  Classical evolutionary approaches for multiobjective optimization are quite
effective but incur a lot of queries to the objectives; this can be prohibitive
when objectives are expensive oracles. A sample-efficient approach to solving
multiobjective optimization is via Gaussian process (GP) surrogates and
Bayesian optimization (BO). Multiobjective Bayesian optimization (MOBO)
involves the construction of an acquisition function which is optimized to
acquire new observation candidates. This ``inner'' optimization can be hard due
to various reasons: acquisition functions being nonconvex, nondifferentiable
and/or unavailable in analytical form; the success of MOBO heavily relies on
this inner optimization. We do away with this hard acquisition function
optimization step and propose a simple, but effective, Thompson sampling based
approach ($q\texttt{POTS}$) where new candidate(s) are chosen from the Pareto
frontier of random GP posterior sample paths obtained by solving a much cheaper
multiobjective optimization problem. To further improve computational
tractability in higher dimensions we propose an automated active set of
candidates selection combined with a Nystr\"{o}m approximation. Our approach
applies to arbitrary GP prior assumptions and demonstrates strong empirical
performance over the state of the art, both in terms of accuracy and
computational efficiency, on synthetic as well as real-world experiments.
