  Data-driven offline model-based optimization (MBO) is an established
practical approach to black-box computational design problems for which the
true objective function is unknown and expensive to query. However, the
standard approach which optimizes designs against a learned proxy model of the
ground truth objective can suffer from distributional shift. Specifically, in
high-dimensional design spaces where valid designs lie on a narrow manifold,
the standard approach is susceptible to producing out-of-distribution, invalid
designs that "fool" the learned proxy model into outputting a high value. Using
an ensemble rather than a single model as the learned proxy can help mitigate
distribution shift, but naive formulations for combining gradient information
from the ensemble, such as minimum or mean gradient, are still suboptimal and
often hampered by non-convergent behavior.
  In this work, we explore alternate approaches for combining gradient
information from the ensemble that are robust to distribution shift without
compromising optimality of the produced designs. More specifically, we explore
two functions, formulated as convex optimization problems, for combining
gradient information: multiple gradient descent algorithm (MGDA) and
conflict-averse gradient descent (CAGrad). We evaluate these algorithms on a
diverse set of five computational design tasks. We compare performance of
ensemble MBO with MGDA and ensemble MBO with CAGrad with three naive baseline
algorithms: (a) standard single-model MBO, (b) ensemble MBO with mean gradient,
and (c) ensemble MBO with minimum gradient.
  Our results suggest that MGDA and CAGrad strike a desirable balance between
conservatism and optimality and can help robustify data-driven offline MBO
without compromising optimality of designs.
