In this work, we generalize the direct policy search algorithms to an algorithm we call Direct Environment Search with (projected stochastic) Gradient Ascent (DESGA). The latter can be used to jointly learn a reinforcement learning (RL) environment and a policy with maximal expected return over a joint hypothesis space of environments and policies. We illustrate the performance of DESGA on two benchmarks. First, we consider a parametrized space of Mass-Spring-Damper (MSD) environments. Then, we use our algorithm for optimizing the size of the components and the operation of a small-scale and autonomous energy system, i.e. a solar off-grid microgrid, composed of photovoltaic panels, batteries, etc.

Gathering labeled data to train well-performing machine learning models is one of the critical challenges in many applications. Active learning aims at reducing the labeling costs by an efficient and effective allocation of costly labeling resources. In this article, we propose a decision-theoretic selection strategy that (1) directly optimizes the gain in misclassification error, and (2) uses a Bayesian approach by introducing a conjugate prior distribution to determine the class posterior to deal with uncertainties. By reformulating existing selection strategies within our proposed model, we can explain which aspects are not covered in current state-of-the-art and why this leads to the superior performance of our approach. Extensive experiments on a large variety of datasets and different kernels validate our claims.

Knowledge distillation is to transfer the knowledge from the data learned by the teacher network to the student network, so that the student has the advantage of less parameters and less calculations, and the accuracy is close to the teacher. In this paper, we propose a new distillation method, which contains two transfer distillation strategies and a loss decay strategy. The first transfer strategy is based on channel-wise attention, called Channel Distillation (CD). CD transfers the channel information from the teacher to the student. The second is Guided Knowledge Distillation (GKD). Unlike Knowledge Distillation (KD), which allows the student to mimic each sample's prediction distribution of the teacher, GKD only enables the student to mimic the correct output of the teacher. The last part is Early Decay Teacher (EDT). During the training process, we gradually decay the weight of the distillation loss. The purpose is to enable the student to gradually control the optimization rather than the teacher. Our proposed method is evaluated on ImageNet and CIFAR100. On ImageNet, we achieve 27.68% of top-1 error with ResNet18, which outperforms state-of-the-art methods. On CIFAR100, we achieve surprising result that the student outperforms the teacher. Code is available at https://github.com/zhouzaida/channel-distillation.

In the artificial neuron, I replace the dot product with the weighted Lehmer mean, which may emulate different cases of a generalized mean. The single neuron instance is replaced by a multiplet of neurons which have the same averaging weights. A group of outputs feed forward, in lieu of the single scalar. The generalization parameter is typically set to a different value for each neuron in the multiplet. I further extend the concept to a multiplet taken from the Gini mean. Derivatives with respect to the weight parameters and with respect to the two generalization parameters are given. Some properties of the network are investigated, showing the capacity to emulate the classical exclusive-or problem organically in two layers and perform some multiplication and division. The network can instantiate truncated power series and variants, which can be used to approximate different functions, provided that parameters are constrained. Moreover, a mean case slope score is derived that can facilitate a learning-rate novelty based on homogeneity of the selected elements. The multiplet neuron equation provides a way to segment regularization timeframes and approaches.

We recall that if $A$ is an invertible and symmetric real $m\times m$ matrix, then it is diagonalisable. Therefore, if we denote by $\mathcal{E}^{+}(A)\subset \mathbb{R}^m$ (respectively $\mathcal{E}^{-}(A)\subset \mathbb{R}^m$) to be the vector subspace generated by eigenvectors with positive eigenvalues of $A$ (correspondingly the vector subspace generated by eigenvectors with negative eigenvalues of $A$), then we have an orthogonal decomposition $\mathbb{R}^m=\mathcal{E}^{+}(A)\oplus \mathcal{E}^{-}(A)$. Hence, every $x\in \mathbb{R}^m$ can be written uniquely as $x=pr_{A,+}(x)+pr_{A,-}(x)$ with $pr_{A,+}(x)\in \mathcal{E}^{+}(A)$ and $pr_{A,-}(x)\in \mathcal{E}^{-}(A)$. We propose the following simple new modification of quasi-Newton's methods. {\bf New Q-Newton's method.} Let $\Delta =\{\delta _0,\delta _1,\delta _2,\ldots \}$ be a countable set of real numbers which has at least $m+1$ elements. Let $f:\mathbb{R}^m\rightarrow \mathbb{R}$ be a $C^2$ function. Let $\alpha >0$. For each $x\in \mathbb{R}^m$ such that $\nabla f(x)\not=0$, let $\delta (x)=\delta _j$, where $j$ is the smallest number so that $\nabla ^2f(x)+\delta _j||\nabla f(x)||^{1+\alpha}Id$ is invertible. (If $\nabla f(x)=0$, then we choose $\delta (x)=\delta _0$.) Let $x_0\in \mathbb{R}^m$ be an initial point. We define a sequence of $x_n\in \mathbb{R}^m$ and invertible and symmetric $m\times m$ matrices $A_n$ as follows: $A_n=\nabla ^2f(x_n)+\delta (x_n) ||\nabla f(x_n)||^{1+\alpha}Id$ and $x_{n+1}=x_n-w_n$, where $w_n=pr_{A_n,+}(v_n)-pr_{A_n,-}(v_n)$ and $v_n=A_n^{-1}\nabla f(x_n)$. The main result of this paper roughly says that if $f$ is $C^3$ and a sequence $\{x_n\}$, constructed by the New Q-Newton's method from a random initial point $x_0$, {\bf converges}, then the limit point is not a saddle point, and the convergence rate is the same as that of Newton's method.

Stochastic optimization algorithms have become indispensable in modern machine learning. An unresolved foundational question in this area is the difference between with-replacement sampling and without-replacement sampling -- does the latter have superior convergence rate compared to the former? A groundbreaking result of Recht and R\'e reduces the problem to a noncommutative analogue of the arithmetic-geometric mean inequality where $n$ positive numbers are replaced by $n$ positive definite matrices. If this inequality holds for all $n$, then without-replacement sampling indeed outperforms with-replacement sampling. The conjectured Recht-R\'e inequality has so far only been established for $n = 2$ and a special case of $n = 3$. We will show that the Recht-R\'e conjecture is false for general $n$. Our approach relies on the noncommutative Positivstellensatz, which allows us to reduce the conjectured inequality to a semidefinite program and the validity of the conjecture to certain bounds for the optimum values, which we show are false as soon as $n = 5$.

Covariance data as represented by symmetric positive definite (SPD) matrices are ubiquitous throughout technical study as efficient descriptors of interdependent systems. Euclidean analysis of SPD matrices, while computationally fast, can lead to skewed and even unphysical interpretations of data. Riemannian methods preserve the geometric structure of SPD data at the cost of expensive eigenvalue computations. In this paper, we propose a geometric method for unsupervised clustering of SPD data based on the Thompson metric. This technique relies upon a novel "inductive midrange" centroid computation for SPD data, whose properties are examined and numerically confirmed. We demonstrate the incorporation of the Thompson metric and inductive midrange into X-means and K-means++ clustering algorithms.

We show that, when we cast meta-learning problem as BRM, the optimal solution Meta-Learning is a family of methods that use is given by the predictive distribution computed from a set of interrelated tasks to learn a model that the posterior distribution of the latent variable conditioned can quickly learn a new query task from a possibly against the contextual dataset. This result justifies the use of small contextual dataset. In this study, we the predictive distribution in many previous studies of meta use a probabilistic framework to formalize what learning, such as (Edwards & Storkey, 2017; Gordon et al., it means for two tasks to be related and reframe 2018; Garnelo et al., 2018). However, the optimality of the the meta-learning problem into the problem of predictive distribution cannot be guaranteed if one uses an Bayesian risk minimization (BRM). In our formulation, approximation of the posterior distribution that violates the the BRM optimal solution is given by the way the posterior distribution changes with the contextual predictive distribution computed from the posterior dataset, and this is unfortunately the case for most of the distribution of the task-specific latent variable aforementioned works. For example, the variance of the conditioned on the contextual dataset, and this posterior in these works do not converge to 0 as we take justifies the philosophy of Neural Process.

The important peaks related to the physical properties of a lithium ion rechargeable battery were extracted from the measured X ray diffraction spectrum by a convolutional neural network based on the Attention mechanism. Among the deep features, the lattice constant of the cathodic active material was selected as a cell voltage predictor, and the crystallographic behavior of the active anodic and cathodic materials revealed the rate property during the charge discharge states. The machine learning automatically selected the significant peaks from the experimental spectrum. Applying the Attention mechanism with appropriate objective variables in multi task trained models, one can selectively visualize the correlations between interesting physical properties. As the deep features are automatically defined, this approach can adapt to the conditions of various physical experiments.

Deep convolution-based single image super-resolution (SISR) networks embrace the benefits of learning from large-scale external image resources for local recovery, yet most existing works have ignored the long-range feature-wise similarities in natural images. Some recent works have successfully leveraged this intrinsic feature correlation by exploring non-local attention modules. However, none of the current deep models have studied another inherent property of images: cross-scale feature correlation. In this paper, we propose the first Cross-Scale Non-Local (CS-NL) attention module with integration into a recurrent neural network. By combining the new CS-NL prior with local and in-scale non-local priors in a powerful recurrent fusion cell, we can find more cross-scale feature correlations within a single low-resolution (LR) image. The performance of SISR is significantly improved by exhaustively integrating all possible priors. Extensive experiments demonstrate the effectiveness of the proposed CS-NL module by setting new state-of-the-arts on multiple SISR benchmarks.