Multitask learning is widely used in practice to train a low-resource target task by augmenting it with multiple related source tasks. Yet, naively combining all the source tasks with a target task does not always improve the prediction performance for the target task due to negative transfers. Thus, a critical problem in multitask learning is identifying subsets of source tasks that would benefit the target task. This problem is computationally challenging since the number of subsets grows exponentially with the number of source tasks; efficient heuristics for subset selection do not always capture the relationship between task subsets and multitask learning performances. In this paper, we introduce an efficient procedure to address this problem via surrogate modeling. In surrogate modeling, we sample (random) subsets of source tasks and precompute their multitask learning performances. Then, we approximate the precomputed performances with a linear regression model that can also predict the multitask performance of unseen task subsets. We show theoretically and empirically that fitting this model only requires sampling linearly many subsets in the number of source tasks. The fitted model provides a relevance score between each source and target task. We use the relevance scores to perform subset selection for multitask learning by thresholding. Through extensive experiments, we show that our approach predicts negative transfers from multiple source tasks to target tasks much more accurately than existing task affinity measures. Additionally, we demonstrate that for several weak supervision datasets, our approach consistently improves upon existing optimization methods for multitask learning.