Daniel D. Lee

Ziyun Wang, Fernando Cladera Ojeda, Anthony Bisulco et al.

Event-based sensors have recently drawn increasing interest in robotic perception due to their lower latency, higher dynamic range, and lower bandwidth requirements compared to standard CMOS-based imagers. These properties make them ideal tools for real-time perception tasks in highly dynamic environments. In this work, we demonstrate an application where event cameras excel: accurately estimating the impact location of fast-moving objects. We introduce a lightweight event representation called Binary Event History Image (BEHI) to encode event data at low latency, as well as a learning-based approach that allows real-time inference of a confidence-enabled control signal to the robot. To validate our approach, we present an experimental catching system in which we catch fast-flying ping-pong balls. We show that the system is capable of achieving a success rate of 81% in catching balls targeted at different locations, with a velocity of up to 13 m/s even on compute-constrained embedded platforms such as the Nvidia Jetson NX.

Niko A. Grupen, Michael Hanlon, Alexis Hao et al.

Large-scale AI systems that combine search and learning have reached super-human levels of performance in game-playing, but have also been shown to fail in surprising ways. The brittleness of such models limits their efficacy and trustworthiness in real-world deployments. In this work, we systematically study one such algorithm, AlphaZero, and identify two phenomena related to the nature of exploration. First, we find evidence of policy-value misalignment -- for many states, AlphaZero's policy and value predictions contradict each other, revealing a tension between accurate move-selection and value estimation in AlphaZero's objective. Further, we find inconsistency within AlphaZero's value function, which causes it to generalize poorly, despite its policy playing an optimal strategy. From these insights we derive VISA-VIS: a novel method that improves policy-value alignment and value robustness in AlphaZero. Experimentally, we show that our method reduces policy-value misalignment by up to 76%, reduces value generalization error by up to 50%, and reduces average value error by up to 55%.

Travers Rhodes, Daniel D. Lee

Human demonstrations of trajectories are an important source of training data for many machine learning problems. However, the difficulty of collecting human demonstration data for complex tasks makes learning efficient representations of those trajectories challenging. For many problems, such as for dexterous manipulation, the exact timings of the trajectories should be factored from their spatial path characteristics. In this work, we propose TimewarpVAE, a fully differentiable manifold-learning algorithm that incorporates Dynamic Time Warping (DTW) to simultaneously learn both timing variations and latent factors of spatial variation. We show how the TimewarpVAE algorithm learns appropriate time alignments and meaningful representations of spatial variations in handwriting and fork manipulation datasets. Our results have lower spatial reconstruction test error than baseline approaches and the learned low-dimensional representations can be used to efficiently generate semantically meaningful novel trajectories. We demonstrate the utility of our algorithm to generate novel high-speed trajectories for a robotic arm.

Patrick Cook, Danny Jammooa, Morten Hjorth-Jensen et al.

We present a general class of machine learning algorithms called parametric matrix models. In contrast with most existing machine learning models that imitate the biology of neurons, parametric matrix models use matrix equations that emulate physical systems. Similar to how physics problems are usually solved, parametric matrix models learn the governing equations that lead to the desired outputs. Parametric matrix models can be efficiently trained from empirical data, and the equations may use algebraic, differential, or integral relations. While originally designed for scientific computing, we prove that parametric matrix models are universal function approximators that can be applied to general machine learning problems. After introducing the underlying theory, we apply parametric matrix models to a series of different challenges that show their performance for a wide range of problems. For all the challenges tested here, parametric matrix models produce accurate results within an efficient and interpretable computational framework that allows for input feature extrapolation.

Chanwoo Chun, SueYeon Chung, Daniel D. Lee

Analyzing the structure of sampled features from an input data distribution is challenging when constrained by limited measurements in both the number of inputs and features. Traditional approaches often rely on the eigenvalue spectrum of the sample covariance matrix derived from finite measurement matrices; however, these spectra are sensitive to the size of the measurement matrix, leading to biased insights. In this paper, we introduce a novel algorithm that provides unbiased estimates of the spectral moments of the kernel integral operator in the limit of infinite inputs and features from finitely sampled measurement matrices. Our method, based on dynamic programming, is efficient and capable of estimating the moments of the operator spectrum. We demonstrate the accuracy of our estimator on radial basis function (RBF) kernels, highlighting its consistency with the theoretical spectra. Furthermore, we showcase the practical utility and robustness of our method in understanding the geometry of learned representations in neural networks.

Chanwoo Chun, Daniel D. Lee

We investigate how sparse neural activity affects the generalization performance of a deep Bayesian neural network at the large width limit. To this end, we derive a neural network Gaussian Process (NNGP) kernel with rectified linear unit (ReLU) activation and a predetermined fraction of active neurons. Using the NNGP kernel, we observe that the sparser networks outperform the non-sparse networks at shallow depths on a variety of datasets. We validate this observation by extending the existing theory on the generalization error of kernel-ridge regression.

Nikhil Chavan-Dafle, Sergiy Popovych, Shubham Agrawal et al.

Being able to grasp objects is a fundamental component of most robotic manipulation systems. In this paper, we present a new approach to simultaneously reconstruct a mesh and a dense grasp quality map of an object from a depth image. At the core of our approach is a novel camera-centric object representation called the "object shell" which is composed of an observed "entry image" and a predicted "exit image". We present an image-to-image residual ConvNet architecture in which the object shell and a grasp-quality map are predicted as separate output channels. The main advantage of the shell representation and the corresponding neural network architecture, ShellGrasp-Net, is that the input-output pixel correspondences in the shell representation are explicitly represented in the architecture. We show that this coupling yields superior generalization capabilities for object reconstruction and accurate grasp quality estimation implicitly considering the object geometry. Our approach yields an efficient dense grasp quality map and an object geometry estimate in a single forward pass. Both of these outputs can be used in a wide range of robotic manipulation applications. With rigorous experimental validation, both in simulation and on a real setup, we show that our shell-based method can be used to generate precise grasps and the associated grasp quality with over 90% accuracy. Diverse grasps computed on shell reconstructions allow the robot to select and execute grasps in cluttered scenes with more than 93% success rate.

Niko A. Grupen, Daniel D. Lee, Bart Selman

Emergent communication has made strides towards learning communication from scratch, but has focused primarily on protocols that resemble human language. In nature, multi-agent cooperation gives rise to a wide range of communication that varies in structure and complexity. In this work, we recognize the full spectrum of communication that exists in nature and propose studying lower-level communication. Specifically, we study emergent implicit signaling in the context of decentralized multi-agent learning in difficult, sparse reward environments. However, learning to coordinate in such environments is challenging. We propose a curriculum-driven strategy that combines: (i) velocity-based environment shaping, tailored to the skill level of the multi-agent team; and (ii) a behavioral curriculum that helps agents learn successful single-agent behaviors as a precursor to learning multi-agent behaviors. Pursuit-evasion experiments show that our approach learns effective coordination, significantly outperforming sophisticated analytical and learned policies. Our method completes the pursuit-evasion task even when pursuers move at half of the evader's speed, whereas the highest-performing baseline fails at 80% of the evader's speed. Moreover, we examine the use of implicit signals in coordination through position-based social influence. We show that pursuers trained with our strategy exchange more than twice as much information (in bits) than baseline methods, indicating that our method has learned, and relies heavily on, the exchange of implicit signals.

Niko A. Grupen, Bart Selman, Daniel D. Lee

We study fairness through the lens of cooperative multi-agent learning. Our work is motivated by empirical evidence that naive maximization of team reward yields unfair outcomes for individual team members. To address fairness in multi-agent contexts, we introduce team fairness, a group-based fairness measure for multi-agent learning. We then prove that it is possible to enforce team fairness during policy optimization by transforming the team's joint policy into an equivariant map. We refer to our multi-agent learning strategy as Fairness through Equivariance (Fair-E) and demonstrate its effectiveness empirically. We then introduce Fairness through Equivariance Regularization (Fair-ER) as a soft-constraint version of Fair-E and show that it reaches higher levels of utility than Fair-E and fairer outcomes than non-equivariant policies. Finally, we present novel findings regarding the fairness-utility trade-off in multi-agent settings; showing that the magnitude of the trade-off is dependent on agent skill.

Travers Rhodes, Daniel D. Lee

There have been many recent advances in representation learning; however, unsupervised representation learning can still struggle with model identification issues related to rotations of the latent space. Variational Auto-Encoders (VAEs) and their extensions such as $β$-VAEs have been shown to improve local alignment of latent variables with PCA directions, which can help to improve model disentanglement under some conditions. Borrowing inspiration from Independent Component Analysis (ICA) and sparse coding, we propose applying an $L_1$ loss to the VAE's generative Jacobian during training to encourage local latent variable alignment with independent factors of variation in images of multiple objects or images with multiple parts. We demonstrate our results on a variety of datasets, giving qualitative and quantitative results using information theoretic and modularity measures that show our added $L_1$ cost encourages local axis alignment of the latent representation with individual factors of variation.

Jinwook Huh, Daniel D. Lee, Volkan Isler

This paper presents a supervised learning method to generate continuous cost-to-go functions of non-holonomic systems directly from the workspace description. Supervision from informative examples reduces training time and improves network performance. The manifold representing the optimal trajectories of a non-holonomic system has high-curvature regions which can not be efficiently captured with uniform sampling. To address this challenge, we present an adaptive sampling method which makes use of sampling-based planners along with local, closed-form solutions to generate training samples. The cost-to-go function over a specific workspace is represented as a neural network whose weights are generated by a second, higher order network. The networks are trained in an end-to-end fashion. In our previous work, this architecture was shown to successfully learn to generate the cost-to-go functions of holonomic systems using uniform sampling. In this work, we show that uniform sampling fails for non-holonomic systems. However, with the proposed adaptive sampling methodology, our network can generate near-optimal trajectories for non-holonomic systems while avoiding obstacles. Experiments show that our method is two orders of magnitude faster compared to traditional approaches in cluttered environments.

Jinwook Huh, Volkan Isler, Daniel D. Lee

This paper presents c2g-HOF networks which learn to generate cost-to-go functions for manipulator motion planning. The c2g-HOF architecture consists of a cost-to-go function over the configuration space represented as a neural network (c2g-network) as well as a Higher Order Function (HOF) network which outputs the weights of the c2g-network for a given input workspace. Both networks are trained end-to-end in a supervised fashion using costs computed from traditional motion planners. Once trained, c2g-HOF can generate a smooth and continuous cost-to-go function directly from workspace sensor inputs (represented as a point cloud in 3D or an image in 2D). At inference time, the weights of the c2g-network are computed very efficiently and near-optimal trajectories are generated by simply following the gradient of the cost-to-go function. We compare c2g-HOF with traditional planning algorithms for various robots and planning scenarios. The experimental results indicate that planning with c2g-HOF is significantly faster than other motion planning algorithms, resulting in orders of magnitude improvement when including collision checking. Furthermore, despite being trained from sparsely sampled trajectories in configuration space, c2g-HOF generalizes to generate smoother, and often lower cost, trajectories. We demonstrate cost-to-go based planning on a 7 DoF manipulator arm where motion planning in a complex workspace requires only 0.13 seconds for the entire trajectory.

Niko A. Grupen, Daniel D. Lee, Bart Selman

In this work, we study emergent communication through the lens of cooperative multi-agent behavior in nature. Using insights from animal communication, we propose a spectrum from low-bandwidth (e.g. pheromone trails) to high-bandwidth (e.g. compositional language) communication that is based on the cognitive, perceptual, and behavioral capabilities of social agents. Through a series of experiments with pursuit-evasion games, we identify multi-agent reinforcement learning algorithms as a computational model for the low-bandwidth end of the communication spectrum.

Anthony Bisulco, Fernando Cladera Ojeda, Volkan Isler et al.

This paper presents a Dynamic Vision Sensor (DVS) based system for reasoning about high speed motion. As a representative scenario, we consider the case of a robot at rest reacting to a small, fast approaching object at speeds higher than 15m/s. Since conventional image sensors at typical frame rates observe such an object for only a few frames, estimating the underlying motion presents a considerable challenge for standard computer vision systems and algorithms. In this paper we present a method motivated by how animals such as insects solve this problem with their relatively simple vision systems. Our solution takes the event stream from a DVS and first encodes the temporal events with a set of causal exponential filters across multiple time scales. We couple these filters with a Convolutional Neural Network (CNN) to efficiently extract relevant spatiotemporal features. The combined network learns to output both the expected time to collision of the object, as well as the predicted collision point on a discretized polar grid. These critical estimates are computed with minimal delay by the network in order to react appropriately to the incoming object. We highlight the results of our system to a toy dart moving at 23.4m/s with a 24.73° error in $θ$, 18.4mm average discretized radius prediction error, and 25.03% median time to collision prediction error.

Jinwook Huh, Galen Xing, Ziyun Wang et al.

Traditional motion planning is computationally burdensome for practical robots, involving extensive collision checking and considerable iterative propagation of cost values. We present a novel neural network architecture which can directly generate the cost-to-go (c2g) function for a given configuration space and a goal configuration. The output of the network is a continuous function whose gradient in configuration space can be directly used to generate trajectories in motion planning without the need for protracted iterations or extensive collision checking. This higher order function (i.e. a function generating another function) representation lies at the core of our motion planning architecture, c2g-HOF, which can take a workspace as input, and generate the cost-to-go function over the configuration space map (C-map). Simulation results for 2D and 3D environments show that c2g-HOF can be orders of magnitude faster at execution time than methods which explore the configuration space during execution. We also present an implementation of c2g-HOF which generates trajectories for robot manipulators directly from an overhead image of the workspace.

Heejin Jeong, Hamed Hassani, Manfred Morari et al.

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.

Ziyun Wang, Eric A. Mitchell, Volkan Isler et al.

Single-view 3D object reconstruction is a challenging fundamental problem in computer vision, largely due to the morphological diversity of objects in the natural world. In particular, high curvature regions are not always captured effectively by methods trained using only set-based loss functions, resulting in reconstructions short-circuiting the surface or cutting corners. In particular, high curvature regions are not always captured effectively by methods trained using only set-based loss functions, resulting in reconstructions short-circuiting the surface or cutting corners. To address this issue, we propose learning an image-conditioned mapping function from a canonical sampling domain to a high dimensional space where the Euclidean distance is equal to the geodesic distance on the object. The first three dimensions of a mapped sample correspond to its 3D coordinates. The additional lifted components contain information about the underlying geodesic structure. Our results show that taking advantage of these learned lifted coordinates yields better performance for estimating surface normals and generating surfaces than using point cloud reconstructions alone. Further, we find that this learned geodesic embedding space provides useful information for applications such as unsupervised object decomposition.

Anthony Bisulco, Fernando Cladera Ojeda, Volkan Isler et al.

This paper presents a novel end-to-end system for pedestrian detection using Dynamic Vision Sensors (DVSs). We target applications where multiple sensors transmit data to a local processing unit, which executes a detection algorithm. Our system is composed of (i) a near-chip event filter that compresses and denoises the event stream from the DVS, and (ii) a Binary Neural Network (BNN) detection module that runs on a low-computation edge computing device (in our case a STM32F4 microcontroller). We present the system architecture and provide an end-to-end implementation for pedestrian detection in an office environment. Our implementation reduces transmission size by up to 99.6% compared to transmitting the raw event stream. The average packet size in our system is only 1397 bits, while 307.2 kb are required to send an uncompressed DVS time window. Our detector is able to perform a detection every 450 ms, with an overall testing F1 score of 83%. The low bandwidth and energy properties of our system make it ideal for IoT applications.

Ziyun Wang, Volkan Isler, Daniel D. Lee

We address the problem of generating a high-resolution surface reconstruction from a single image. Our approach is to learn a Higher Order Function (HOF) which takes an image of an object as input and generates a mapping function. The mapping function takes samples from a canonical domain (e.g. the unit sphere) and maps each sample to a local tangent plane on the 3D reconstruction of the object. Each tangent plane is represented as an origin point and a normal vector at that point. By efficiently learning a continuous mapping function, the surface can be generated at arbitrary resolution in contrast to other methods which generate fixed resolution outputs. We present the Surface HOF in which both the higher order function and the mapping function are represented as neural networks, and train the networks to generate reconstructions of PointNet objects. Experiments show that Surface HOF is more accurate and uses more efficient representations than other state of the art methods for surface reconstruction. Surface HOF is also easier to train: it requires minimal input pre-processing and output post-processing and generates surface representations that are more parameter efficient. Its accuracy and convenience make Surface HOF an appealing method for single image reconstruction.

Heejin Jeong, Brent Schlotfeldt, Hamed Hassani et al.

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.

Selim Engin, Eric Mitchell, Daewon Lee et al.

We consider the problem of planning views for a robot to acquire images of an object for visual inspection and reconstruction. In contrast to offline methods which require a 3D model of the object as input or online methods which rely on only local measurements, our method uses a neural network which encodes shape information for a large number of objects. We build on recent deep learning methods capable of generating a complete 3D reconstruction of an object from a single image. Specifically, in this work, we extend a recent method which uses Higher Order Functions (HOF) to represent the shape of the object. We present a new generalization of this method to incorporate multiple images as input and establish a connection between visibility and reconstruction quality. This relationship forms the foundation of our view planning method where we compute viewpoints to visually cover the output of the multi-view HOF network with as few images as possible. Experiments indicate that our method provides a good compromise between online and offline methods: Similar to online methods, our method does not require the true object model as input. In terms of number of views, it is much more efficient. In most cases, its performance is comparable to the optimal offline case even on object classes the network has not been trained on.

Jinwook Huh, Omur Arslan, Daniel D. Lee

In this paper, we introduce a new probabilistically safe local steering primitive for sampling-based motion planning in complex high-dimensional configuration spaces. Our local steering procedure is based on a new notion of a convex probabilistically safe corridor that is constructed around a configuration using tangent hyperplanes of confidence ellipsoids of Gaussian mixture models learned from prior collision history. Accordingly, we propose to expand a random motion planning graph towards a sample goal using its projection onto probabilistically safe corridors, which efficiently exploits the local geometry of configuration spaces for selecting proper steering direction and adapting steering stepsize. We observe that the proposed local steering procedure generates effective steering motion around difficult regions of configuration spaces, such as narrow passages, while minimizing collision likelihood. We evaluate the proposed steering method with randomized motion planners in a number of planning scenarios, both in simulation and on a physical 7DoF robot arm, demonstrating the effectiveness of our safety guided local planner over the standard straight-line planner.

Ty Nguyen, Tolga Ozaslan, Ian D. Miller et al.

Periodical inspection and maintenance of critical infrastructure such as dams, penstocks, and locks are of significant importance to prevent catastrophic failures. Conventional manual inspection methods require inspectors to climb along a penstock to spot corrosion, rust and crack formation which is unsafe, labor-intensive, and requires intensive training. This work presents an alternative approach using a Micro Aerial Vehicle (MAV) that autonomously flies to collect imagery which is then fed into a pretrained deep-learning model to identify corrosion. Our simplified U-Net trained with less than 40 image samples can do inference at 12 fps on a single GPU. We analyze different loss functions to solve the class imbalance problem, followed by a discussion on choosing proper metrics and weights for object classes. Results obtained with the dataset collected from Center Hill Dam, TN show that focal loss function, combined with a proper set of class weights yield better segmentation results than the base loss, Softmax cross entropy. Our method can be used in combination with planning algorithm to offer a complete, safe and cost-efficient solution to autonomous infrastructure inspection.

Mark Eisen, Clark Zhang, Luiz F. O. Chamon et al.

This paper considers the design of optimal resource allocation policies in wireless communication systems which are generically modeled as a functional optimization problem with stochastic constraints. These optimization problems have the structure of a learning problem in which the statistical loss appears as a constraint, motivating the development of learning methodologies to attempt their solution. To handle stochastic constraints, training is undertaken in the dual domain. It is shown that this can be done with small loss of optimality when using near-universal learning parameterizations. In particular, since deep neural networks (DNN) are near-universal their use is advocated and explored. DNNs are trained here with a model-free primal-dual method that simultaneously learns a DNN parametrization of the resource allocation policy and optimizes the primal and dual variables. Numerical simulations demonstrate the strong performance of the proposed approach on a number of common wireless resource allocation problems.

Clark Zhang, Jinwook Huh, Daniel D. Lee

Sampling-based motion planners have experienced much success due to their ability to efficiently and evenly explore the state space. However, for many tasks, it may be more efficient to not uniformly explore the state space, especially when there is prior information about its structure. Previous methods have attempted to modify the sampling distribution using hand selected heuristics that can work well for specific environments but not universally. In this paper, a policy- search based method is presented as an adaptive way to learn implicit sampling distributions for different environments. It utilizes information from past searches in similar environments to generate better distributions in novel environments, thus reducing overall computational cost. Our method can be incor- porated with a variety of sampling-based planners to improve performance. Our approach is validated on a number of tasks, including a 7DOF robot arm, showing marked improvement in number of collision checks as well as number of nodes expanded compared with baseline methods.

J. Jon Ryu, Shouvik Ganguly, Young-Han Kim et al.

A new approach to $L_2$-consistent estimation of a general density functional using $k$-nearest neighbor distances is proposed, where the functional under consideration is in the form of the expectation of some function $f$ of the densities at each point. The estimator is designed to be asymptotically unbiased, using the convergence of the normalized volume of a $k$-nearest neighbor ball to a Gamma distribution in the large-sample limit, and naturally involves the inverse Laplace transform of a scaled version of the function $f.$ Some instantiations of the proposed estimator recover existing $k$-nearest neighbor based estimators of Shannon and Rényi entropies and Kullback--Leibler and Rényi divergences, and discover new consistent estimators for many other functionals such as logarithmic entropies and divergences. The $L_2$-consistency of the proposed estimator is established for a broad class of densities for general functionals, and the convergence rate in mean squared error is established as a function of the sample size for smooth, bounded densities.

Arbaaz Khan, Clark Zhang, Daniel D. Lee et al.

In this paper, we explore using deep reinforcement learning for problems with multiple agents. Most existing methods for deep multi-agent reinforcement learning consider only a small number of agents. When the number of agents increases, the dimensionality of the input and control spaces increase as well, and these methods do not scale well. To address this, we propose casting the multi-agent reinforcement learning problem as a distributed optimization problem. Our algorithm assumes that for multi-agent settings, policies of individual agents in a given population live close to each other in parameter space and can be approximated by a single policy. With this simple assumption, we show our algorithm to be extremely effective for reinforcement learning in multi-agent settings. We demonstrate its effectiveness against existing comparable approaches on co-operative and competitive tasks.

Heejin Jeong, Clark Zhang, George J. Pappas et al.

While off-policy temporal difference (TD) methods have widely been used in reinforcement learning due to their efficiency and simple implementation, their Bayesian counterparts have not been utilized as frequently. One reason is that the non-linear max operation in the Bellman optimality equation makes it difficult to define conjugate distributions over the value functions. In this paper, we introduce a novel Bayesian approach to off-policy TD methods, called as ADFQ, which updates beliefs on state-action values, Q, through an online Bayesian inference method known as Assumed Density Filtering. We formulate an efficient closed-form solution for the value update by approximately estimating analytic parameters of the posterior of the Q-beliefs. Uncertainty measures in the beliefs not only are used in exploration but also provide a natural regularization for the value update considering all next available actions. ADFQ converges to Q-learning as the uncertainty measures of the Q-beliefs decrease and improves common drawbacks of other Bayesian RL algorithms such as computational complexity. We extend ADFQ with a neural network. Our empirical results demonstrate that ADFQ outperforms comparable algorithms on various Atari 2600 games, with drastic improvements in highly stochastic domains or domains with a large action space.

SueYeon Chung, Daniel D. Lee, Haim Sompolinsky

Perceptual manifolds arise when a neural population responds to an ensemble of sensory signals associated with different physical features (e.g., orientation, pose, scale, location, and intensity) of the same perceptual object. Object recognition and discrimination requires classifying the manifolds in a manner that is insensitive to variability within a manifold. How neuronal systems give rise to invariant object classification and recognition is a fundamental problem in brain theory as well as in machine learning. Here we study the ability of a readout network to classify objects from their perceptual manifold representations. We develop a statistical mechanical theory for the linear classification of manifolds with arbitrary geometry revealing a remarkable relation to the mathematics of conic decomposition. Novel geometrical measures of manifold radius and manifold dimension are introduced which can explain the classification capacity for manifolds of various geometries. The general theory is demonstrated on a number of representative manifolds, including L2 ellipsoids prototypical of strictly convex manifolds, L1 balls representing polytopes consisting of finite sample points, and orientation manifolds which arise from neurons tuned to respond to a continuous angle variable, such as object orientation. The effects of label sparsity on the classification capacity of manifolds are elucidated, revealing a scaling relation between label sparsity and manifold radius. Theoretical predictions are corroborated by numerical simulations using recently developed algorithms to compute maximum margin solutions for manifold dichotomies. Our theory and its extensions provide a powerful and rich framework for applying statistical mechanics of linear classification to data arising from neuronal responses to object stimuli, as well as to artificial deep networks trained for object recognition tasks.

Arbaaz Khan, Clark Zhang, Nikolay Atanasov et al.

Planning problems in partially observable environments cannot be solved directly with convolutional networks and require some form of memory. But, even memory networks with sophisticated addressing schemes are unable to learn intelligent reasoning satisfactorily due to the complexity of simultaneously learning to access memory and plan. To mitigate these challenges we introduce the Memory Augmented Control Network (MACN). The proposed network architecture consists of three main parts. The first part uses convolutions to extract features and the second part uses a neural network-based planning module to pre-plan in the environment. The third part uses a network controller that learns to store those specific instances of past information that are necessary for planning. The performance of the network is evaluated in discrete grid world environments for path planning in the presence of simple and complex obstacles. We show that our network learns to plan and can generalize to new environments.

Arbaaz Khan, Clark Zhang, Nikolay Atanasov et al.

We investigate how a neural network can learn perception actions loops for navigation in unknown environments. Specifically, we consider how to learn to navigate in environments populated with cul-de-sacs that represent convex local minima that the robot could fall into instead of finding a set of feasible actions that take it to the goal. Traditional methods rely on maintaining a global map to solve the problem of over coming a long cul-de-sac. However, due to errors induced from local and global drift, it is highly challenging to maintain such a map for long periods of time. One way to mitigate this problem is by using learning techniques that do not rely on hand engineered map representations and instead output appropriate control policies directly from their sensory input. We first demonstrate that such a problem cannot be solved directly by deep reinforcement learning due to the sparse reward structure of the environment. Further, we demonstrate that deep supervised learning also cannot be used directly to solve this problem. We then investigate network models that offer a combination of reinforcement learning and supervised learning and highlight the significance of adding fully differentiable memory units to such networks. We evaluate our networks on their ability to generalize to new environments and show that adding memory to such networks offers huge jumps in performance

SueYeon Chung, Uri Cohen, Haim Sompolinsky et al.

We consider the problem of classifying data manifolds where each manifold represents invariances that are parameterized by continuous degrees of freedom. Conventional data augmentation methods rely upon sampling large numbers of training examples from these manifolds; instead, we propose an iterative algorithm called M_{CP} based upon a cutting-plane approach that efficiently solves a quadratic semi-infinite programming problem to find the maximum margin solution. We provide a proof of convergence as well as a polynomial bound on the number of iterations required for a desired tolerance in the objective function. The efficiency and performance of M_{CP} are demonstrated in high-dimensional simulations and on image manifolds generated from the ImageNet dataset. Our results indicate that M_{CP} is able to rapidly learn good classifiers and shows superior generalization performance compared with conventional maximum margin methods using data augmentation methods.

Steven W Chen, Nikolay Atanasov, Arbaaz Khan et al.

This paper highlights the significance of including memory structures in neural networks when the latter are used to learn perception-action loops for autonomous robot navigation. Traditional navigation approaches rely on global maps of the environment to overcome cul-de-sacs and plan feasible motions. Yet, maintaining an accurate global map may be challenging in real-world settings. A possible way to mitigate this limitation is to use learning techniques that forgo hand-engineered map representations and infer appropriate control responses directly from sensed information. An important but unexplored aspect of such approaches is the effect of memory on their performance. This work is a first thorough study of memory structures for deep-neural-network-based robot navigation, and offers novel tools to train such networks from supervision and quantify their ability to generalize to unseen scenarios. We analyze the separation and generalization abilities of feedforward, long short-term memory, and differentiable neural computer networks. We introduce a new method to evaluate the generalization ability by estimating the VC-dimension of networks with a final linear readout layer. We validate that the VC estimates are good predictors of actual test performance. The reported method can be applied to deep learning problems beyond robotics.

SueYeon Chung, Daniel D. Lee, Haim Sompolinsky

Objects are represented in sensory systems by continuous manifolds due to sensitivity of neuronal responses to changes in physical features such as location, orientation, and intensity. What makes certain sensory representations better suited for invariant decoding of objects by downstream networks? We present a theory that characterizes the ability of a linear readout network, the perceptron, to classify objects from variable neural responses. We show how the readout perceptron capacity depends on the dimensionality, size, and shape of the object manifolds in its input neural representation.

Pedro A. Ortega, Koby Crammer, Daniel D. Lee

This paper introduces a new probabilistic model for online learning which dynamically incorporates information from stochastic gradients of an arbitrary loss function. Similar to probabilistic filtering, the model maintains a Gaussian belief over the optimal weight parameters. Unlike traditional Bayesian updates, the model incorporates a small number of gradient evaluations at locations chosen using Thompson sampling, making it computationally tractable. The belief is then transformed via a linear flow field which optimally updates the belief distribution using rules derived from information theoretic principles. Several versions of the algorithm are shown using different constraints on the flow field and compared with conventional online learning algorithms. Results are given for several classification tasks including logistic regression and multilayer neural networks.

Pedro A. Ortega, Daniel D. Lee

Recently, there has been a growing interest in modeling planning with information constraints. Accordingly, an agent maximizes a regularized expected utility known as the free energy, where the regularizer is given by the information divergence from a prior to a posterior policy. While this approach can be justified in various ways, including from statistical mechanics and information theory, it is still unclear how it relates to decision-making against adversarial environments. This connection has previously been suggested in work relating the free energy to risk-sensitive control and to extensive form games. Here, we show that a single-agent free energy optimization is equivalent to a game between the agent and an imaginary adversary. The adversary can, by paying an exponential penalty, generate costs that diminish the decision maker's payoffs. It turns out that the optimal strategy of the adversary consists in choosing costs so as to render the decision maker indifferent among its choices, which is a definining property of a Nash equilibrium, thus tightening the connection between free energy optimization and game theory.