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.

翻译：数据驱动的离线模型优化（MBO）是一种成熟的实用方法，适用于真实目标函数未知且查询成本高昂的黑箱计算设计问题。然而，针对学习到的代理模型优化设计的标准方法可能遭受分布偏移问题。具体而言，在有效设计位于狭窄流形上的高维设计空间中，标准方法容易产生超出分布的无效设计，这些设计会"欺骗"学习到的代理模型输出高值。使用集成而非单一模型作为学习代理有助于缓解分布偏移，但结合集成梯度信息的朴素公式（如最小梯度或平均梯度）仍然次优，且常受困于非收敛行为。本研究探索了结合集成梯度信息的替代方法，这些方法既能抵抗分布偏移，又不损害所生成设计的最优性。具体而言，我们研究了两种通过凸优化公式结合梯度信息的函数：多重梯度下降算法（MGDA）和冲突规避梯度下降（CAGrad）。我们在五个不同的计算设计任务上评估了这些算法。我们将集成MBO结合MGDA和集成MBO结合CAGrad的表现与三种朴素基线算法进行了比较：(a) 标准单模型MBO，(b) 平均梯度集成MBO，(c) 最小梯度集成MBO。结果表明，MGDA和CAGrad在保守性与最优性之间取得了理想平衡，有助于在不牺牲设计最优性的前提下增强数据驱动离线MBO的鲁棒性。