Cost-aware Multi-objective Bayesian optimisation
This work addresses the challenge of optimizing expensive black-box functions where evaluation costs vary by input, which is incremental but relevant for applications like hyperparameter tuning in machine learning.
The paper tackles the problem of Bayesian optimization with non-uniform evaluation costs across different inputs in the search space, introducing cost-aware constraints and a new acquisition function that achieves competitive performance on synthetic and real-world hyperparameter tuning tasks.
The notion of expense in Bayesian optimisation generally refers to the uniformly expensive cost of function evaluations over the whole search space. However, in some scenarios, the cost of evaluation for black-box objective functions is non-uniform since different inputs from search space may incur different costs for function evaluations. We introduce a cost-aware multi-objective Bayesian optimisation with non-uniform evaluation cost over objective functions by defining cost-aware constraints over the search space. The cost-aware constraints are a sorted tuple of indexes that demonstrate the ordering of dimensions of the search space based on the user's prior knowledge about their cost of usage. We formulate a new multi-objective Bayesian optimisation acquisition function with detailed analysis of the convergence that incorporates this cost-aware constraints while optimising the objective functions. We demonstrate our algorithm based on synthetic and real-world problems in hyperparameter tuning of neural networks and random forests.