In offline model-based optimization, we strive to maximize a black-box objective function by only leveraging a static dataset of designs and their scores. This problem setting arises in numerous fields including the design of materials, robots, DNA sequences, and proteins. Recent approaches train a deep neural network (DNN) on the static dataset to act as a proxy function, and then perform gradient ascent on the existing designs to obtain potentially high-scoring designs. This methodology frequently suffers from the out-of-distribution problem where the proxy function often returns poor designs. To mitigate this problem, we propose BiDirectional learning for offline Infinite-width model-based optimization (BDI). BDI consists of two mappings: the forward mapping leverages the static dataset to predict the scores of the high-scoring designs, and the backward mapping leverages the high-scoring designs to predict the scores of the static dataset. The backward mapping, neglected in previous work, can distill more information from the static dataset into the high-scoring designs, which effectively mitigates the out-of-distribution problem. For a finite-width DNN model, the loss function of the backward mapping is intractable and only has an approximate form, which leads to a significant deterioration of the design quality. We thus adopt an infinite-width DNN model, and propose to employ the corresponding neural tangent kernel to yield a closed-form loss for more accurate design updates. Experiments on various tasks verify the effectiveness of BDI. The code is available at https://github.com/GGchen1997/BDI.

翻译：在离线基于模型优化中，我们仅利用设计及其得分的静态数据集来最大化黑盒目标函数。该问题出现在众多领域，包括材料设计、机器人设计、DNA序列设计和蛋白质设计。近期方法在静态数据集上训练深度神经网络（DNN）作为代理函数，随后对现有设计执行梯度上升以获得潜在高分设计。该方法常面临分布外问题，即代理函数经常返回低质量设计。为缓解该问题，我们提出离线无限宽度基于模型优化的双向学习（BDI）。BDI包含两个映射：前向映射利用静态数据集预测高分设计的得分，反向映射则利用高分设计预测静态数据集的得分。这一反向映射在以往工作中被忽视，它能从静态数据集中提取更多信息注入高分设计，有效缓解分布外问题。对于有限宽度DNN模型，反向映射的损失函数难以计算且仅存在近似形式，导致设计质量显著下降。因此我们采用无限宽度DNN模型，并提出使用对应的神经正切核生成闭式损失以实现更精确的设计更新。多种任务上的实验验证了BDI的有效性。代码开源在https://github.com/GGchen1997/BDI。