PropertyDAG: Multi-objective Bayesian optimization of partially ordered, mixed-variable properties for biological sequence design

Ji Won Park, Samuel Don Stanton, Saeed Saremi, Andrew Martin Watkins, Henri Dwyer, Vladimir Gligorijevic, Richard Bonneau, Stephen Ra, Kyunghyun Cho

Keywords: active learning, Bayesian optimization, multi-objective optimization, probabilistic graphical models

Abstract: Bayesian optimization offers a sample-efficient framework for navigating the exploration-exploitation trade-off in the vast design space of biological sequences. Whereas it is possible to optimize the various properties of interest jointly using a multi-objective acquisition function, such as the expected hypervolume improvement (EHVI), this approach does not account for objectives with a hierarchical dependency structure. We consider a common use case where some regions of the Pareto frontier are prioritized over others according to a specified $\textit{partial ordering}$ in the objectives. For instance, when designing antibodies, we maximize the binding affinity to a target antigen only if it can be expressed in live cell culture---modeling the experimental dependency in which affinity can only be measured for antibodies that can be expressed and thus produced in viable quantities. In general, we may want to confer a partial ordering to the properties such that each property is optimized conditioned on its parent properties satisfying some feasibility condition. To this end, we present PropertyDAG, a framework that operates on top of the traditional multi-objective BO to impose a desired partial ordering on the objectives, e.g. expression $\rightarrow$ affinity. We demonstrate its performance over multiple simulated active learning iterations on a penicillin production task, toy numerical problem, and a real-world antibody design task.

TL;DR: multi-objective Bayesian optimization of objectives with hierarchical structure