CooL-BO: Constraint-aligned Latent Bayesian Optimization for High-dimensional Problems

Recent methods employing variational autoencoders (VAEs) to map discrete, high-dimensional input spaces to continuous latent representations, have achieved remarkable success in high-dimensional Bayesian optimization (BO) in unconstrained settings. However, real-world problems (e.g., molecule design, robotic control tasks) are often subject to practical constraints (e.g., drug likeliness of proposed molecules, safety constraints) that are not explicitly captured by standard VAE training. Consequently, the trained VAE may map feasible and infeasible inputs to overlapping latent regions. As a result, nearby latent points can decode to candidates with different feasibility, producing an irregular feasible region that complicates acquisition-function optimization and reduces sampling efficiency. In this paper, we propose CooL-BO, which explicitly shapes the learned latent manifold with respect to input feasibility. By introducing a discriminator and a dynamic mechanism for learning priors, we enforce separability in the latent domain during pre-training of the VAE, thereby facilitating the selection of promising feasible candidates for latent space BO. Consequently, CooL-BO achieves a higher BO objective than state-of-the-art latent space BO methods, while reducing computation time by up to $10$ times across various high-dimensional benchmark tasks. Our results highlight the importance of leveraging both feasible and infeasible inputs in representation learning for latent-space BO, motivating the need for learning representations tailored for latent BO tasks.