When f is convex with respect tox, many efficient algorithms can be powerful tools for solving Problem(1). One well-known algorithm is mirror descent (MD) [5]which is based on Bregman divergence.

In this work, we propose a new approach to R-D estimation from the perspective of optimal transport.

Moreover, Evolution Gym is easy to use.

Bayesian Optimization specifically aims toincrease sample efficiencyfor hard optimization algorithms, and consequently can help achieve better solutions without incurring large societal costs. In the 2-objective case, instead of padding the box decomposition, the Pareto frontier under each posterior sample can be padded instead by repeating a point on the Pareto Frontier such that the padded Pareto frontier under every posterior sample has exactlymaxt|Pt| points. Since the sequentialNEHVIis equivalent to theqNEHVIwith q = 1, we prove Theorem 1 for the generalq > 1 case. Recall from Section C.2, that using the method of common random numbers tofixthebasesamples, theIEPandCBDformulations areequivalent. Note that the box decomposition of the non-dominated space{S1,...,SKt} and the number of rectangles in the box decomposition depend onζt.