Learning low-dimensional embeddings for black-box optimization

Black-box optimization (BBO) is a valuable alternative to gradient-based methods when differentiating the objective function is not feasible. However, BBO often struggles with high-dimensional decision spaces and limited evaluation budgets. In this work, we propose a meta-learning approach that pre-computes a reduced-dimensional manifold capturing the optimal solutions of a class of optimization problems. For new problem instances drawn from the same class, BBO is then performed in the latent space, substantially reducing the computational effort required to reach near-optimal solutions. We further establish probabilistic upper bounds on the performance gap between solving the original problem and its reduced-dimensional counterpart. The effectiveness of the method is demonstrated both on benchmark optimization problems and on the automatic tuning of model predictive controllers.