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We study adversarially robust transfer learning, wherein, given labeled data on multiple (source) tasks, the goal is to train a model with small robust error on a previously unseen (target) task. In particular, we consider a multi-task representation learning (MTRL) setting, i.e., we assume that the source and target tasks admit a simple (linear) predictor on top of a shared representation (e.g., the final hidden layer of a deep neural network). In this general setting, we provide rates on the excess adversarial (transfer) risk for Lipschitz losses and smooth nonnegative losses. These rates show that learning a representation using adversarial training on diverse tasks helps protect against inference-time attacks in data-scarce environments. Additionally, we provide novel rates for the single-task setting. 

We study the limits and capability of public-data assisted differentially private (PA-DP) algorithms. Specifically, we focus on the problem of stochastic convex optimization (SCO) with either labeled or unlabeled public data. For complete/labeled public data, we show lower bounds on the excess risk for any PA-DP algorithm in terms of the dimension d, the number of public samples, npub and the number of private samples, npriv. These lower bounds are established via our new lower bounds for PA-DP mean estimation. Up to constant factors, these lower bounds show that the simple strategy of either treating all data as private or discarding the private data, is optimal. We also study PA-DP supervised learning with unlabeled public samples. In contrast to our previous result, we here show novel methods for leveraging public data in private supervised learning. For generalized linear models (GLM) with unlabeled public data, we show an efficient algorithm which achieves a dimension independent rate. We develop new lower bounds for this setting which shows that this rate cannot be improved with more public samples, and any fewer public samples leads to a worse rate. Finally, we provide extensions of this result to general hypothesis classes with finite fat-shattering dimension with applications to neural networks and non-Euclidean geometries. 

Recent works show that adversarial examples exist for random neural networks [Daniely and Shacham, 2020] and that these examples can be found using a single step of gradient ascent [Bubeck et al., 2021]. In this work, we extend this line of work to the “lazy training” of neural networks – a dominant model in deep learning theory in which neural networks are provably efficiently learnable. We show that over-parametrized neural networks that are guaranteed to generalize well and enjoy strong computational guarantees remain vulnerable to attacks generated using a single step of gradient ascent.