Learning to Track Dynamic Targets in Partially Known Environments

We solve active target tracking, one of the essential tasks in autonomous systems, using a deep reinforcement learning (RL) approach. In this problem, an autonomous agent is tasked with acquiring information about targets of interests using its onboard sensors. The classical challenges in this problem are system model dependence and the difficulty of computing information-theoretic cost functions for a long planning horizon. RL provides solutions for these challenges as the length of its effective planning horizon does not affect the computational complexity, and it drops the strong dependency of an algorithm on system models. In particular, we introduce Active Tracking Target Network (ATTN), a unified RL policy that is capable of solving major sub-tasks of active target tracking -- in-sight tracking, navigation, and exploration. The policy shows robust behavior for tracking agile and anomalous targets with a partially known target model. Additionally, the same policy is able to navigate in obstacle environments to reach distant targets as well as explore the environment when targets are positioned in unexpected locations.

Provable tradeoffs in adversarially robust classification

Machine learning methods can be vulnerable to small, adversarially-chosen perturbations of their inputs, prompting much research into theoretical explanations and algorithms toward improving adversarial robustness. Although a rich and insightful literature has developed around these ideas, many foundational open problems remain. In this paper, we seek to address several of these questions by deriving optimal robust classifiers for two- and three-class Gaussian classification problems with respect to adversaries in both the $\ell_2$ and $\ell_\infty$ norms. While the standard non-robust version of this problem has a long history, the corresponding robust setting contains many unexplored problems, and indeed deriving optimal robust classifiers turns out to pose a variety of new challenges. We develop new analysis tools for this task. Our results reveal intriguing tradeoffs between usual and robust accuracy. Furthermore, we give results for data lying on low-dimensional manifolds and study the landscape of adversarially robust risk over linear classifiers, including proving Fisher consistency in some cases. Lastly, we provide novel results concerning finite sample adversarial risk in the Gaussian classification setting.

Model-Based Robust Deep Learning

While deep learning has resulted in major breakthroughs in many application domains, the frameworks commonly used in deep learning remain fragile to artificially-crafted and imperceptible changes in the data. In response to this fragility, adversarial training has emerged as a principled approach for enhancing the robustness of deep learning with respect to norm-bounded perturbations. However, there are other sources of fragility for deep learning that are arguably more common and less thoroughly studied. Indeed, natural variation such as lighting or weather conditions can significantly degrade the accuracy of trained neural networks, proving that such natural variation presents a significant challenge for deep learning. In this paper, we propose a paradigm shift from perturbation-based adversarial robustness toward {\em model-based robust deep learning}. Our objective is to provide general training algorithms that can be used to train deep neural networks to be robust against natural variation in data. Critical to our paradigm is first obtaining a \emph{model of natural variation} which can be used to vary data over a range of natural conditions. Such models may be either known a priori or else learned from data. In the latter case, we show that deep generative models can be used to learn models of natural variation that are consistent with realistic conditions. We then exploit such models in three novel model-based robust training algorithms in order to enhance the robustness of deep learning with respect to the given model. Our extensive experiments show that across a variety of naturally-occurring conditions and across various datasets, deep neural networks trained with our model-based algorithms significantly outperform both standard deep learning algorithms as well as norm-bounded robust deep learning algorithms.

Quantized Push-sum for Gossip and Decentralized Optimization over Directed Graphs

We consider a decentralized stochastic learning problem where data points are distributed among computing nodes communicating over a directed graph. As the model size gets large, decentralized learning faces a major bottleneck that is the heavy communication load due to each node transmitting large messages (model updates) to its neighbors. To tackle this bottleneck, we propose the quantized decentralized stochastic learning algorithm over directed graphs that is based on the push-sum algorithm in decentralized consensus optimization. More importantly, we prove that our algorithm achieves the same convergence rates of the decentralized stochastic learning algorithm with exact-communication for both convex and non-convex losses. A key technical challenge of the work is to prove exact convergence of the proposed decentralized learning algorithm in the presence of quantization noise with unbounded variance over directed graphs. We provide numerical evaluations that corroborate our main theoretical results and illustrate significant speed-up compared to the exact-communication methods.

Precise Tradeoffs in Adversarial Training for Linear Regression

Despite breakthrough performance, modern learning models are known to be highly vulnerable to small adversarial perturbations in their inputs. While a wide variety of recent \emph{adversarial training} methods have been effective at improving robustness to perturbed inputs (robust accuracy), often this benefit is accompanied by a decrease in accuracy on benign inputs (standard accuracy), leading to a tradeoff between often competing objectives. Complicating matters further, recent empirical evidence suggest that a variety of other factors (size and quality of training data, model size, etc.) affect this tradeoff in somewhat surprising ways. In this paper we provide a precise and comprehensive understanding of the role of adversarial training in the context of linear regression with Gaussian features. In particular, we characterize the fundamental tradeoff between the accuracies achievable by any algorithm regardless of computational power or size of the training data. Furthermore, we precisely characterize the standard/robust accuracy and the corresponding tradeoff achieved by a contemporary mini-max adversarial training approach in a high-dimensional regime where the number of data points and the parameters of the model grow in proportion to each other. Our theory for adversarial training algorithms also facilitates the rigorous study of how a variety of factors (size and quality of training data, model overparametrization etc.) affect the tradeoff between these two competing accuracies.

Online Continuous Submodular Maximization: From Full-Information to Bandit Feedback

In this paper, we propose three online algorithms for submodular maximisation. The first one, Mono-Frank-Wolfe, reduces the number of per-function gradient evaluations from $T^{1/2}$ [Chen2018Online] and $T^{3/2}$ [chen2018projection] to 1, and achieves a $(1-1/e)$-regret bound of $O(T^{4/5})$. The second one, Bandit-Frank-Wolfe, is the first bandit algorithm for continuous DR-submodular maximization, which achieves a $(1-1/e)$-regret bound of $O(T^{8/9})$. Finally, we extend Bandit-Frank-Wolfe to a bandit algorithm for discrete submodular maximization, Responsive-Frank-Wolfe, which attains a $(1-1/e)$-regret bound of $O(T^{8/9})$ in the responsive bandit setting.

Learning Q-network for Active Information Acquisition

In this paper, we propose a novel Reinforcement Learning approach for solving the Active Information Acquisition problem, which requires an agent to choose a sequence of actions in order to acquire information about a process of interest using on-board sensors. The classic challenges in the information acquisition problem are the dependence of a planning algorithm on known models and the difficulty of computing information-theoretic cost functions over arbitrary distributions. In contrast, the proposed framework of reinforcement learning does not require any knowledge on models and alleviates the problems during an extended training stage. It results in policies that are efficient to execute online and applicable for real-time control of robotic systems. Furthermore, the state-of-the-art planning methods are typically restricted to short horizons, which may become problematic with local minima. Reinforcement learning naturally handles the issue of planning horizon in information problems as it maximizes a discounted sum of rewards over a long finite or infinite time horizon. We discuss the potential benefits of the proposed framework and compare the performance of the novel algorithm to an existing information acquisition method for multi-target tracking scenarios.

FedPAQ: A Communication-Efficient Federated Learning Method with Periodic Averaging and Quantization

Federated learning is a distributed framework according to which a model is trained over a set of devices, while keeping data localized. This framework faces several systems-oriented challenges which include (i) communication bottleneck since a large number of devices upload their local updates to a parameter server, and (ii) scalability as the federated network consists of millions of devices. Due to these systems challenges as well as issues related to statistical heterogeneity of data and privacy concerns, designing a provably efficient federated learning method is of significant importance yet it remains challenging. In this paper, we present FedPAQ, a communication-efficient Federated Learning method with Periodic Averaging and Quantization. FedPAQ relies on three key features: (1) periodic averaging where models are updated locally at devices and only periodically averaged at the server; (2) partial device participation where only a fraction of devices participate in each round of the training; and (3) quantized message-passing where the edge nodes quantize their updates before uploading to the parameter server. These features address the communications and scalability challenges in federated learning. We also show that FedPAQ achieves near-optimal theoretical guarantees for strongly convex and non-convex loss functions and empirically demonstrate the communication-computation tradeoff provided by our method.

One Sample Stochastic Frank-Wolfe

One of the beauties of the projected gradient descent method lies in its rather simple mechanism and yet stable behavior with inexact, stochastic gradients, which has led to its wide-spread use in many machine learning applications. However, once we replace the projection operator with a simpler linear program, as is done in the Frank-Wolfe method, both simplicity and stability take a serious hit. The aim of this paper is to bring them back without sacrificing the efficiency. In this paper, we propose the first one-sample stochastic Frank-Wolfe algorithm, called 1-SFW, that avoids the need to carefully tune the batch size, step size, learning rate, and other complicated hyper parameters. In particular, 1-SFW achieves the optimal convergence rate of $\mathcal{O}(1/\epsilon^2)$ for reaching an $\epsilon$-suboptimal solution in the stochastic convex setting, and a $(1-1/e)-\epsilon$ approximate solution for a stochastic monotone DR-submodular maximization problem. Moreover, in a general non-convex setting, 1-SFW finds an $\epsilon$-first-order stationary point after at most $\mathcal{O}(1/\epsilon^3)$ iterations, achieving the current best known convergence rate. All of this is possible by designing a novel unbiased momentum estimator that governs the stability of the optimization process while using a single sample at each iteration.