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The similarity of feature representations plays a pivotal role in the success of domain adaptation and generalization. Feature similarity includes both the invariance of marginal distributions and the closeness of conditional distributions given the desired response $y$ (e.g., class labels). Unfortunately, traditional methods always learn such features without fully taking into consideration the information in $y$, which in turn may lead to a mismatch of the conditional distributions or the mix-up of discriminative structures underlying data distributions. In this work, we introduce the recently proposed von Neumann conditional divergence to improve the transferability across multiple domains. We show that this new divergence is differentiable and eligible to easily quantify the functional dependence between features and $y$. Given multiple source tasks, we integrate this divergence to capture discriminative information in $y$ and design novel learning objectives assuming those source tasks are observed either simultaneously or sequentially. In both scenarios, we obtain favorable performance against state-of-the-art methods in terms of smaller generalization error on new tasks and less catastrophic forgetting on source tasks (in the sequential setup).
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We study the learnability of a class of compact operators known as Schatten--von Neumann operators. These operators between infinite-dimensional function spaces play a central role in a variety of applications in learning theory and inverse problems. We address the question of sample complexity of learning Schatten-von Neumann operators and provide an upper bound on the number of measurements required for the empirical risk minimizer to generalize with arbitrary precision and probability, as a function of class parameter $p$. Our results give generalization guarantees for regression of infinite-dimensional signals from infinite-dimensional data. Next, we adapt the representer theorem of Abernethy emph{et al.} to show that empirical risk minimization over an a priori infinite-dimensional, non-compact set, can be converted to a convex finite dimensional optimization problem over a compact set. In summary, the class of $p$-Schatten--von Neumann operators is probably approximately correct (PAC)-learnable via a practical convex program for any $p < infty$.
Classical linear metric learning methods have recently been extended along two distinct lines: deep metric learning methods for learning embeddings of the data using neural networks, and Bregman divergence learning approaches for extending learning Euclidean distances to more general divergence measures such as divergences over distributions. In this paper, we introduce deep Bregman divergences, which are based on learning and parameterizing functional Bregman divergences using neural networks, and which unify and extend these existing lines of work. We show in particular how deep metric learning formulations, kernel metric learning, Mahalanobis metric learning, and moment-matching functions for comparing distributions arise as special cases of these divergences in the symmetric setting. We then describe a deep learning framework for learning general functional Bregman divergences, and show in experiments that this method yields superior performance on benchmark datasets as compared to existing deep metric learning approaches. We also discuss novel applications, including a semi-supervised distributional clustering problem, and a new loss function for unsupervised data generation.
Transfer learning aims to learn robust classifiers for the target domain by leveraging knowledge from a source domain. Since the source and the target domains are usually from different distributions, existing methods mainly focus on adapting the cross-domain marginal or conditional distributions. However, in real applications, the marginal and conditional distributions usually have different contributions to the domain discrepancy. Existing methods fail to quantitatively evaluate the different importance of these two distributions, which will result in unsatisfactory transfer performance. In this paper, we propose a novel concept called Dynamic Distribution Adaptation (DDA), which is capable of quantitatively evaluating the relative importance of each distribution. DDA can be easily incorporated into the framework of structural risk minimization to solve transfer learning problems. On the basis of DDA, we propose two novel learning algorithms: (1) Manifold Dynamic Distribution Adaptation (MDDA) for traditional transfer learning, and (2) Dynamic Distribution Adaptation Network (DDAN) for deep transfer learning. Extensive experiments demonstrate that MDDA and DDAN significantly improve the transfer learning performance and setup a strong baseline over the latest deep and adversarial methods on digits recognition, sentiment analysis, and image classification. More importantly, it is shown that marginal and conditional distributions have different contributions to the domain divergence, and our DDA is able to provide good quantitative evaluation of their relative importance which leads to better performance. We believe this observation can be helpful for future research in transfer learning.
The recent advances in deep transfer learning reveal that adversarial learning can be embedded into deep networks to learn more transferable features to reduce the distribution discrepancy between two domains. Existing adversarial domain adaptation methods either learn a single domain discriminator to align the global source and target distributions or pay attention to align subdomains based on multiple discriminators. However, in real applications, the marginal (global) and conditional (local) distributions between domains are often contributing differently to the adaptation. There is currently no method to dynamically and quantitatively evaluate the relative importance of these two distributions for adversarial learning. In this paper, we propose a novel Dynamic Adversarial Adaptation Network (DAAN) to dynamically learn domain-invariant representations while quantitatively evaluate the relative importance of global and local domain distributions. To the best of our knowledge, DAAN is the first attempt to perform dynamic adversarial distribution adaptation for deep adversarial learning. DAAN is extremely easy to implement and train in real applications. We theoretically analyze the effectiveness of DAAN, and it can also be explained in an attention strategy. Extensive experiments demonstrate that DAAN achieves better classification accuracy compared to state-of-the-art deep and adversarial methods. Results also imply the necessity and effectiveness of the dynamic distribution adaptation in adversarial transfer learning.
In many settings, it is desirable to learn decision-making and control policies through learning or bootstrapping from expert demonstrations. The most common approaches under this Imitation Learning (IL) framework are Behavioural Cloning (BC), and Inverse Reinforcement Learning (IRL). Recent methods for IRL have demonstrated the capacity to learn effective policies with access to a very limited set of demonstrations, a scenario in which BC methods often fail. Unfortunately, due to multiple factors of variation, directly comparing these methods does not provide adequate intuition for understanding this difference in performance. In this work, we present a unified probabilistic perspective on IL algorithms based on divergence minimization. We present $f$-MAX, an $f$-divergence generalization of AIRL [Fu et al., 2018], a state-of-the-art IRL method. $f$-MAX enables us to relate prior IRL methods such as GAIL [Ho & Ermon, 2016] and AIRL [Fu et al., 2018], and understand their algorithmic properties. Through the lens of divergence minimization we tease apart the differences between BC and successful IRL approaches, and empirically evaluate these nuances on simulated high-dimensional continuous control domains. Our findings conclusively identify that IRLs state-marginal matching objective contributes most to its superior performance. Lastly, we apply our new understanding of IL methods to the problem of state-marginal matching, where we demonstrate that in simulated arm pushing environments we can teach agents a diverse range of behaviours using simply hand-specified state distributions and no reward functions or expert demonstrations. For datasets and reproducing results please refer to https://github.com/KamyarGh/rl_swiss/blob/master/reproducing/fmax_paper.md .
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