[Paper Review] BOSS: Bayesian Optimization over String Spaces

Henry B. Moss, Daniel Beck+3 more|arXiv (Cornell University)|Oct 2, 2020

Machine Learning and Algorithms28 references20 citations

TL;DR

This paper introduces BOSS, a Bayesian optimization framework that directly operates on raw strings using string kernel-based Gaussian processes, eliminating the need for latent space mapping. It achieves superior optimization performance over constrained string spaces—such as those governed by context-free grammars—by combining string kernels with genetic algorithm-based acquisition function maximization, outperforming VAE-based baselines with minimal data and no hyperparameter tuning beyond two kernel parameters.

ABSTRACT

This article develops a Bayesian optimization (BO) method which acts directly over raw strings, proposing the first uses of string kernels and genetic algorithms within BO loops. Recent applications of BO over strings have been hindered by the need to map inputs into a smooth and unconstrained latent space. Learning this projection is computationally and data-intensive. Our approach instead builds a powerful Gaussian process surrogate model based on string kernels, naturally supporting variable length inputs, and performs efficient acquisition function maximization for spaces with syntactical constraints. Experiments demonstrate considerably improved optimization over existing approaches across a broad range of constraints, including the popular setting where syntax is governed by a context-free grammar.

Motivation & Objective

• To address the limitations of existing Bayesian optimization (BO) methods for string spaces, which rely on costly and data-intensive encoding into continuous latent spaces.
• To eliminate the need for variational autoencoders (VAEs) or fixed-length vector representations (e.g., bags-of-ngrams) in BO over strings.
• To develop an efficient acquisition function maximization strategy for discrete, syntactically constrained string spaces.
• To enable direct optimization over raw strings using a kernel-based surrogate model that captures non-contiguous subsequence similarities.
• To demonstrate improved optimization efficiency and robustness across diverse string-constrained problems, including molecular and gene design.

Proposed method

• Proposes a string-specific kernel (SSK) based on convolutional string kernels to measure similarity between variable-length strings via shared non-contiguous subsequences.
• Employs a Gaussian process (GP) surrogate model with the SSK as the kernel function, enabling smooth modeling of objective functions over raw string inputs.
• Introduces a suite of genetic algorithms tailored for acquisition function maximization in discrete, syntactically constrained string spaces, including those defined by context-free grammars.
• Fine-tunes the two hyperparameters of the SSK using only a few function evaluations, avoiding the need for large-scale unsupervised pre-training.
• Uses kernel principal component analysis (KPCA) to visualize the intrinsic feature space of the SSK, demonstrating better alignment with objective function smoothness than VAE-based latent spaces.
• Integrates the SSK-GP model into standard BO loops, supporting extensions to multi-fidelity, multi-objective, and batch BO.

Experimental results

Research questions

• RQ1 Can a string kernel-based Gaussian process surrogate model outperform traditional VAE-based latent space mappings in Bayesian optimization over string spaces with minimal data?
• RQ2 How effective is a genetic algorithm-based acquisition function maximization strategy for exploring discrete, syntactically constrained string spaces?
• RQ3 To what extent can a string kernel with only two tunable parameters capture complex objective functions in molecular and gene design tasks?
• RQ4 Does direct optimization over raw strings using SSK avoid the 'dead zones' and poor generalization issues common in VAE-based approaches?
• RQ5 Can the SSK-GP model better preserve smoothness in the objective function landscape compared to VAE-learned latent spaces?

Key findings

• The SSK-GP model outperforms VAE-based baselines in optimizing SMILES strings for molecular design, achieving better exploration within a constrained candidate set.
• The framework successfully optimizes over variable-length strings with syntactic constraints, including those governed by context-free grammars, without requiring fixed-length encoding.
• Only two kernel parameters in the SSK need to be tuned, and they can be reliably estimated with just a handful of function evaluations, reducing data dependency.
• Genetic algorithms effectively maximize acquisition functions in discrete string spaces, enabling efficient exploration even under complex syntactic rules.
• KPCA visualization shows that the SSK’s feature space better captures the smoothness of the objective function than the latent space of a VAE, which fails to align with the true objective landscape.
• The method avoids the 'dead zones' and invalid string decoding issues common in VAEs, as the genetic algorithm ensures only valid strings are explored.