We consider streaming principal component analysis when the stochastic datagenerating model is subject to perturbations. While existing models assume a fixed covariance, we adopt a robust perspective where the covariance matrix belongs to a temporal uncertainty set. Under this setting, we provide fundamental limits on convergence of any algorithm recovering principal components. We analyze the convergence of the noisy power method and Oja's algorithm, both studied for the stationary data generating model, and argue that the noisy power method is rate-optimal in our setting. Finally, we demonstrate the validity of our analysis through numerical experiments on synthetic and real-world dataset.

In order to expand the polynomial surface fitting in 3D dimensional space into the high dimensional feature space using a neural network with parameter Θ, we define f1(gω):= g and f2(cυ):= c, where f means MLP layer. Then, the multiplication of real numbers gω cυ in the polynomial function is represented as g c, i.e., gω cυ:= g c, and the orders ω,υ [0,1,...,τ]. Then, the final bivariate function used in our hyper surface fitting is Nθ,τ(G,C) = Θ(G C), where Gand C are high dimensional features of the 3D point clouds extracted by the two different modules, which are introduced in Sec.3.3 and Sec.3.4 of the paper, respectively. The other terms except the principal terms in the polynomial equation are not used in the estimation of the normal. Based on this, we use the max-pooling over all features from the hyper surface fitting 2 Figure 1: Visualization of the contribution of each 3D point to estimate the normal of the query point (black).

It aims to transfer the pose of a source mesh to a target mesh and keep the identity (e.g., body shape) of the target mesh. Some previous works require key point annotations to build reliable correspondence between the source and target meshes, while other methods do not consider any shape correspondence between sources and targets, which leads to limited generation quality. In this work, we propose a correspondence-refinement network to achieve the 3D pose transfer for both human and animal meshes. The correspondence between source and target meshes is first established by solving an optimal transport problem. Then, we warp the source mesh according to the dense correspondence and obtain a coarse warped mesh. The warped mesh will be better refined with our proposed Elastic Instance Normalization, which is a conditional normalization layer and can help to generate highquality meshes. Extensive experimental results show that the proposed architecture can effectively transfer the poses from source to target meshes and produce better results with satisfied visual performance than state-of-the-art methods.

We consider Model-Agnostic Meta-Learning (MAML) methods for Reinforcement Learning (RL) problems, where the goal is to find a policy using data from several tasks represented by Markov Decision Processes (MDPs) that can be updated by one step of stochastic policy gradient for the realized MDP. In particular, using stochastic gradients in MAML update steps is crucial for RL problems since computation of exact gradients requires access to a large number of possible trajectories. For this formulation, we propose a variant of the MAML method, named Stochastic Gradient Meta-Reinforcement Learning (SG-MRL), and study its convergence properties. We derive the iteration and sample complexity of SGMRL to find an -first-order stationary point, which, to the best of our knowledge, provides the first convergence guarantee for model-agnostic meta-reinforcement learning algorithms. We further show how our results extend to the case where more than one step of stochastic policy gradient method is used at test time. Finally, we empirically compare SG-MRL and MAML in several deep RL environments.