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：预训练在迁移到下游任务时已取得显著成功。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行为。这一理念同样适用于预训练基础模型。然而，基础模型在多个相关下游任务上可能无法表现均匀。例如，当进行掩码恢复回归时，恢复能力或训练实例出现差异，如预训练中主要提取模式特征，但下游任务仍需语义特征，便会出现此类情况。本文考虑预训练一个能保证在下游任务上表现均匀良好的模型，我们将此目标称为“下游任务鲁棒性”。我们的方法首先将上游任务拆分为若干代表性任务，并应用简单的最小最大损失进行预训练。随后，我们设计了一种高效算法求解该最小最大损失，并证明其在凸优化条件下的收敛性。实验表明，在大型自然语言处理与计算机视觉数据集上，我们的方法提升了最差情况下游任务的指标。此外，我们还从理论上解释了该损失的有效性，具体而言，证明了在某些情况下，最困难的下游任务本质上需要更少的样本。