In recent years, machine learning systems have been developed that demonstrate remarkable performance on many tasks. However, naive metrics of performance, such as the accuracy of a classifier on test samples drawn from the same distribution as the training set, can provide an overly optimistic view of the suitability of a model for real-world deployment. In this dissertation, we develop models that are robust, in addition to performing well on large-scale tasks.

One notion of robustness is adversarial robustness, which characterizes the performance of models under adversarial attacks. Adversarial attacks are small, often imperceptible, distortions to the inputs of machine learning systems which are crafted to substantially change the output of the system. These attacks represent a real security threat, and are especially concerning when machine learning systems are used in safety-critical applications.

To mitigate this threat, certifiably robust classification techniques have been developed. In a certifiably robust classifier, for each input sample, in addition to a classification, the classifier also produces a certificate, which is a guaranteed lower bound on the magnitude of any perturbation required to change the classification. Existing methods for certifiable robustness have significant limitations, which we address in Parts I and II of this dissertation:

(i) Currently, randomized smoothing techniques are the only certification techniques that are viable for large-scale image classification (i.e. ImageNet). However, randomized smoothing techniques generally provide only high-probability, rather than exact, certificate results. To address this, we develop deterministic randomized smoothing-based algorithms, which produce exact certificates with finite computational costs. In particular, in Part I of this dissertation, we present to our knowledge the first deterministic, ImageNet-scale certification methods under the L_1, L_p (for p < 1), and "L_0" metrics.

(ii) Certification results only apply to particular metrics of perturbation size. There is therefore a need to develop new techniques to provide provable robustness against different types of attacks. In Part II of this dissertation, we develop randomized smoothing-based algorithms for several new types of adversarial perturbation, including Wasserstein adversarial attacks, Patch adversarial attacks, and Data Poisoning attacks. The methods developed for Patch and Poisoning attacks are also deterministic, allowing for efficient exact certification.

In Part III of this dissertation, we consider a different notion of robustness: test-time adaptability to new objectives in reinforcement learning. This is formalized as goal-conditioned reinforcement learning (GCRL), in which each episode is conditioned by a new "goal," which determines the episode's reward function. In this work, we explore a connection between off-policy GCRL and knowledge distillation, which leads us to apply Gradient-Based Attention Transfer, a knowledge distillation technique, to the Q-function update. We show, empirically and theoretically, that this can improve the performance of off-policy GCRL when the space of goals is high-dimensional.