Resolve the SDR–DML interaction in BO–VAE

Develop a principled integration of Sequential Domain Reduction (SDR) within the Deep Metric Learning (DML) retraining BO–VAE framework that prevents exclusion of the global minimiser. Specifically, determine SDR update rules and conditions under which SDR can be safely applied in the DML-shaped latent space used by the retraining BO–VAE algorithm, ensuring reliable convergence without prematurely shrinking the latent search domain away from the true optimum.

Background

The paper introduces a retraining BO–VAE algorithm enhanced with Deep Metric Learning (DML), using a soft triplet loss to shape the latent space for improved Gaussian-process modelling. In this variant, SDR is intentionally omitted due to observed interference between SDR’s domain shrinkage and DML’s latent-space structuring.

The authors note that applying SDR alongside DML can lead to prematurely excluding the global optimum, and they explicitly defer addressing this interference. Resolving how to combine SDR with DML effectively is therefore identified as a concrete unresolved issue critical to robust latent-space Bayesian optimization.