access Materials Project database have a negative Poisson's ratio. However, current state-of-the-art optimization algorithms are not designed with the capabilities to find solutions to these challenging multidimensional Needle-in-a-Haystack problems, resulting in slow convergence to a global optimum or pigeonholing into a local minimum. In this paper, we present a Zooming Memory-Based Initialization algorithm, entitled ZoMBI. ZoMBI actively extracts knowledge from the previously best-performing evaluated experiments to iteratively zoom in the sampling search bounds towards the global optimum "needle" and then prunes the memory of low-performing historical experiments to accelerate compute times by reducing the algorithm time complexity from $O(n^3)$ to $O(\phi^3)$ for $\phi$ forward experiments per activation, which trends to a constant $O(1)$ over several activations. Additionally, ZoMBI implements two custom adaptive acquisition functions to further guide the sampling of new experiments toward the global optimum. We validate the algorithm's optimization performance on three real-world datasets exhibiting Needle-in-a-Haystack and further stress-test the algorithm's performance on an additional 174 analytical datasets. The ZoMBI algorithm demonstrates compute time speed-ups of 400x compared to traditional Bayesian optimization as well as efficiently discovering optima in under 100 experiments that are up to 3x more highly optimized than those discovered by similar methods MiP-EGO, TuRBO, and HEBO.

• The paper presents ZoMBI, which refines search boundaries and prunes low-performing memory to significantly accelerate optimization in needle-in-a-haystack problems.
• It implements adaptive acquisition functions, LCB Adaptive and EI Abrupt, to dynamically balance exploration and exploitation.
• The algorithm achieved up to 400x speed improvements over traditional methods on real-world datasets, validating its efficiency and robustness.

Evaluation of a Zooming Memory-Based Initialization Approach in Bayesian Optimization

The paper "Fast Bayesian Optimization of Needle-in-a-Haystack Problems using Zooming Memory-Based Initialization (ZoMBI)" introduces a new algorithm designed to address the inherent challenges of optimizing Needle-in-a-Haystack (NiaH) problems. These problems are characterized by a small number of optimal solutions within a vast search space, leading to extreme imbalances in data. Conventional optimization algorithms struggle with such challenges due to convergence issues and prolonged compute times, which ZoMBI aims to mitigate.

Overview of the Approach

The ZoMBI algorithm enhances the conventional Bayesian Optimization framework by employing two primary strategies: (1) iterative inward bounding of the search space based on past experiments, and (2) pruning of low-performing memory to accelerate computations. This approach refines search bounds iteratively, focusing on promising regions that contain the potential needle, i.e., the global optimum. Additionally, ZoMBI incorporates custom adaptive acquisition functions, LCB Adaptive and EI Abrupt, which fine-tune their sampling strategies by using dynamic adjustments informed by prior observations.

Methodology and Implementation

The methodology comprises two main components: the core ZoMBI algorithm and adaptive acquisition functions. The algorithm uses previous best-performing experiments to adjust search boundaries, focusing more acutely on areas likely containing the global optimum. By limiting the number of memory points retained for further computations, ZoMBI reduces time complexity, ensuring a trend towards constant computational time over multiple iterations.

The acquisition functions implemented in ZoMBI dynamically balance exploration and exploitation by adjusting parameters like $\beta$ in LCB Adaptive based on sampled data trends. Such adaptive learning dimensions enhance the algorithm's ability to escape local minima pigeonholes effectively—a notorious issue in standard static acquisition functions.

Performance Validation

The performance of ZoMBI was tested on three real-world NiaH datasets, including materials with rare mechanical and thermoelectric properties, and environments conducive to wildfires. The results evidenced notable computational speed-ups, achieving up to 400x faster times than traditional Bayesian optimization while identifying global optima. For example, ZoMBI was able to discern highly negative Poisson's ratios and high thermoelectric figures of merit in significantly fewer trials compared to benchmarks like MiP-EGO, TuRBO, and HEBO.

Moreover, ZoMBI’s robustness was evaluated against 174 additional analytical datasets showing resilience in discovering optima across varying dimensionality and initialization conditions. These extensive tests highlight ZoMBI’s capability to consistently handle complex manifold topologies pertinent to NiaH problems.

Implications and Future Directions

The implications of ZoMBI extend across fields where extreme data imbalances govern optimization tasks. Practically, this approach can accelerate material discovery, enhance ecological monitoring systems, and refine automated detection processes in fields ranging from rare disease prediction to fraud detection. Theoretically, ZoMBI introduces a potentially valuable framework for enhancing adaptive learning mechanisms in optimization algorithms.

For future developments, a deeper exploration into integrating Neural Networks (NN) with ZoMBI could further enhance its computational efficiency and effectiveness. Additionally, examining the applicability in broader AI domains and across varied datasets will strengthen its utility and offer insights into improving adaptive algorithm designs.

In summary, the ZoMBI algorithm offers a significant advancement in tackling the complexities of NiaH problems. While it effectively addresses multiple challenges of traditional methods, continued research and refinement will unlock its full potential, paving the way for faster and more efficient solutions to diverse optimization problems in science and engineering.