Offline optimization aims to maximize a black-box objective function with a
static dataset and has wide applications. In addition to the objective function
being black-box and expensive to evaluate, numerous complex real-world problems
entail optimizing multiple conflicting objectives, i.e., multi-objective
optimization (MOO). Nevertheless, offline MOO has not progressed as much as
offline single-objective optimization (SOO), mainly due to the lack of
benchmarks like Design-Bench for SOO. To bridge this gap, we propose a first
benchmark for offline MOO, covering a range of problems from synthetic to
real-world tasks. This benchmark provides tasks, datasets, and open-source
examples, which can serve as a foundation for method comparisons and
advancements in offline MOO. Furthermore, we analyze how the current related
methods can be adapted to offline MOO from four fundamental perspectives,
including data, model architecture, learning algorithm, and search algorithm.
Empirical results show improvements over the best value of the training set,
demonstrating the effectiveness of offline MOO methods. As no particular method
stands out significantly, there is still an open challenge in further enhancing
the effectiveness of offline MOO. We finally discuss future challenges for
offline MOO, with the hope of shedding some light on this emerging field. Our
code is available at https://github.com/lamda-bbo/offline-moo.

离线优化涉及最大化一个黑盒目标函数，存在广泛的应用。然而，与离线单目标优化相比，离线多目标优化进展不足，主要原因是缺乏像单目标优化的 Design-Bench 这样的基准。为了填补这一差距，我们提出了离线多目标优化的第一个基准，覆盖了从合成到真实任务的一系列问题。该基准提供了任务、数据集和开源示例，可作为方法比较和离线多目标优化进展的基础。此外，我们从数据、模型架构、学习算法和搜索算法四个基本角度分析了如何将当前相关方法调整为离线多目标优化。实证结果显示，离线多目标优化方法相较于训练集的最佳值有所改进，证明了其有效性。由于没有特定的方法明显优于其他方法，进一步提高离线多目标优化的效果仍然是一个开放性挑战。最后，我们探讨了离线多目标优化的未来挑战，希望为这个新兴领域带来一些启示。我们的代码可在 https://github.com/lamda-bbo/offline-moo 找到。