arXiv Machine Learning

Nonlinear Dimensionality Reduction Techniques for Bayesian Optimization

The paper investigates nonlinear dimensionality reduction for Bayesian optimisation (BO) by transforming high‑dimensional black‑box optimisation problems into a sequence of low‑dimensional latent‑space BO (LSBO) tasks. It extends earlier linear embedding approaches by using variational autoencoders (VAEs), deep metric loss, and adaptive retraining to better capture nonlinear structure, and couples LSBO with sequential domain reduction (SDR‑LSBO) to progressively narrow search domains. Experiments on GPU‑accelerated BoTorch with Matérn‑5/2 Gaussian‑process surrogates show that VAE‑based LSBO outperforms adaptive linear embeddings, and the authors provide a theoretical analysis of latent‑space error versus representation gap under PAC‑Bayes conditions.

arXiv Machine Learning
Oct 23

SABLE: Scalable Affine Bayesian Latent-space Exploration

SABLE is a Bayesian optimisation method designed for high‑dimensional latent spaces where the latent dimension far exceeds the evaluation budget. It uses a Bayesian affine surrogate that decomposes each query into an in‑span component optimized by expected improvement and an off‑span component governed by a scalar norm, with a finite‑horizon schedule to avoid under‑exploration. A recompression scheme reduces the number of pseudo‑observations to ≠O(M), keeping refitting costs manageable while achieving high sample efficiency and rapid decision times on synthetic and latent‑space optimisation tasks.

By Erik Bodin, Lisa Maria Kreusser, Donney Fan, Henry Moss, Geoff Pleiss, Nicolas Durrande
arXiv Machine Learning
Aug 27

Gradient-based Sample Selection for Faster Bayesian Optimization

The paper introduces Gradient-based Sample Selection Bayesian Optimization (GSSBO), a method that builds the Gaussian process surrogate on a strategically chosen subset of samples rather than the full dataset. By using gradient information to eliminate redundant points while keeping diversity and representativeness, GSSBO achieves sublinear regret bounds and reduces the cubic computational cost of standard BO. Experiments on synthetic and real-world tasks show that this approach maintains comparable optimization performance while significantly cutting GP fitting time and resource usage.

By Qiyu Wei, Haowei Wang, Zirui Cao, Songhao Wang, Richard Allmendinger, Mauricio A \'Alvarez
arXiv AI
Oct 31

Rethinking Bayesian Optimization for Co-Optimizing LLM Training Configurations

The paper introduces JoBS, a Bayesian optimization framework that co‑optimizes data and model configurations for large language model training without requiring full training runs at each iteration. JoBS first allocates part of the budget to train a scaling‑law‑inspired performance predictor using only a few training steps, then uses this predictor to guide subsequent BO iterations, thereby exploring many more configurations within the same budget. The authors analyze JoBS’s regret, derive optimal budget splits, and demonstrate that it outperforms both independent optimization and existing multi‑fidelity BO baselines across diverse downstream tasks.

By Zhiliang Chen, Alfred Wei Lun Leong, Shao Yong Ong, Apivich Hemachandra, Gregory Kang Ruey Lau, Chuan-Sheng Foo, Zhengyuan Liu, Nancy F. Chen, Bryan Kian Hsiang Low
arXiv AI
Oct 28

BoLT: A Benchmark to Democratize Black-box Optimization Research for Expensive LLM Tasks

BoLT is a new benchmark designed to make black-box optimization research for large language model (LLM) tasks more accessible. It presents a suite of realistic LLM optimization problems—covering multi‑fidelity, multi‑objective, heteroscedastic noise, and high‑dimensional search spaces—grounded in thousands of real experiments and represented by lightweight surrogate models. The authors evaluate a wide range of Bayesian and other black‑box optimization methods on BoLT, finding that some BO techniques consistently outperform others and revealing gaps in current methods for LLM optimization.

By Ruth Wan Theng Chew, Zhiliang Chen, Apivich Hemachandra, Bryan Kian Hsiang Low
arXiv Machine Learning
Sep 4

No-Regret Bayesian Optimization with Finite-Library Input-Warped Kernels

The paper introduces Finite-Library Input-Warped Bayesian Optimization (FLIWBO), a method that selects input warps from a finite library to adapt the geometry used by Gaussian‑process Bayesian optimization. FLIWBO maintains high‑probability convergence guarantees while improving sample efficiency on problems where raw coordinates poorly match the objective’s geometry, such as log‑scaled hyperparameters or localized peaks. Experiments on synthetic benchmarks, Fashion‑MNIST hyperparameter tuning, and a 20‑dimensional multi‑agent system design demonstrate that FLIWBO‑UCB outperforms raw‑coordinate GP‑UCB and other methods with regret guarantees, especially under misspecified geometry.

By Edvin Ketabati Augustinsson, Robert A. Bridges