  In many real-world scenarios, decision makers seek to efficiently optimize
multiple competing objectives in a sample-efficient fashion. Multi-objective
Bayesian optimization (BO) is a common approach, but many of the
best-performing acquisition functions do not have known analytic gradients and
suffer from high computational overhead. We leverage recent advances in
programming models and hardware acceleration for multi-objective BO using
Expected Hypervolume Improvement (EHVI)---an algorithm notorious for its high
computational complexity. We derive a novel formulation of q-Expected
Hypervolume Improvement (qEHVI), an acquisition function that extends EHVI to
the parallel, constrained evaluation setting. qEHVI is an exact computation of
the joint EHVI of q new candidate points (up to Monte-Carlo (MC) integration
error). Whereas previous EHVI formulations rely on gradient-free acquisition
optimization or approximated gradients, we compute exact gradients of the MC
estimator via auto-differentiation, thereby enabling efficient and effective
optimization using first-order and quasi-second-order methods. Our empirical
evaluation demonstrates that qEHVI is computationally tractable in many
practical scenarios and outperforms state-of-the-art multi-objective BO
algorithms at a fraction of their wall time.
