Learning and Inference in Hilbert Space with Quantum Graphical Models

Quantum Graphical Models (QGMs) generalize classical graphical models by adopting the formalism for reasoning about uncertainty from quantum mechanics. Unlike classical graphical models, QGMs represent uncertainty with density matrices in complex Hilbert spaces. Hilbert space embeddings (HSEs) also generalize Bayesian inference in Hilbert spaces. We investigate the link between QGMs and HSEs and show that the sum rule and Bayes rule for QGMs are equivalent to the kernel sum rule in HSEs and a special case of Nadaraya-Watson kernel regression, respectively. We show that these operations can be kernelized, and use these insights to propose a Hilbert Space Embedding of Hidden Quantum Markov Models (HSE-HQMM) to model dynamics. We present experimental results showing that HSE-HQMMs are competitive with state-of-the-art models like LSTMs and PSRNNs on several datasets, while also providing a nonparametric method for maintaining a probability distribution over continuous-valued features.

Orthogonally Decoupled Variational Gaussian Processes

Gaussian processes (GPs) provide a powerful non-parametric framework for reasoning over functions. Despite appealing theory, its superlinear computational and memory complexities have presented a long-standing challenge. State-of-the-art sparse variational inference methods trade modeling accuracy against complexity. However, the complexities of these methods still scale superlinearly in the number of basis functions, implying that that sparse GP methods are able to learn from large datasets only when a small model is used. Recently, a decoupled approach was proposed that removes the unnecessary coupling between the complexities of modeling the mean and the covariance functions of a GP. It achieves a linear complexity in the number of mean parameters, so an expressive posterior mean function can be modeled. While promising, this approach suffers from optimization difficulties due to ill-conditioning and non-convexity. In this work, we propose an alternative decoupled parametrization. It adopts an orthogonal basis in the mean function to model the residues that cannot be learned by the standard coupled approach. Therefore, our method extends, rather than replaces, the coupled approach to achieve strictly better performance. This construction admits a straightforward natural gradient update rule, so the structure of the information manifold that is lost during decoupling can be leveraged to speed up learning. Empirically, our algorithm demonstrates significantly faster convergence in multiple experiments.

Truncated Back-propagation for Bilevel Optimization

Bilevel optimization has been recently revisited for designing and analyzing algorithms in hyperparameter tuning and meta learning tasks. However, due to its nested structure, evaluating exact gradients for high-dimensional problems is computationally challenging. One heuristic to circumvent this difficulty is to use the approximate gradient given by performing truncated back-propagation through the iterative optimization procedure that solves the lower-level problem. Although promising empirical performance has been reported, its theoretical properties are still unclear. In this paper, we analyze the properties of this family of approximate gradients and establish sufficient conditions for convergence. We validate this on several hyperparameter tuning and meta learning tasks. We find that optimization with the approximate gradient computed using few-step back-propagation often performs comparably to optimization with the exact gradient, while requiring far less memory and half the computation time.

Predictor-Corrector Policy Optimization

We present a predictor-corrector framework, called PicCoLO, that can transform a first-order model-free reinforcement or imitation learning algorithm into a new hybrid method that leverages predictive models to accelerate policy learning. The new "PicCoLOed" algorithm optimizes a policy by recursively repeating two steps: In the Prediction Step, the learner uses a model to predict the unseen future gradient and then applies the predicted estimate to update the policy; in the Correction Step, the learner runs the updated policy in the environment, receives the true gradient, and then corrects the policy using the gradient error. Unlike previous algorithms, PicCoLO corrects for the mistakes of using imperfect predicted gradients and hence does not suffer from model bias. The development of PicCoLO is made possible by a novel reduction from predictable online learning to adversarial online learning, which provides a systematic way to modify existing first-order algorithms to achieve the optimal regret with respect to predictable information. We show, in both theory and simulation, that the convergence rate of several first-order model-free algorithms can be improved by PicCoLO.

Accelerating Imitation Learning with Predictive Models

Sample efficiency is critical in solving real-world reinforcement learning problems, where agent-environment interactions can be costly. Imitation learning from expert advice has proved to be an effective strategy for reducing the number of interactions required to train a policy. Online imitation learning, which interleaves policy evaluation and policy optimization, is a particularly effective technique with provable performance guarantees. In this work, we seek to further accelerate the convergence rate of online imitation learning, thereby making it more sample efficient. We propose two model-based algorithms inspired by Follow-the-Leader (FTL) with prediction: MoBIL-VI based on solving variational inequalities and MoBIL-Prox based on stochastic first-order updates. These two methods leverage a model to predict future gradients to speed up policy learning. When the model oracle is learned online, these algorithms can provably accelerate the best known convergence rate up to an order. Our algorithms can be viewed as a generalization of stochastic Mirror-Prox (Juditsky et al., 2011), and admit a simple constructive FTL-style analysis of performance.

Agile Off-Road Autonomous Driving Using End-to-End Deep Imitation Learning

We present an end-to-end imitation learning system for agile, off-road autonomous driving using only low-cost on-board sensors. By imitating a model predictive controller equipped with advanced sensors, we train a deep neural network control policy to map raw, high-dimensional observations to continuous steering and throttle commands. Compared with recent approaches to similar tasks, our method requires neither state estimation nor on-the-fly planning to navigate the vehicle. Our approach relies on, and experimentally validates, recent imitation learning theory. Empirically, we show that policies trained with online imitation learning overcome well-known challenges related to covariate shift and generalize better than policies trained with batch imitation learning. Built on these insights, our autonomous driving system demonstrates successful high-speed off-road driving, matching the state-of-the-art performance.

Learning to Align Images using Weak Geometric Supervision

Image alignment tasks require accurate pixel correspondences, which are usually recovered by matching local feature descriptors. Such descriptors are often derived using supervised learning on existing datasets with ground truth correspondences. However, the cost of creating such datasets is usually prohibitive. In this paper, we propose a new approach to align two images related by an unknown 2D homography where the local descriptor is learned from scratch from the images and the homography is estimated simultaneously. Our key insight is that a siamese convolutional neural network can be trained jointly while iteratively updating the homography parameters by optimizing a single loss function. Our method is currently weakly supervised because the input images need to be roughly aligned. We have used this method to align images of different modalities such as RGB and near-infra-red (NIR) without using any prior labeled data. Images automatically aligned by our method were then used to train descriptors that generalize to new images. We also evaluated our method on RGB images. On the HPatches benchmark, our method achieves comparable accuracy to deep local descriptors that were trained offline in a supervised setting.

Learning Generalizable Robot Skills from Demonstrations in Cluttered Environments

Learning from Demonstration (LfD) is a popular approach to endowing robots with skills without having to program them by hand. Typically, LfD relies on human demonstrations in clutter-free environments. This prevents the demonstrations from being affected by irrelevant objects, whose influence can obfuscate the true intention of the human or the constraints of the desired skill. However, it is unrealistic to assume that the robot's environment can always be restructured to remove clutter when capturing human demonstrations. To contend with this problem, we develop an importance weighted batch and incremental skill learning approach, building on a recent inference-based technique for skill representation and reproduction. Our approach reduces unwanted environmental influences on the learned skill, while still capturing the salient human behavior. We provide both batch and incremental versions of our approach and validate our algorithms on a 7-DOF JACO2 manipulator with reaching and placing skills.

STEAP: simultaneous trajectory estimation and planning

We present a unified probabilistic framework for simultaneous trajectory estimation and planning (STEAP). Estimation and planning problems are usually considered separately, however, within our framework we show that solving them simultaneously can be more accurate and efficient. The key idea is to compute the full continuous-time trajectory from start to goal at each time-step. While the robot traverses the trajectory, the history portion of the trajectory signifies the solution to the estimation problem, and the future portion of the trajectory signifies a solution to the planning problem. Building on recent probabilistic inference approaches to continuous-time localization and mapping and continuous-time motion planning, we solve the joint problem by iteratively recomputing the maximum a posteriori trajectory conditioned on all available sensor data and cost information. Our approach can contend with high-degree-of-freedom (DOF) trajectory spaces, uncertainty due to limited sensing capabilities, model inaccuracy, the stochastic effect of executing actions, and can find a solution in real-time. We evaluate our framework empirically in both simulation and on a mobile manipulator.

Semantically Meaningful View Selection

An understanding of the nature of objects could help robots to solve both high-level abstract tasks and improve performance at lower-level concrete tasks. Although deep learning has facilitated progress in image understanding, a robot's performance in problems like object recognition often depends on the angle from which the object is observed. Traditionally, robot sorting tasks rely on a fixed top-down view of an object. By changing its viewing angle, a robot can select a more semantically informative view leading to better performance for object recognition. In this paper, we introduce the problem of semantic view selection, which seeks to find good camera poses to gain semantic knowledge about an observed object. We propose a conceptual formulation of the problem, together with a solvable relaxation based on clustering. We then present a new image dataset consisting of around 10k images representing various views of 144 objects under different poses. Finally we use this dataset to propose a first solution to the problem by training a neural network to predict a "semantic score" from a top view image and camera pose. The views predicted to have higher scores are then shown to provide better clustering results than fixed top-down views.