Lemma A.5 of [ 19 ] we have By substituting ( A.5) into ( A.1) we have, All experiments are conducted on a single NVIDIA V100. It runs on the GNU Linux Debian 4.9 operating The experiment is implemented via PyTorch 1.6.0. This makes the learning problem of CIFAR100 much harder. To demonstrate the fact that the over-fitting problem all comes from perturbation stability in Section 3.2(3), we We found this schedule is the most effective one when only training on the original CIFAR10. In this part, we provide a complete visualization for the two parts in Eqn. We test WideResNet-34 on CIFAR10 and CIFAR10.

Probabilistic dynamics model ensemble is widely used in existing model-based reinforcement learning methods as it outperforms a single dynamics model in both asymptotic performance and sample efficiency. In this paper, we provide both practical and theoretical insights on the empirical success of the probabilistic dynamics model ensemble through the lens of Lipschitz continuity. We find that, for a value function, the stronger the Lipschitz condition is, the smaller the gap between the true dynamics-and learned dynamics-induced Bellman operators is, thus enabling the converged value function to be closer to the optimal value function. Hence, we hypothesize that the key functionality of the probabilistic dynamics model ensemble is to regularize the Lipschitz condition of the value function using generated samples. To test this hypothesis, we devise two practical robust training mechanisms through computing the adversarial noise and regularizing the value network's spectral norm to directly regularize the Lipschitz condition of the value functions. Empirical results show that combined with our mechanisms, model-based RL algorithms with a single dynamics model outperform those with an ensemble of probabilistic dynamics models. These findings not only support the theoretical insight, but also provide a practical solution for developing computationally efficient model-based RL algorithms. Model-based reinforcement learning (MBRL) improves the sample efficiency of an agent by learning a model of the underlying dynamics in a real environment. One of the most fundamental questions in this area is how to learn a model to generate good samples so that it maximally boosts the sample efficiency of policy learning. To address this question, various model architectures are proposed such as Bayesian nonparametric models (Kocijan et al., 2004; Nguyen-Tuong et al., 2008; Kamthe & Deisenroth, 2018), inverse dynamics model (Pathak et al., 2017; Liu et al., 2022), multistep model (Asadi et al., 2019), and hypernetwork (Huang et al., 2021).

Model-agnostic meta-learning (MAML) has emerged as one of the most successful meta-learning techniques in few-shot learning. It enables us to learn a meta-initialization} of model parameters (that we call meta-model) to rapidly adapt to new tasks using a small amount of labeled training data. Despite the generalization power of the meta-model, it remains elusive that how adversarial robustness can be maintained by MAML in few-shot learning. In addition to generalization, robustness is also desired for a meta-model to defend adversarial examples (attacks). Toward promoting adversarial robustness in MAML, we first study WHEN a robustness-promoting regularization should be incorporated, given the fact that MAML adopts a bi-level (fine-tuning vs. meta-update) learning procedure. We show that robustifying the meta-update stage is sufficient to make robustness adapted to the task-specific fine-tuning stage even if the latter uses a standard training protocol. We also make additional justification on the acquired robustness adaptation by peering into the interpretability of neurons' activation maps. Furthermore, we investigate HOW robust regularization can efficiently be designed in MAML. We propose a general but easily-optimized robustness-regularized meta-learning framework, which allows the use of unlabeled data augmentation, fast adversarial attack generation, and computationally-light fine-tuning. In particular, we for the first time show that the auxiliary contrastive learning task can enhance the adversarial robustness of MAML. Finally, extensive experiments are conducted to demonstrate the effectiveness of our proposed methods in robust few-shot learning.