From Function to Distribution Modeling: A PAC-Generative Approach to
  Offline Optimization
Qiang Zhang Ruida Zhou Yang Shen Tie Liu
This paper considers the problem of offline optimization, where the objective
function is unknown except for a collection of ``offline" data examples. While
recent years have seen a flurry of work on applying various machine learning
techniques to the offline optimization problem, the majority of these work
focused on learning a surrogate of the unknown objective function and then
applying existing optimization algorithms. While the idea of modeling the
unknown objective function is intuitive and appealing, from the learning point
of view it also makes it very difficult to tune the objective of the learner
according to the objective of optimization. Instead of learning and then
optimizing the unknown objective function, in this paper we take on a less
intuitive but more direct view that optimization can be thought of as a process
of sampling from a generative model. To learn an effective generative model
from the offline data examples, we consider the standard technique of
``re-weighting", and our main technical contribution is a probably
approximately correct (PAC) lower bound on the natural optimization objective,
which allows us to jointly learn a weight function and a score-based generative
model. The robustly competitive performance of the proposed approach is
demonstrated via empirical studies using the standard offline optimization
benchmarks.