We study square loss in a realizable time-series framework with martingale difference noise. Our main result is a fast rate excess risk bound which shows that whenever a trajectory hypercontractivity condition holds, the risk of the leastsquares estimator on dependent data matches the iid rate order-wise after a burn-in time. In comparison, many existing results in learning from dependent data have rates where the effective sample size is deflated by a factor of the mixing-time of the underlying process, even after the burn-in time. Furthermore, our results allow the covariate process to exhibit long range correlations which are substantially weaker than geometric ergodicity. We call this phenomenon learning with little mixing, and present several examples for when it occurs: bounded function classes for which the L2 and L2+ε norms are equivalent, ergodic finite state Markov chains, various parametric models, and a broad family of infinite dimensional ℓ2(N)ellipsoids. By instantiating our main result to system identification of nonlinear dynamics with generalized linear model transitions, we obtain a nearly minimax optimal excess risk bound after only a polynomial burn-in time.

When solving two-player zero-sum games, multi-agent reinforcement learning (MARL) algorithms often create populations of agents where, at each iteration, a new agent is discovered as the best response to a mixture over the opponent population. Within such a process, the update rules of "who to compete with" (i.e., the opponent mixture) and "how to beat them" (i.e., finding best responses) are underpinned by manually developed game theoretical principles such as fictitious play and Double Oracle. In this paper1, we introduce a novel framework--Neural Auto-Curricula (NAC)--that leverages meta-gradient descent to automate the discovery of the learning update rule without explicit human design. Specifically, we parameterise the opponent selection module by neural networks and the bestresponse module by optimisation subroutines, and update their parameters solely via interaction with the game engine, where both players aim to minimise their exploitability. Surprisingly, even without human design, the discovered MARL algorithms achieve competitive or even better performance with the state-of-the-art population-based game solvers (e.g., PSRO) on Games of Skill, differentiable Lotto, non-transitive Mixture Games, Iterated Matching Pennies, and Kuhn Poker. Additionally, we show that NAC is able to generalise from small games to large games, for example training on Kuhn Poker and outperforming PSRO on Leduc Poker. Our work inspires a promising future direction to discover general MARL algorithms solely from data.

This work presents ReSync, a Riemannian subgradient-based algorithm for solving the robust rotation synchronization problem, which arises in various engineering applications. ReSync solves a least-unsquared minimization formulation over the rotation group, which is nonsmooth and nonconvex, and aims at recovering the underlying rotations directly. We provide strong theoretical guarantees for ReSync under the random corruption setting. Specifically, we first show that the initialization procedure of ReSyncyields a proper initial point that lies in a local region around the ground-truth rotations. We next establish the weak sharpness property of the aforementioned formulation and then utilize this property to derive the local linear convergence of ReSyncto the ground-truth rotations. By combining these guarantees, we conclude that ReSync converges linearly to the ground-truth rotations under appropriate conditions. Experiment results demonstrate the effectiveness of ReSync.

In this section, we theoretically analyze the dynamics of the DAM mask gi at the i-th layer as the training process unfolds. The loss function for training the neural network for the target task can then be denoted as L= L(f(x,Θ,βi)) (e.g., cross-entropy loss for supervised structured pruning problems and reconstruction error for representation learning problems), where xdenotes the input features to the neural network. Using gradient descent methods with a learning rate of η, the expected update formula of βi in DAM is given by: βi = ηEx Dtr [ βiL(f(x,Θ,βi)) + λ βiβi/(l 1)] (2) = ηEx Dtr [ βiL(f(x,Θ,βi))] ηλ/(l 1) (3) Let hi be the layer output before applying the DAM mask, and the masked output be represented as oi = hi gi after applying the gate. For the j-th neuron, gij/ βi = 0 if and only if ξj(βi)/ βi = 0. Since tanh(z) has non-zero gradients for z >0, the gradient of ξj(βi) is 0 only when kj/ni + βi 0, i.e., the mask value of the neuron is 0 (or in other words, it is deactivated or dead). Let us denote the set of all neuron indices with non-zero mask values (also referred to as active neurons) as J. Equation 4 can then be simplified as: βiL(f(x,Θ,βi)) = αi X We can make the following two observations: (i) only those neurons that are active (i.e., have non-zero mask values) have a contribution towards updating βi and moving the gate function. We name these neurons as support neurons and their position in the ordering of neurons as the transitioning zone of the gate function.

We construct SEIDNet based on PyTorch1. There are 26 convolutional layers for extracting the visual feature map from the rainy image. The feature masking contains two convolutional layers. It computes the rain (or object) feature map. There is a pair of batch normalization and ReLU layers between the adjacent convolutional layers. The size of kernels in each convolutional layer is 3 3. Vid generates 3 3kernel for deraining each pixel.

Image rain removal requires the accurate separation between the pixels of the rain streaks and object textures. But the confusing appearances of rains and objects lead to the misunderstanding of pixels, thus remaining the rain streaks or missing the object details in the result. In this paper, we propose SEIDNet equipped with the generative Status Estimation and Information Decoupling for rain removal. In the status estimation, we embed the pixel-wise statuses into the status space, where each status indicates a pixel of the rain or object. The status space allows sampling multiple statuses for a pixel, thus capturing the confusing rain or object. In the information decoupling, we respect the pixel-wise statuses, decoupling the appearance information of rain and object from the pixel. Based on the decoupled information, we construct the kernel space, where multiple kernels are sampled for the pixel to remove the rain and recover the object appearance. We evaluate SEIDNet on the public datasets, achieving state-of-the-art performances of image rain removal. The experimental results also demonstrate the generalization of SEIDNet, which can be easily extended to achieve state-of-the-art performances on other image restoration tasks (e.g., snow, haze, and shadow removal).

Algorithm 1 Hard-gating Algorithm for In-Stage IDKCascade Input Ds: Training data containing Ns samples in stage-s Ms: Sorted list of the models trained for stage-s C: Dictionary of models' spatio-temporal costs cs: User-defined budget of spatio-temporal cost for stage-s q: Confidence function maxA: Value for the upper bound of the cutoffs to avoid over-fitting nBins: Number of bins for the grid search Output s: The optimal IDK cutoff vector for stage-s 1: procedure HARDGATING(Ds, Ms, cs, C, q, maxA, nBins) 2: s =[], ModelAssign = 1, cost = P We use the Sepsis-3 toolkit3 to obtain the suspected infection time in patients, and following the process in Seymour et al. (2016) to finally label the onset of sepsis. We result at a total number of 20,009 sepsis patients out of the 52,902 adult patients from MIMIC-III database. We exclude those patients who stay in ICUs less than 6 hours and also exclude those patients who developed sepsis within the first 6 hours after ICU admission. This reduces our cohort to a total of 34,475ICU patient, and only 2,370(6.8%) Then according to Singer et al. (2016), we identify the onset of septic shock as Algorithm 3 End-to-End Training algorithm for UnfoldML Input D: Full training data containing N instances M: Full model zoo C: Dictionary of models' spatio-temporal costs q: Confidence criterion Output: the optimal ICK1 gate parameters (or a,b): the optimal IDK gate parameters 1: procedure END-TO-ENDTRAINING (D, M) 2: Pre-allocate costs cs for each stage s. Figure 4: Transitions in model calls: both cascades always call the first model per each stage for an entrance and transition to next models (IDK) or next stage (ICK).