SOBER: Highly Parallel Bayesian Optimization and Bayesian Quadrature over Discrete and Mixed Spaces
This addresses a bottleneck in fields like drug discovery and simulation-based inference where parallel querying of expensive functions is needed, offering a scalable solution for discrete and mixed spaces.
The paper tackles the scalability issue of batch Bayesian optimization and quadrature for large batch sizes, presenting SOBER, a novel algorithm that reformulates batch selection as a quadrature problem, achieving superior performance over 11 baselines on 12 synthetic and real-world tasks.
Batch Bayesian optimisation and Bayesian quadrature have been shown to be sample-efficient methods of performing optimisation and quadrature where expensive-to-evaluate objective functions can be queried in parallel. However, current methods do not scale to large batch sizes -- a frequent desideratum in practice (e.g. drug discovery or simulation-based inference). We present a novel algorithm, SOBER, which permits scalable and diversified batch global optimisation and quadrature with arbitrary acquisition functions and kernels over discrete and mixed spaces. The key to our approach is to reformulate batch selection for global optimisation as a quadrature problem, which relaxes acquisition function maximisation (non-convex) to kernel recombination (convex). Bridging global optimisation and quadrature can efficiently solve both tasks by balancing the merits of exploitative Bayesian optimisation and explorative Bayesian quadrature. We show that SOBER outperforms 11 competitive baselines on 12 synthetic and diverse real-world tasks.