We study the statistical guarantees for the Imitation Learning (IL) problem in episodic MDPs.

Private data analysis suffers a costly curse of dimensionality. However, the data1 often has an underlying low-dimensional structure. For example, when optimizing2 via gradient descent, the gradients often lie in or near a low-dimensional subspace.3 If that low-dimensional structure can be identified, then we can avoid paying (in4 terms of privacy or accuracy) for the high ambient dimension.5 We present differentially private algorithms that take input data sampled from6 a low-dimensional linear subspace (possibly with a small amount of error) and7 output that subspace (or an approximation to it). These algorithms can serve as a8 pre-processing step for other procedures.9

Popular object detection models generate bounding boxes in a different way than we humans. As an example, modern detectors yield object box either upon the regression of its center and width/height (center-guided detector), or by grouping paired estimated corners (corner-guided detector). However, that is not the pattern we manually label an object due to high degrees of freedom in searching centers or low efficiency of grouping corners. Empirically, humans run two steps to locate an object bounding box manually: 1) click the mouse at the top-left corner of object, and then drag the mouse to the bottom-right corner; 2) refine the corner positions to make the bounding box more precisely, if necessary. Inspired by this manual labeling process, we propose a novel human-like detector, termed as HumanLiker, which is devised as a two-stage end-to-end detector to simulate the two aforementioned. Like we humans in manual labeling, HumanLiker can effectively avert both the thorny center searching and heuristic corner grouping. Different from the mainstream detector branches, i.e., the center/corner-guided methods, the HumanLiker provides a new paradigm which integrates the advantages of both branches to balance the detection efficiency and bounding box quality. On MS-COCO test-dev set, HumanLiker can achieve 50.2%/51.6%

The bound in Equation 5 of the main paper can be interpreted using a rank-1 Nyström approximation for f(xt,xt). By holding w fixed and maximizing for q in the right hand side of Equation 5, we get q = f(w,w) P t ytf(xt,w) where f(w,w) indicates the pseudo-inverse.1 Typically the weight vector w, often called a "landmark", used in the Nyström approximation is set either by setting it to a random input or by more sophisticated schemes like setting it with KMeans. In our case, we are directly optimizing the landmarks via Equation 6 in the main paper. To our knowledge the only other work to do this was performed in Fu [2014]. The code used in the main training loop of our algorithm is shown in Figure 1.

Recent works have derived neural networks with online correlation-based learning rules to perform kernel similarity matching. These works applied existing linear similarity matching algorithms to nonlinear features generated with random Fourier methods. In this paper we attempt to perform kernel similarity matching by directly learning the nonlinear features. Our algorithm proceeds by deriving and then minimizing an upper bound for the sum of squared errors between output and input kernel similarities. The construction of our upper bound leads to online correlation-based learning rules which can be implemented with a 1 layer recurrent neural network. In addition to generating high-dimensional linearly separable representations, we show that our upper bound naturally yields representations which are sparse and selective for specific input patterns. We compare the approximation quality of our method to neural random Fourier method and variants of the popular but non-biological "Nyström" method for approximating the kernel matrix. Our method appears to be comparable or better than randomly sampled Nyström methods when the outputs are relatively low dimensional (although still potentially higher dimensional than the inputs) but less faithful when the outputs are very high dimensional.

In this paper we study the training dynamics for gradient flow on over-parametrized tensor decomposition problems. Empirically, such training process often first fits larger components and then discovers smaller components, which is similar to a tensor deflation process that is commonly used in tensor decomposition algorithms. We prove that for orthogonally decomposable tensor, a slightly modified version of gradient flow would follow a tensor deflation process and recover all the tensor components. Our proof suggests that for orthogonal tensors, gradient flow dynamics works similarly as greedy low-rank learning in the matrix setting, which is a first step towards understanding the implicit regularization effect of over-parametrized models for low-rank tensors.

Federated learning is a distributed learning paradigm where multiple agents, each only with access to local data, jointly learn a global model. There has recently been an explosion of research aiming not only to improve the accuracy rates of federated learning, but also provide certain guarantees around social good properties such as total error. One branch of this research has taken a game-theoretic approach, and in particular, prior work has viewed federated learning as a hedonic game, where error-minimizing players arrange themselves into federating coalitions. This past work proves the existence of stable coalition partitions, but leaves open a wide range of questions, including how far from optimal these stable solutions are. In this work, we motivate and define a notion of optimality given by the average error rates among federating agents (players).