We present a meta-learning approach based on learning an adaptive, high-dimensional loss function that can generalize across multiple tasks and different model architectures. We develop a fully differentiable pipeline for learning a loss function targeted at maximizing the performance of an optimizee trained using this loss function. We observe that the loss landscape produced by our learned loss significantly improves upon the original task-specific loss. We evaluate our method on supervised and reinforcement learning tasks. Furthermore, we show that our pipeline is able to operate in sparse reward and self-supervised reinforcement learning scenarios.
Our framework falls into the category of learning loss landscapes; similar to @cite_2 , we aim at learning a separate optimization procedure that can be applied to various optimizee models. However, in contrast to @cite_2 and @cite_1 , our framework does not require a specific recurrent architecture of the optimizer and can operate without an explicit external loss or reward function during test time. Furthermore, as our learned loss functions are independent of the models to be optimized, they can be easily transferred to other optimizee models, in contrast to @cite_11 , where the learned representation can not be separated from the original model of the optimizee.
@cite_11 @cite_1 @cite_2
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Due to the success of deep learning to solving a variety of challenging machine learning tasks, there is a rising interest in understanding loss functions for training neural networks from a theoretical aspect. Particularly, the properties of critical points and the landscape around them are of importance to determine the convergence performance of optimization algorithms. In this paper, we provide full (necessary and sufficient) characterization of the analytical forms for the critical points (as well as global minimizers) of the square loss functions for various neural networks. We show that the analytical forms of the critical points characterize the values of the corresponding loss functions as well as the necessary and sufficient conditions to achieve global minimum. Furthermore, we exploit the analytical forms of the critical points to characterize the landscape properties for the loss functions of these neural networks. One particular conclusion is that: The loss function of linear networks has no spurious local minimum, while the loss function of one-hidden-layer nonlinear networks with ReLU activation function does have local minimum that is not global minimum. The choice of the loss function is critical in extreme multi-label learning where the objective is to annotate each data point with the most relevant subset of labels from an extremely large label set. Unfortunately, existing loss functions, such as the Hamming loss, are unsuitable for learning, model selection, hyperparameter tuning and performance evaluation. This paper addresses the issue by developing propensity scored losses which: (a) prioritize predicting the few relevant labels over the large number of irrelevant ones; (b) do not erroneously treat missing labels as irrelevant but instead provide unbiased estimates of the true loss function even when ground truth labels go missing under arbitrary probabilistic label noise models; and (c) promote the accurate prediction of infrequently occurring, hard to predict, but rewarding tail labels. Another contribution is the development of algorithms which efficiently scale to extremely large datasets with up to 9 million labels, 70 million points and 2 million dimensions and which give significant improvements over the state-of-the-art. This paper's results also apply to tagging, recommendation and ranking which are the motivating applications for extreme multi-label learning. They generalize previous attempts at deriving unbiased losses under the restrictive assumption that labels go missing uniformly at random from the ground truth. Furthermore, they provide a sound theoretical justification for popular label weighting heuristics used to recommend rare items. Finally, they demonstrate that the proposed contributions align with real world applications by achieving superior clickthrough rates on sponsored search advertising in Bing. Objectives: To investigate whether (1) machine learning classifiers can help identify nonrandomized studies eligible for full-text screening by systematic reviewers; (2) classifier performance varies with optimization; and (3) the number of citations to screen can be reduced. Methods: We used an open-source, data-mining suite to process and classify biomedical citations that point to mostly nonrandomized studies from 2 systematic reviews. We built training and test sets for citation portions and compared classifier performance by considering the value of indexing, various feature sets, and optimization. We conducted our experiments in 2 phases. The design of phase I with no optimization was: 4 classifiersx3 feature setsx3 citation portions. Classifiers included k-nearest neighbor, naive Bayes, complement naive Bayes, and evolutionary support vector machine. Feature sets included bag of words, and 2- and 3-term n-grams. Citation portions included titles, titles and abstracts, and full citations with metadata. Phase II with optimization involved a subset of the classifiers, as well as features extracted from full citations, and full citations with overweighted titles. We optimized features and classifier parameters by manually setting information gain thresholds outside of a process for iterative grid optimization with 10-fold cross-validations. We independently tested models on data reserved for that purpose and statistically compared classifier performance on 2 types of feature sets. We estimated the number of citations needed to screen by reviewers during a second pass through a reduced set of citations. Results: In phase I, the evolutionary support vector machine returned the best recall for bag of words extracted from full citations; the best classifier with respect to overall performance was k-nearest neighbor. No classifier attained good enough recall for this task without optimization. In phase II, we boosted performance with optimization for evolutionary support vector machine and complement naive Bayes classifiers. Generalization performance was better for the latter in the independent tests. For evolutionary support vector machine and complement naive Bayes classifiers, the initial retrieval set was reduced by 46 and 35 , respectively. Conclusions: Machine learning classifiers can help identify nonrandomized studies eligible for full-text screening by systematic reviewers. Optimization can markedly improve performance of classifiers. However, generalizability varies with the classifier. The number of citations to screen during a second independent pass through the citations can be substantially reduced. We propose a met alearning approach for learning gradient-based reinforcement learning (RL) algorithms. The idea is to evolve a differentiable loss function, such that an agent, which optimizes its policy to minimize this loss, will achieve high rewards. The loss is parametrized via temporal convolutions over the agent's experience. Because this loss is highly flexible in its ability to take into account the agent's history, it enables fast task learning. Empirical results show that our evolved policy gradient algorithm (EPG) achieves faster learning on several randomized environments compared to an off-the-shelf policy gradient method. We also demonstrate that EPG's learned loss can generalize to out-of-distribution test time tasks, and exhibits qualitatively different behavior from other popular met alearning algorithms. We propose a met alearning approach for learning gradient-based reinforcement learning (RL) algorithms. The idea is to evolve a differentiable loss function, such that an agent, which optimizes its policy to minimize this loss, will achieve high rewards. The loss is parametrized via temporal convolutions over the agent's experience. Because this loss is highly flexible in its ability to take into account the agent's history, it enables fast task learning. Empirical results show that our evolved policy gradient algorithm (EPG) achieves faster learning on several randomized environments compared to an off-the-shelf policy gradient method. We also demonstrate that EPG's learned loss can generalize to out-of-distribution test time tasks, and exhibits qualitatively different behavior from other popular met alearning algorithms. In discriminative machine learning one is interested in training a system to optimize a certain desired measure of performance, or loss. In binary classification one typically tries to minimizes the error rate. But in structured prediction each task often has its own measure of performance such as the BLEU score in machine translation or the intersection-over-union score in PASCAL segmentation. The most common approaches to structured prediction, structural SVMs and CRFs, do not minimize the task loss: the former minimizes a surrogate loss with no guarantees for task loss and the latter minimizes log loss independent of task loss. The main contribution of this paper is a theorem stating that a certain perceptron-like learning rule, involving features vectors derived from loss-adjusted inference, directly corresponds to the gradient of task loss. We give empirical results on phonetic alignment of a standard test set from the TIMIT corpus, which surpasses all previously reported results on this problem. We present an approach to automate the process of discovering optimization methods, with a focus on deep learning architectures. We train a Recurrent Neural Network controller to generate a string in a domain specific language that describes a mathematical update equation based on a list of primitive functions, such as the gradient, running average of the gradient, etc. The controller is trained with Reinforcement Learning to maximize the performance of a model after a few epochs. On CIFAR-10, our method discovers several update rules that are better than many commonly used optimizers, such as Adam, RMSProp, or SGD with and without Momentum on a ConvNet model. We introduce two new optimizers, named PowerSign and AddSign, which we show transfer well and improve training on a variety of different tasks and architectures, including ImageNet classification and Google's neural machine translation system. We present an approach to automate the process of discovering optimization methods, with a focus on deep learning architectures. We train a Recurrent Neural Network controller to generate a string in a specific domain language that describes a mathematical update equation based on a list of primitive functions, such as the gradient, running average of the gradient, etc. The controller is trained with Reinforcement Learning to maximize the performance of a model after a few epochs. On CIFAR-10, our method discovers several update rules that are better than many commonly used optimizers, such as Adam, RMSProp, or SGD with and without Momentum on a ConvNet model. These optimizers can also be transferred to perform well on different neural network architectures, including Google's neural machine translation system. We examine gradient descent on unregularized logistic regression problems, with homogeneous linear predictors on linearly separable datasets. We show the predictor converges to the direction of the max-margin (hard margin SVM) solution. The result also generalizes to other monotone decreasing loss functions with an infimum at infinity, to multi-class problems, and to training a weight layer in a deep network in a certain restricted setting. Furthermore, we show this convergence is very slow, and only logarithmic in the convergence of the loss itself. This can help explain the benefit of continuing to optimize the logistic or cross-entropy loss even after the training error is zero and the training loss is extremely small, and, as we show, even if the validation loss increases. Our methodology can also aid in understanding implicit regularization n more complex models and with other optimization methods. This paper introduces a novel method to perform transfer learning across domains and tasks, formulating it as a problem of learning to cluster. The key insight is that, in addition to features, we can transfer similarity information and this is sufficient to learn a similarity function and clustering network to perform both domain adaptation and cross-task transfer learning. We begin by reducing categorical information to pairwise constraints, which only considers whether two instances belong to the same class or not. This similarity is category-agnostic and can be learned from data in the source domain using a similarity network. We then present two novel approaches for performing transfer learning using this similarity function. First, for unsupervised domain adaptation, we design a new loss function to regularize classification with a constrained clustering loss, hence learning a clustering network with the transferred similarity metric generating the training inputs. Second, for cross-task learning (i.e., unsupervised clustering with unseen categories), we propose a framework to reconstruct and estimate the number of semantic clusters, again using the clustering network. Since the similarity network is noisy, the key is to use a robust clustering algorithm, and we show that our formulation is more robust than the alternative constrained and unconstrained clustering approaches. Using this method, we first show state of the art results for the challenging cross-task problem, applied on Omniglot and ImageNet. Our results show that we can reconstruct semantic clusters with high accuracy. We then evaluate the performance of cross-domain transfer using images from the Office-31 and SVHN-MNIST tasks and present top accuracy on both datasets. Our approach doesn't explicitly deal with domain discrepancy. If we combine with a domain adaptation loss, it shows further improvement. We propose a weakly-supervised approach that takes image-sentence pairs as input and learns to visually ground (i.e., localize) arbitrary linguistic phrases, in the form of spatial attention masks. Specifically, the model is trained with images and their associated image-level captions, without any explicit region-to-phrase correspondence annotations. To this end, we introduce an end-to-end model which learns visual groundings of phrases with two types of carefully designed loss functions. In addition to the standard discriminative loss, which enforces that attended image regions and phrases are consistently encoded, we propose a novel structural loss which makes use of the parse tree structures induced by the sentences. In particular, we ensure complementarity among the attention masks that correspond to sibling noun phrases, and compositionality of attention masks among the children and parent phrases, as defined by the sentence parse tree. We validate the effectiveness of our approach on the Microsoft COCO and Visual Genome datasets. We propose a weakly-supervised approach that takes image-sentence pairs as input and learns to visually ground (i.e., localize) arbitrary linguistic phrases, in the form of spatial attention masks. Specifically, the model is trained with images and their associated image-level captions, without any explicit region-to-phrase correspondence annotations. To this end, we introduce an end-to-end model which learns visual groundings of phrases with two types of carefully designed loss functions. In addition to the standard discriminative loss, which enforces that attended image regions and phrases are consistently encoded, we propose a novel structural loss which makes use of the parse tree structures induced by the sentences. In particular, we ensure complementarity among the attention masks that correspond to sibling noun phrases, and compositionality of attention masks among the children and parent phrases, as defined by the sentence parse tree. We validate the effectiveness of our approach on the Microsoft COCO and Visual Genome datasets. Despite the availability of a huge amount of video data accompanied by descriptive texts, it is not always easy to exploit the information contained in natural language in order to automatically recognize video concepts. Towards this goal, in this paper we use textual cues as means of supervision, introducing two weakly supervised techniques that extend the Multiple Instance Learning (MIL) framework: the Fuzzy Sets Multiple Instance Learning (FSMIL) and the Probabilistic Labels Multiple Instance Learning (PLMIL). The former encodes the spatio-temporal imprecision of the linguistic descriptions with Fuzzy Sets, while the latter models different interpretations of each description's semantics with Probabilistic Labels, both formulated through a convex optimization algorithm. In addition, we provide a novel technique to extract weak labels in the presence of complex semantics, that consists of semantic similarity computations. We evaluate our methods on two distinct problems, namely face and action recognition, in the challenging and realistic setting of movies accompanied by their screenplays, contained in the COGNIMUSE database. We show that, on both tasks, our method considerably outperforms a state-of-the-art weakly supervised approach, as well as other baselines. While convex losses for binary classification are attractive due to the existence of numerous (provably) efficient methods for finding their global optima, they are sensitive to outliers. On the other hand, while the nonconvex 0-1 loss is robust to outliers, it is NP-hard to optimize and thus rarely directly optimized in practice. In this paper, however, we do just that: we explore a variety of practical methods for direct (approximate) optimization of the 0-1 loss based on branch and bound search, combinatorial search, and coordinate descent on smooth, differentiable relaxations of 0-1 loss. Empirically, we compare our proposed algorithms to logistic regression, SVM, and the Bayes point machine showing that the proposed 0-1 loss optimization algorithms perform at least as well and offer a clear advantage in the presence of outliers. To this end, we believe this work reiterates the importance of 0-1 loss and its robustness properties while challenging the notion that it is difficult to directly optimize. We study the implicit bias of gradient descent methods in solving a binary classification problem over a linearly separable dataset. The classifier is described by a nonlinear ReLU model and the objective function adopts the exponential loss function. We first characterize the landscape of the loss function and show that there can exist spurious asymptotic local minima besides asymptotic global minima. We then show that gradient descent (GD) can converge to either a global or a local max-margin direction, or may diverge from the desired max-margin direction in a general context. For stochastic gradient descent (SGD), we show that it converges in expectation to either the global or the local max-margin direction if SGD converges. We further explore the implicit bias of these algorithms in learning a multi-neuron network under certain stationary conditions, and show that the learned classifier maximizes the margins of each sample pattern partition under the ReLU activation. Abstract Several competing human behavior models have been proposed to model boundedly rational adversaries in repeated Stackelberg Security Games (SSG). However, these existing models fail to address three main issues which are detrimental to defender performance. First, while they attempt to learn adversary behavior models from adversaries' past actions (“attacks on targets”), they fail to take into account adversaries' future adaptation based on successes or failures of these past actions. Second, existing algorithms fail to learn a reliable model of the adversary unless there exists sufficient data collected by exposing enough of the attack surface – a situation that often arises in initial rounds of the repeated SSG. Third, current leading models have failed to include probability weighting functions, even though it is well known that human beings' weighting of probability is typically nonlinear. To address these limitations of existing models, this article provides three main contributions. Our first contribution is a new human behavior model, SHARP, which mitigates these three limitations as follows: (i) SHARP reasons based on success or failure of the adversary's past actions on exposed portions of the attack surface to model adversary adaptivity; (ii) SHARP reasons about similarity between exposed and unexposed areas of the attack surface, and also incorporates a discounting parameter to mitigate adversary's lack of exposure to enough of the attack surface; and (iii) SHARP integrates a non-linear probability weighting function to capture the adversary's true weighting of probability. Our second contribution is a first “repeated measures study” – at least in the context of SSGs – of competing human behavior models. This study, where each experiment lasted a period of multiple weeks with individual sets of human subjects on the Amazon Mechanical Turk platform, illustrates the strengths and weaknesses of different models and shows the advantages of SHARP. Our third major contribution is to demonstrate SHARP's superiority by conducting real-world human subjects experiments at the Bukit Barisan Seletan National Park in Indonesia against wildlife security experts. We suggest a new loss for learning deep embeddings. The key characteristics of the new loss is the absence of tunable parameters and very good results obtained across a range of datasets and problems. The loss is computed by estimating two distribution of similarities for positive (matching) and negative (non-matching) point pairs, and then computing the probability of a positive pair to have a lower similarity score than a negative pair based on these probability estimates. We show that these operations can be performed in a simple and piecewise-differentiable manner using 1D histograms with soft assignment operations. This makes the proposed loss suitable for learning deep embeddings using stochastic optimization. The experiments reveal favourable results compared to recently proposed loss functions. We present a theoretically grounded approach to train deep neural networks, including recurrent networks, subject to class-dependent label noise. We propose two procedures for loss correction that are agnostic to both application domain and network architecture. They simply amount to at most a matrix inversion and multiplication, provided that we know the probability of each class being corrupted into another. We further show how one can estimate these probabilities, adapting a recent technique for noise estimation to the multi-class setting, and thus providing an end-to-end framework. Extensive experiments on MNIST, IMDB, CIFAR-10, CIFAR-100 and a large scale dataset of clothing images employing a diversity of architectures --- stacking dense, convolutional, pooling, dropout, batch normalization, word embedding, LSTM and residual layers --- demonstrate the noise robustness of our proposals. Incidentally, we also prove that, when ReLU is the only non-linearity, the loss curvature is immune to class-dependent label noise. The scale of modern datasets necessitates the development of efficient distributed optimization methods for machine learning. We present a general-purpose framework for distributed computing environments, CoCoA, that has an efficient communication scheme and is applicable to a wide variety of problems in machine learning and signal processing. We extend the framework to cover general non-strongly-convex regularizers, including L1-regularized problems like lasso, sparse logistic regression, and elastic net regularization, and show how earlier work can be derived as a special case. We provide convergence guarantees for the class of convex regularized loss minimization objectives, leveraging a novel approach in handling non-strongly-convex regularizers and non-smooth loss functions. The resulting framework has markedly improved performance over state-of-the-art methods, as we illustrate with an extensive set of experiments on real distributed datasets. Matching images and sentences demands a fine understanding of both modalities. In this paper, we propose a new system to discriminatively embed the image and text to a shared visual-textual space. In this field, most existing works apply the ranking loss to pull the positive image text pairs close and push the negative pairs apart from each other. However, directly deploying the ranking loss is hard for network learning, since it starts from the two heterogeneous features to build inter-modal relationship. To address this problem, we propose the instance loss which explicitly considers the intra-modal data distribution. It is based on an unsupervised assumption that each image text group can be viewed as a class. So the network can learn the fine granularity from every image text group. The experiment shows that the instance loss offers better weight initialization for the ranking loss, so that more discriminative embeddings can be learned. Besides, existing works usually apply the off-the-shelf features, i.e., word2vec and fixed visual feature. So in a minor contribution, this paper constructs an end-to-end dual-path convolutional network to learn the image and text representations. End-to-end learning allows the system to directly learn from the data and fully utilize the supervision. On two generic retrieval datasets (Flickr30k and MSCOCO), experiments demonstrate that our method yields competitive accuracy compared to state-of-the-art methods. Moreover, in language based person retrieval, we improve the state of the art by a large margin. The code has been made publicly available.