arXiv subjects

Anima Anandkumar

Publications and source records attributed to Anima Anandkumar.

At least 253 records · Page 14Linked to original sources

arXiv2020

Automated Synthetic-to-Real Generalization

Models trained on synthetic images often face degraded generalization to real data. As a convention, these models are often initialized with ImageNet pre-trained representation. Yet the role of ImageNet knowledge is seldom discussed despite common practices that leverage this knowledge to maintain the generalization ability. An example is the careful hand-tuning of early stopping and layer-wise learning rates, which is shown to improve synthetic-to-real generalization but is also laborious and heuristic. In this work, we explicitly encourage the synthetically trained model to maintain similar representations with the ImageNet pre-trained model, and propose a \textit{learning-to-optimize (L2O)} strategy to automate the selection of layer-wise learning rates. We demonstrate that the proposed framework can significantly improve the synthetic-to-real generalization performance without seeing and training on real data, while also benefiting downstream tasks such as domain adaptation. Code is available at: https://github.com/NVlabs/ASG.

cs.LG↗

arXiv2020

Angular Visual Hardness

Recent convolutional neural networks (CNNs) have led to impressive performance but often suffer from poor calibration. They tend to be overconfident, with the model confidence not always reflecting the underlying true ambiguity and hardness. In this paper, we propose angular visual hardness (AVH), a score given by the normalized angular distance between the sample feature embedding and the target classifier to measure sample hardness. We validate this score with an in-depth and extensive scientific study, and observe that CNN models with the highest accuracy also have the best AVH scores. This agrees with an earlier finding that state-of-art models improve on the classification of harder examples. We observe that the training dynamics of AVH is vastly different compared to the training loss. Specifically, AVH quickly reaches a plateau for all samples even though the training loss keeps improving. This suggests the need for designing better loss functions that can target harder examples more effectively. We also find that AVH has a statistically significant correlation with human visual hardness. Finally, we demonstrate the benefit of AVH to a variety of applications such as self-training for domain adaptation and domain generalization.

cs.LG↗

arXiv2020

Competitive Gradient Descent

We introduce a new algorithm for the numerical computation of Nash equilibria of competitive two-player games. Our method is a natural generalization of gradient descent to the two-player setting where the update is given by the Nash equilibrium of a regularized bilinear local approximation of the underlying game. It avoids oscillatory and divergent behaviors seen in alternating gradient descent. Using numerical experiments and rigorous analysis, we provide a detailed comparison to methods based on \emph{optimism} and \emph{consensus} and show that our method avoids making any unnecessary changes to the gradient dynamics while achieving exponential (local) convergence for (locally) convex-concave zero sum games. Convergence and stability properties of our method are robust to strong interactions between the players, without adapting the stepsize, which is not the case with previous methods. In our numerical experiments on non-convex-concave problems, existing methods are prone to divergence and instability due to their sensitivity to interactions among the players, whereas we never observe divergence of our algorithm. The ability to choose larger stepsizes furthermore allows our algorithm to achieve faster convergence, as measured by the number of model evaluations.

math.OC↗

arXiv2020

Robust Regression for Safe Exploration in Control

We study the problem of safe learning and exploration in sequential control problems. The goal is to safely collect data samples from operating in an environment, in order to learn to achieve a challenging control goal (e.g., an agile maneuver close to a boundary). A central challenge in this setting is how to quantify uncertainty in order to choose provably-safe actions that allow us to collect informative data and reduce uncertainty, thereby achieving both improved controller safety and optimality. To address this challenge, we present a deep robust regression model that is trained to directly predict the uncertainty bounds for safe exploration. We derive generalization bounds for learning, and connect them with safety and stability bounds in control. We demonstrate empirically that our robust regression approach can outperform the conventional Gaussian process (GP) based safe exploration in settings where it is difficult to specify a good GP prior.

cs.LG↗

arXiv2020

Adaptive Control and Regret Minimization in Linear Quadratic Gaussian (LQG) Setting

We study the problem of adaptive control in partially observable linear quadratic Gaussian control systems, where the model dynamics are unknown a priori. We propose LqgOpt, a novel reinforcement learning algorithm based on the principle of optimism in the face of uncertainty, to effectively minimize the overall control cost. We employ the predictor state evolution representation of the system dynamics and deploy a recently proposed closed-loop system identification method, estimation, and confidence bound construction. LqgOpt efficiently explores the system dynamics, estimates the model parameters up to their confidence interval, and deploys the controller of the most optimistic model for further exploration and exploitation. We provide stability guarantees for LqgOpt and prove the regret upper bound of $\tilde{\mathcal{O}}(\sqrt{T})$ for adaptive control of linear quadratic Gaussian (LQG) systems, where $T$ is the time horizon of the problem.

cs.LG↗

arXiv2020

Logarithmic Regret Bound in Partially Observable Linear Dynamical Systems

We study the problem of system identification and adaptive control in partially observable linear dynamical systems. Adaptive and closed-loop system identification is a challenging problem due to correlations introduced in data collection. In this paper, we present the first model estimation method with finite-time guarantees in both open and closed-loop system identification. Deploying this estimation method, we propose adaptive control online learning (AdaptOn), an efficient reinforcement learning algorithm that adaptively learns the system dynamics and continuously updates its controller through online learning steps. AdaptOn estimates the model dynamics by occasionally solving a linear regression problem through interactions with the environment. Using policy re-parameterization and the estimated model, AdaptOn constructs counterfactual loss functions to be used for updating the controller through online gradient descent. Over time, AdaptOn improves its model estimates and obtains more accurate gradient updates to improve the controller. We show that AdaptOn achieves a regret upper bound of $\text{polylog}\left(T\right)$, after $T$ time steps of agent-environment interaction. To the best of our knowledge, AdaptOn is the first algorithm that achieves $\text{polylog}\left(T\right)$ regret in adaptive control of unknown partially observable linear dynamical systems which includes linear quadratic Gaussian (LQG) control.

cs.LG↗

arXiv2020

Competitive Policy Optimization

A core challenge in policy optimization in competitive Markov decision processes is the design of efficient optimization methods with desirable convergence and stability properties. To tackle this, we propose competitive policy optimization (CoPO), a novel policy gradient approach that exploits the game-theoretic nature of competitive games to derive policy updates. Motivated by the competitive gradient optimization method, we derive a bilinear approximation of the game objective. In contrast, off-the-shelf policy gradient methods utilize only linear approximations, and hence do not capture interactions among the players. We instantiate CoPO in two ways:(i) competitive policy gradient, and (ii) trust-region competitive policy optimization. We theoretically study these methods, and empirically investigate their behavior on a set of comprehensive, yet challenging, competitive games. We observe that they provide stable optimization, convergence to sophisticated strategies, and higher scores when played against baseline policy gradient methods.

cs.LG↗

arXiv2020

Competitive Mirror Descent

Constrained competitive optimization involves multiple agents trying to minimize conflicting objectives, subject to constraints. This is a highly expressive modeling language that subsumes most of modern machine learning. In this work we propose competitive mirror descent (CMD): a general method for solving such problems based on first order information that can be obtained by automatic differentiation. First, by adding Lagrange multipliers, we obtain a simplified constraint set with an associated Bregman potential. At each iteration, we then solve for the Nash equilibrium of a regularized bilinear approximation of the full problem to obtain a direction of movement of the agents. Finally, we obtain the next iterate by following this direction according to the dual geometry induced by the Bregman potential. By using the dual geometry we obtain feasible iterates despite only solving a linear system at each iteration, eliminating the need for projection steps while still accounting for the global nonlinear structure of the constraint set. As a special case we obtain a novel competitive multiplicative weights algorithm for problems on the positive cone.

math.OC↗

arXiv2020

Spectral Learning on Matrices and Tensors

Spectral methods have been the mainstay in several domains such as machine learning and scientific computing. They involve finding a certain kind of spectral decomposition to obtain basis functions that can capture important structures for the problem at hand. The most common spectral method is the principal component analysis (PCA). It utilizes the top eigenvectors of the data covariance matrix, e.g. to carry out dimensionality reduction. This data pre-processing step is often effective in separating signal from noise. PCA and other spectral techniques applied to matrices have several limitations. By limiting to only pairwise moments, they are effectively making a Gaussian approximation on the underlying data and fail on data with hidden variables which lead to non-Gaussianity. However, in most data sets, there are latent effects that cannot be directly observed, e.g., topics in a document corpus, or underlying causes of a disease. By extending the spectral decomposition methods to higher order moments, we demonstrate the ability to learn a wide range of latent variable models efficiently. Higher-order moments can be represented by tensors, and intuitively, they can encode more information than just pairwise moment matrices. More crucially, tensor decomposition can pick up latent effects that are missed by matrix methods, e.g. uniquely identify non-orthogonal components. Exploiting these aspects turns out to be fruitful for provable unsupervised learning of a wide range of latent variable models. We also outline the computational techniques to design efficient tensor decomposition methods. We introduce Tensorly, which has a simple python interface for expressing tensor operations. It has a flexible back-end system supporting NumPy, PyTorch, TensorFlow and MXNet amongst others, allowing multi-GPU and CPU operations and seamless integration with deep-learning functionalities.

cs.LG↗

arXiv2020

Regret Minimization in Partially Observable Linear Quadratic Control

We study the problem of regret minimization in partially observable linear quadratic control systems when the model dynamics are unknown a priori. We propose ExpCommit, an explore-then-commit algorithm that learns the model Markov parameters and then follows the principle of optimism in the face of uncertainty to design a controller. We propose a novel way to decompose the regret and provide an end-to-end sublinear regret upper bound for partially observable linear quadratic control. Finally, we provide stability guarantees and establish a regret upper bound of $\tilde{\mathcal{O}}(T^{2/3})$ for ExpCommit, where $T$ is the time horizon of the problem.

cs.LG↗

arXiv2020

Neural Operator: Graph Kernel Network for Partial Differential Equations

The classical development of neural networks has been primarily for mappings between a finite-dimensional Euclidean space and a set of classes, or between two finite-dimensional Euclidean spaces. The purpose of this work is to generalize neural networks so that they can learn mappings between infinite-dimensional spaces (operators). The key innovation in our work is that a single set of network parameters, within a carefully designed network architecture, may be used to describe mappings between infinite-dimensional spaces and between different finite-dimensional approximations of those spaces. We formulate approximation of the infinite-dimensional mapping by composing nonlinear activation functions and a class of integral operators. The kernel integration is computed by message passing on graph networks. This approach has substantial practical consequences which we will illustrate in the context of mappings between input data to partial differential equations (PDEs) and their solutions. In this context, such learned networks can generalize among different approximation methods for the PDE (such as finite difference or finite element methods) and among approximations corresponding to different underlying levels of resolution and discretization. Experiments confirm that the proposed graph kernel network does have the desired properties and show competitive performance compared to the state of the art solvers.

cs.LG↗

arXiv2020

Multi Sense Embeddings from Topic Models

Distributed word embeddings have yielded state-of-the-art performance in many NLP tasks, mainly due to their success in capturing useful semantic information. These representations assign only a single vector to each word whereas a large number of words are polysemous (i.e., have multiple meanings). In this work, we approach this critical problem in lexical semantics, namely that of representing various senses of polysemous words in vector spaces. We propose a topic modeling based skip-gram approach for learning multi-prototype word embeddings. We also introduce a method to prune the embeddings determined by the probabilistic representation of the word in each topic. We use our embeddings to show that they can capture the context and word similarity strongly and outperform various state-of-the-art implementations.

cs.LG↗

arXiv2019

Guaranteed Scalable Learning of Latent Tree Models

We present an integrated approach for structure and parameter estimation in latent tree graphical models. Our overall approach follows a "divide-and-conquer" strategy that learns models over small groups of variables and iteratively merges onto a global solution. The structure learning involves combinatorial operations such as minimum spanning tree construction and local recursive grouping; the parameter learning is based on the method of moments and on tensor decompositions. Our method is guaranteed to correctly recover the unknown tree structure and the model parameters with low sample complexity for the class of linear multivariate latent tree models which includes discrete and Gaussian distributions, and Gaussian mixtures. Our bulk asynchronous parallel algorithm is implemented in parallel and the parallel computation complexity increases only logarithmically with the number of variables and linearly with dimensionality of each variable.

cs.LG↗

arXiv2019

A Bayesian Perspective of Convolutional Neural Networks through a Deconvolutional Generative Model

Inspired by the success of Convolutional Neural Networks (CNNs) for supervised prediction in images, we design the Deconvolutional Generative Model (DGM), a new probabilistic generative model whose inference calculations correspond to those in a given CNN architecture. The DGM uses a CNN to design the prior distribution in the probabilistic model. Furthermore, the DGM generates images from coarse to finer scales. It introduces a small set of latent variables at each scale, and enforces dependencies among all the latent variables via a conjugate prior distribution. This conjugate prior yields a new regularizer based on paths rendered in the generative model for training CNNs-the Rendering Path Normalization (RPN). We demonstrate that this regularizer improves generalization, both in theory and in practice. In addition, likelihood estimation in the DGM yields training losses for CNNs, and inspired by this, we design a new loss termed as the Max-Min cross entropy which outperforms the traditional cross-entropy loss for object classification. The Max-Min cross entropy suggests a new deep network architecture, namely the Max-Min network, which can learn from less labeled data while maintaining good prediction performance. Our experiments demonstrate that the DGM with the RPN and the Max-Min architecture exceeds or matches the-state-of-art on benchmarks including SVHN, CIFAR10, and CIFAR100 for semi-supervised and supervised learning tasks.

cs.CV↗

arXiv2019

InfoCNF: An Efficient Conditional Continuous Normalizing Flow with Adaptive Solvers

Continuous Normalizing Flows (CNFs) have emerged as promising deep generative models for a wide range of tasks thanks to their invertibility and exact likelihood estimation. However, conditioning CNFs on signals of interest for conditional image generation and downstream predictive tasks is inefficient due to the high-dimensional latent code generated by the model, which needs to be of the same size as the input data. In this paper, we propose InfoCNF, an efficient conditional CNF that partitions the latent space into a class-specific supervised code and an unsupervised code that shared among all classes for efficient use of labeled information. Since the partitioning strategy (slightly) increases the number of function evaluations (NFEs), InfoCNF also employs gating networks to learn the error tolerances of its ordinary differential equation (ODE) solvers for better speed and performance. We show empirically that InfoCNF improves the test accuracy over the baseline while yielding comparable likelihood scores and reducing the NFEs on CIFAR10. Furthermore, applying the same partitioning strategy in InfoCNF on time-series data helps improve extrapolation performance.

cs.LG↗

arXiv2019

Finding Social Media Trolls: Dynamic Keyword Selection Methods for Rapidly-Evolving Online Debates

Online harassment is a significant social problem. Prevention of online harassment requires rapid detection of harassing, offensive, and negative social media posts. In this paper, we propose the use of word embedding models to identify offensive and harassing social media messages in two aspects: detecting fast-changing topics for more effective data collection and representing word semantics in different domains. We demonstrate with preliminary results that using the GloVe (Global Vectors for Word Representation) model facilitates the discovery of new and relevant keywords to use for data collection and trolling detection. Our paper concludes with a discussion of a research agenda to further develop and test word embedding models for identification of social media harassment and trolling.

cs.LG↗

arXiv2019

Triply Robust Off-Policy Evaluation

We propose a robust regression approach to off-policy evaluation (OPE) for contextual bandits. We frame OPE as a covariate-shift problem and leverage modern robust regression tools. Ours is a general approach that can be used to augment any existing OPE method that utilizes the direct method. When augmenting doubly robust methods, we call the resulting method Triply Robust. We prove upper bounds on the resulting bias and variance, as well as derive novel minimax bounds based on robust minimax analysis for covariate shift. Our robust regression method is compatible with deep learning, and is thus applicable to complex OPE settings that require powerful function approximators. Finally, we demonstrate superior empirical performance across the standard OPE benchmarks, especially in the case where the logging policy is unknown and must be estimated from data.

cs.LG↗

arXiv2019

Turbulence forecasting via Neural ODE

Fluid turbulence is characterized by strong coupling across a broad range of scales. Furthermore, besides the usual local cascades, such coupling may extend to interactions that are non-local in scale-space. As such the computational demands associated with explicitly resolving the full set of scales and their interactions, as in the Direct Numerical Simulation (DNS) of the Navier-Stokes equations, in most problems of practical interest are so high that reduced modeling of scales and interactions is required before further progress can be made. While popular reduced models are typically based on phenomenological modeling of relevant turbulent processes, recent advances in machine learning techniques have energized efforts to further improve the accuracy of such reduced models. In contrast to such efforts that seek to improve an existing turbulence model, we propose a machine learning(ML) methodology that captures, de novo, underlying turbulence phenomenology without a pre-specified model form. To illustrate the approach, we consider transient modeling of the dissipation of turbulent kinetic energy, a fundamental turbulent process that is central to a wide range of turbulence models using a Neural ODE approach. After presenting details of the methodology, we show that this approach outperforms state-of-the-art approaches.

physics.comp-ph↗