Reinforcement learning algorithms, though successful, tend to over-fit to training environments hampering their application to the real-world. This paper proposes WR @math L; a robust reinforcement learning algorithm with significant robust performance on low and high-dimensional control tasks. Our method formalises robust reinforcement learning as a novel min-max game with a Wasserstein constraint for a correct and convergent solver. Apart from the formulation, we also propose an efficient and scalable solver following a novel zero-order optimisation method that we believe can be useful to numerical optimisation in general. We contribute both theoretically and empirically. On the theory side, we prove that WR @math L converges to a stationary point in the general setting of continuous state and action spaces. Empirically, we demonstrate significant gains compared to standard and robust state-of-the-art algorithms on high-dimensional MuJuCo environments.
More recently, @cite_2 studies robustness with respect to action perturbations. There are two forms of perturbation addressed: (i) Probabilistic Action Robust MDP (PR-MDP), and (ii) Noisy Action Robust MDP (NR-MDP). In PR-MDP, when an action is taken by an agent, with probability @math , a different, possibly adversarial action is taken instead. In NR-MDP, when an action is taken, a perturbation is added to the action itself. Like @cite_11 and @cite_13 , the algorithm is suitable for applying deep neural networks, and the paper reports experiments on InvertedPendulum, Hopper, Walker2d and Humanoid. We tested against PR-MDP in some of our experiments, and found it to be lacking in robustness (see Section , Figure and Figure ).
@cite_11 @cite_13 @cite_2
1554120378 2793079679 2217248474 2911793117
Learning to act optimally in a complex, dynamic and noisy environment is a hard problem. Various threads of research from reinforcement learning, animal conditioning, operations research, machine learning, statistics and optimal control are beginning to come together to offer solutions to this problem. I present a thesis in which novel algorithms are presented for learning the dynamics, learning the value function, and selecting good actions for Markov decision processes. The problems considered have high-dimensional factored state and action spaces, and are either fully or partially observable. The approach I take is to recognize similarities between the problems being solved in the reinforcement learning and graphical models literature, and to use and combine techniques from the two fields in novel ways. In particular I present two new algorithms. First, the DBN algorithm learns a compact representation of the core process of a partially observable MDP. Because inference in the DBN is intractable, I use approximate inference to maintain the belief state. A belief state action-value function is learned using reinforcement learning. I show that this DBN algorithm can solve POMDPs with very large state spaces and useful hidden state. Second, the PoE algorithm learns an approximation to value functions over large factored state-action spaces. The algorithm approximates values as (negative) free energies in a product of experts model. The model parameters can be learned efficiently because inference is tractable in a product of experts. I show that good actions can be found even in large factored action spaces by the use of brief Gibbs sampling. These two new algorithms take techniques from the machine learning community and apply them in new ways to reinforcement learning problems. Simulation results show that these new methods can be used to solve very large problems. The DBN method is used to solve a POMDP with a hidden state space and an observation space of size greater than 2180. The DBN model of the core process has 232 states represented as 32 binary variables. The PoE method is used to find actions in action spaces of size 240 . Although adversarial samples of deep neural networks (DNNs) have been intensively studied on static images, their extensions in videos are never explored. Compared with images, attacking a video needs to consider not only spatial cues but also temporal cues. Moreover, to improve the imperceptibility as well as reduce the computation cost, perturbations should be added on as fewer frames as possible, i.e., adversarial perturbations are temporally sparse. This further motivates the propagation of perturbations, which denotes that perturbations added on the current frame can transfer to the next frames via their temporal interactions. Thus, no (or few) extra perturbations are needed for these frames to misclassify them. To this end, we propose an l2,1-norm based optimization algorithm to compute the sparse adversarial perturbations for videos. We choose the action recognition as the targeted task, and networks with a CNN+RNN architecture as threat models to verify our method. Thanks to the propagation, we can compute perturbations on a shortened version video, and then adapt them to the long version video to fool DNNs. Experimental results on the UCF101 dataset demonstrate that even only one frame in a video is perturbed, the fooling rate can still reach 59.7 . We show that adversarial examples, i.e., the visually imperceptible perturbations that result in Convolutional Neural Networks (CNNs) fail, can be alleviated with a mechanism based on foveations---applying the CNN in different image regions. To see this, first, we report results in ImageNet that lead to a revision of the hypothesis that adversarial perturbations are a consequence of CNNs acting as a linear classifier: CNNs act locally linearly to changes in the image regions with objects recognized by the CNN, and in other regions the CNN may act non-linearly. Then, we corroborate that when the neural responses are linear, applying the foveation mechanism to the adversarial example tends to significantly reduce the effect of the perturbation. This is because, hypothetically, the CNNs for ImageNet are robust to changes of scale and translation of the object produced by the foveation, but this property does not generalize to transformations of the perturbation. As a result, the accuracy after a foveation is almost the same as the accuracy of the CNN without the adversarial perturbation, even if the adversarial perturbation is calculated taking into account a foveation. Consider a Markov decision process (MDP) that admits a set of state-action features, which can linearly express the process's probabilistic transition model. We propose a parametric Q-learning algorithm that finds an approximate-optimal policy using a sample size proportional to the feature dimension @math and invariant with respect to the size of the state space. To further improve its sample efficiency, we exploit the monotonicity property and intrinsic noise structure of the Bellman operator, provided the existence of anchor state-actions that imply implicit non-negativity in the feature space. We augment the algorithm using techniques of variance reduction, monotonicity preservation, and confidence bounds. It is proved to find a policy which is @math -optimal from any initial state with high probability using @math sample transitions for arbitrarily large-scale MDP with a discount factor @math . A matching information-theoretical lower bound is proved, confirming the sample optimality of the proposed method with respect to all parameters (up to polylog factors).