Haydn T. Jones

Kaiwen Wu, Jonathan Wenger, Haydn Jones et al.

Training and inference in Gaussian processes (GPs) require solving linear systems with $n\times n$ kernel matrices. To address the prohibitive $\mathcal{O}(n^3)$ time complexity, recent work has employed fast iterative methods, like conjugate gradients (CG). However, as datasets increase in magnitude, the kernel matrices become increasingly ill-conditioned and still require $\mathcal{O}(n^2)$ space without partitioning. Thus, while CG increases the size of datasets GPs can be trained on, modern datasets reach scales beyond its applicability. In this work, we propose an iterative method which only accesses subblocks of the kernel matrix, effectively enabling mini-batching. Our algorithm, based on alternating projection, has $\mathcal{O}(n)$ per-iteration time and space complexity, solving many of the practical challenges of scaling GPs to very large datasets. Theoretically, we prove the method enjoys linear convergence. Empirically, we demonstrate its fast convergence in practice and robustness to ill-conditioning. On large-scale benchmark datasets with up to four million data points, our approach accelerates GP training and inference by speed-up factors up to $27\times$ and $72 \times$, respectively, compared to CG.

Jeffrey Tao, Yimeng Zeng, Haydn Thomas Jones et al.

Benchmark workloads are extremely important to the database management research community, especially as more machine learning components are integrated into database systems. Here, we propose a Bayesian optimization technique to automatically search for difficult benchmark queries, significantly reducing the amount of manual effort usually required. In preliminary experiments, we show that our approach can generate queries with more than double the optimization headroom compared to existing benchmarks.

Natalie Maus, Kyurae Kim, Yimeng Zeng et al.

In multi-objective black-box optimization, the goal is typically to find solutions that optimize a set of $T$ black-box objective functions, $f_1, \ldots f_T$, simultaneously. Traditional approaches often seek a single Pareto-optimal set that balances trade-offs among all objectives. In contrast, we consider a problem setting that departs from this paradigm: finding a small set of $K < T$ solutions, that collectively "cover" the $T$ objectives. A set of solutions is defined as "covering" if, for each objective $f_1, \ldots f_T$, there is at least one good solution. A motivating example for this problem setting occurs in drug design. For example, we may have $T$ pathogens and aim to identify a set of $K < T$ antibiotics such that at least one antibiotic can be used to treat each pathogen. This problem, known as coverage optimization, has yet to be tackled with the Bayesian optimization (BO) framework. To fill this void, we develop Multi-Objective Coverage Bayesian Optimization (MOCOBO), a BO algorithm for solving coverage optimization. Our approach is based on a new acquisition function reminiscent of expected improvement in the vanilla BO setup. We demonstrate the performance of our method on high-dimensional black-box optimization tasks, including applications in peptide and molecular design. Results show that the coverage of the $K < T$ solutions found by MOCOBO matches or nearly matches the coverage of $T$ solutions obtained by optimizing each objective individually. Furthermore, in in vitro experiments, the peptides found by MOCOBO exhibited high potency against drug-resistant pathogens, further demonstrating the potential of MOCOBO for drug discovery. All of our code is publicly available at the following link: https://github.com/nataliemaus/mocobo.

Yimeng Zeng, Natalie Maus, Haydn Thomas Jones et al.

In multi-task Bayesian optimization, the goal is to leverage experience from optimizing existing tasks to improve the efficiency of optimizing new ones. While approaches using multi-task Gaussian processes or deep kernel transfer exist, the performance improvement is marginal when scaling beyond a moderate number of tasks. We introduce a novel approach leveraging large language models (LLMs) to learn from, and improve upon, previous optimization trajectories, scaling to approximately 1500 distinct tasks. Specifically, we propose a feedback loop in which an LLM is fine-tuned on the high quality solutions to specific tasks found by Bayesian optimization (BO). This LLM is then used to generate initialization points for future BO searches for new tasks. The trajectories of these new searches provide additional training data for fine-tuning the LLM, completing the loop. We evaluate our method on two distinct domains: database query optimization and antimicrobial peptide design. Results demonstrate that our approach creates a positive feedback loop, where the LLM's generated initializations gradually improve, leading to better optimization performance. As this feedback loop continues, we find that the LLM is eventually able to generate solutions to new tasks in just a few shots that are better than the solutions produced by "from scratch" by Bayesian optimization while simultaneously requiring significantly fewer oracle calls.

Natalie Maus, Haydn T. Jones, Juston S. Moore et al.

Bayesian optimization over the latent spaces of deep autoencoder models (DAEs) has recently emerged as a promising new approach for optimizing challenging black-box functions over structured, discrete, hard-to-enumerate search spaces (e.g., molecules). Here the DAE dramatically simplifies the search space by mapping inputs into a continuous latent space where familiar Bayesian optimization tools can be more readily applied. Despite this simplification, the latent space typically remains high-dimensional. Thus, even with a well-suited latent space, these approaches do not necessarily provide a complete solution, but may rather shift the structured optimization problem to a high-dimensional one. In this paper, we propose LOL-BO, which adapts the notion of trust regions explored in recent work on high-dimensional Bayesian optimization to the structured setting. By reformulating the encoder to function as both an encoder for the DAE globally and as a deep kernel for the surrogate model within a trust region, we better align the notion of local optimization in the latent space with local optimization in the input space. LOL-BO achieves as much as 20 times improvement over state-of-the-art latent space Bayesian optimization methods across six real-world benchmarks, demonstrating that improvement in optimization strategies is as important as developing better DAE models.