  Real-world optimisation problems often feature complex combinations of (1)
diverse constraints, (2) discrete and mixed spaces, and are (3) highly
parallelisable. (4) There are also cases where the objective function cannot be
queried if unknown constraints are not satisfied, e.g. in drug discovery,
safety on animal experiments (unknown constraints) must be established before
human clinical trials (querying objective function) may proceed. However, most
existing works target each of the above three problems in isolation and do not
consider (4) unknown constraints with query rejection. For problems with
diverse constraints and/or unconventional input spaces, it is difficult to
apply these techniques as they are often mutually incompatible. We propose
cSOBER, a domain-agnostic prudent parallel active sampler for Bayesian
optimisation, based on SOBER of Adachi et al. (2023). We consider infeasibility
under unknown constraints as a type of integration error that we can estimate.
We propose a theoretically-driven approach that propagates such error as a
tolerance in the quadrature precision that automatically balances exploitation
and exploration with the expected rejection rate. Moreover, our method flexibly
accommodates diverse constraints and/or discrete and mixed spaces via adaptive
tolerance, including conventional zero-risk cases. We show that cSOBER
outperforms competitive baselines on diverse real-world blackbox-constrained
problems, including safety-constrained drug discovery, and
human-relationship-aware team optimisation over graph-structured space.

Machine Learning;Artificial Intelligence;Numerical Analysis;Numerical Analysis;Computation;Machine Learning