Intrinsic Bayesian Optimisation on Complex Constrained Domain
This addresses optimization challenges in spatial domains with complex constraints, such as geographic features, but is incremental as it adapts existing Bayesian optimization to manifolds.
The authors tackled the problem of Bayesian optimization on complex constrained domains like irregular-shaped manifolds, proposing Intrinsic Bayesian Optimization (In-BO) using Sparse Intrinsic Gaussian Processes, and demonstrated its efficiency with simulation studies on domains such as a U-shaped area and a real Aral sea dataset, showing improved performance over traditional methods.
Motivated by the success of Bayesian optimisation algorithms in the Euclidean space, we propose a novel approach to construct Intrinsic Bayesian optimisation (In-BO) on manifolds with a primary focus on complex constrained domains or irregular-shaped spaces arising as submanifolds of R2, R3 and beyond. Data may be collected in a spatial domain but restricted to a complex or intricately structured region corresponding to a geographic feature, such as lakes. Traditional Bayesian Optimisation (Tra-BO) defined with a Radial basis function (RBF) kernel cannot accommodate these complex constrained conditions. The In-BO uses the Sparse Intrinsic Gaussian Processes (SIn-GP) surrogate model to take into account the geometric structure of the manifold. SInGPs are constructed using the heat kernel of the manifold which is estimated as the transition density of the Brownian Motion on manifolds. The efficiency of In-BO is demonstrated through simulation studies on a U-shaped domain, a Bitten torus, and a real dataset from the Aral sea. Its performance is compared to that of traditional BO, which is defined in Euclidean space.