High Dimensional Bayesian Optimisation and Bandits via Additive Models
This work addresses the problem of high-dimensional optimization for researchers and practitioners in fields like scientific simulation and machine learning, offering a more expressive framework than previous restrictive settings.
The paper tackles the challenge of scaling Bayesian Optimization (BO) to high dimensions by assuming an additive structure for the function, proving that regret has only linear dependence on D and demonstrating performance improvements over naive BO in synthetic and real-world examples.
Bayesian Optimisation (BO) is a technique used in optimising a $D$-dimensional function which is typically expensive to evaluate. While there have been many successes for BO in low dimensions, scaling it to high dimensions has been notoriously difficult. Existing literature on the topic are under very restrictive settings. In this paper, we identify two key challenges in this endeavour. We tackle these challenges by assuming an additive structure for the function. This setting is substantially more expressive and contains a richer class of functions than previous work. We prove that, for additive functions the regret has only linear dependence on $D$ even though the function depends on all $D$ dimensions. We also demonstrate several other statistical and computational benefits in our framework. Via synthetic examples, a scientific simulation and a face detection problem we demonstrate that our method outperforms naive BO on additive functions and on several examples where the function is not additive.