Pre-training has achieved remarkable success when transferred to downstream tasks. In machine learning, we care about not only the good performance of a model but also its behavior under reasonable shifts of condition. The same philosophy holds when pre-training a foundation model. However, the foundation model may not uniformly behave well for a series of related downstream tasks. This happens, for example, when conducting mask recovery regression where the recovery ability or the training instances diverge like pattern features are extracted dominantly on pre-training, but semantic features are also required on a downstream task. This paper considers pre-training a model that guarantees a uniformly good performance over the downstream tasks. We call this goal as $\textit{downstream-task robustness}$. Our method first separates the upstream task into several representative ones and applies a simple minimax loss for pre-training. We then design an efficient algorithm to solve the minimax loss and prove its convergence in the convex setting. In the experiments, we show both on large-scale natural language processing and computer vision datasets our method increases the metrics on worse-case downstream tasks. Additionally, some theoretical explanations for why our loss is beneficial are provided. Specifically, we show fewer samples are inherently required for the most challenging downstream task in some cases.

翻译：预训练在下游任务迁移中取得了显著成功。在机器学习中，我们不仅关注模型的良好性能，还关注其在条件合理变化下的表现。这一理念同样适用于基础模型的预训练。然而，基础模型在一系列相关下游任务上可能无法统一表现良好。例如，当进行掩码恢复回归时，恢复能力或训练实例存在差异——预训练阶段主要提取模式特征，而下游任务却需要语义特征。本文考虑预训练一个能保证下游任务统一良好性能的模型，我们将这一目标称为"下游任务鲁棒性"。该方法首先将上游任务分解为若干代表性任务，并采用简单的极小极大损失进行预训练。随后我们设计了一种高效算法来求解该极小极大损失，并证明了其在凸情形下的收敛性。实验表明，在大规模自然语言处理和计算机视觉数据集上，我们的方法提升了最差下游任务的性能指标。此外，我们提供了理论解释说明该损失的优越性——具体而言，在某些情况下，最具挑战性的下游任务本质上需要更少的样本。