MONGOOSE: Path-wise Smooth Bayesian Optimisation via Meta-learning

TL;DR

This work tackles optimization of expensive black-box functions under movement costs between evaluations. It introduces MONGOOSE, a memory-based meta-learning approach using a non-myopic objective that incorporates movement costs to produce smooth evaluation trajectories, obviating explicit non-myopic acquisition computations. Key contributions are a smooth-path training objective ${\mathcal{L}_{div}}$, injection of global structure into training functions, and Fourier-feature-based meta-training to scale GP-like samples. Empirical results on standard BO benches, the COCO suite across dimensions $2$–$6$, and a real-world lake-contamination task show that MONGOOSE achieves a superior regret-versus-movement-cost trade-off while remaining computationally efficient. The method promises practical impact for real-world systems where reconfiguration or transport between measurements is costly, enabling robust, scalable, and cost-aware Bayesian optimization.

Abstract

In Bayesian optimisation, we often seek to minimise the black-box objective functions that arise in real-world physical systems. A primary contributor to the cost of evaluating such black-box objective functions is often the effort required to prepare the system for measurement. We consider a common scenario where preparation costs grow as the distance between successive evaluations increases. In this setting, smooth optimisation trajectories are preferred and the jumpy paths produced by the standard myopic (i.e.\ one-step-optimal) Bayesian optimisation methods are sub-optimal. Our algorithm, MONGOOSE, uses a meta-learnt parametric policy to generate smooth optimisation trajectories, achieving performance gains over existing methods when optimising functions with large movement costs.

Figures (52)

• Figure 1: 50 minisation steps (orange dots to yellow dots) on a toy function (background). Standard BO with EI (a) incurs large movement costs, whereas EI per unit cost (b) fails to reach the global minima (star). Our non-myopic approach (c) finds the minima whilst following a smooth trajectory.
• Figure 2: Top: trajectories MONGOOSE with different cost scalings on a single function sample from the meta-training distribution (background colour). Cost scalings $\alpha = 0.00, 0.01, 0.05$ from left to right as labelled on titles. Background with colour scale represent the function sample. Orange/yellow dots denote the evaluations chosen by each method, where darker colours (more orange) denote points earlier in the optimisation, and lighter colors (more yellow) denote points later in the optimisation. Consecutive evaluations are joined by lines. Bottom: $L_2$ distance (i.e. moving cost) to traverse each optimisation trajectory.
• Figure 3: Regret versus cost on standard benchmark objective functions for two versions of MONGOOSE and BO baselines. We plot the mean and a $90\%$ confidence interval of regret for each method.
• Figure 4: Regret against cost averaged across 24 Coco functions for a range of dimensions.
• Figure 5: Optimisation trajectories generated when searching for contaminates across the Ypacarai Lake.