Task-Motion Planning for Navigation in Belief Space Antony Thomas, Fulvio Mastrogiovanni, and Marco Baglietto Abstract We present an integrated Task-Motion Planning (TMP) framework for navigation in large-scale environment. Autonomous robots operating in real world complex scenarios require planning in the discrete (task) space and the continuous (motion) space. In knowledge intensive domains, on the one hand, a robot has to reason at the highest-level, for example the regions to navigate to; on the other hand, the feasibility of the respective navigation tasks have to be checked at the execution level. This presents a need for motion-planning-aware task planners. We discuss a probabilistically complete approach that leverages this task-motion interaction for navigating in indoor domains, returning a plan that is optimal at the task-level. Furthermore, our framework is intended for motion planning under motion and sensing uncertainty, which is formally known as belief space planning. The underlying methodology is validated with a simulated office environment in Gazebo. In addition, we discuss the limitations and provide suggestions for improvements and future work. 1 Introduction Autonomous robots operating in complex real world scenarios require different levels of planning to execute their tasks. High-level (task) planning helps break down a given set of tasks into a sequence of sub-tasks. Actual execution of each of these sub-tasks would require low-level control actions to generate appropriate robot motions. In fact, the dependency between logical and geometrical aspects is pervasive in both task planning and execution.

We consider the verification of multiple expected reward objectives at once on Markov decision processes (MDPs). This enables a trade-off analysis among multiple objectives by obtaining the Pareto front. We focus on strategies that are easy to employ and implement. That is, strategies that are pure (no randomization) and have bounded memory. We show that checking whether a point is achievable by a pure stationary strategy is NP-complete, even for two objectives, and we provide an MILP encoding to solve the corresponding problem. The bounded memory case can be reduced to the stationary one by a product construction. Experimental results using \Storm and Gurobi show the feasibility of our algorithms.

In this paper, we propose a new estimation procedure for discovering the structure of Gaussian Markov random fields (MRFs) with false discovery rate (FDR) control, making use of the sorted l1-norm (SL1) regularization. A Gaussian MRF is an acyclic graph representing a multivariate Gaussian distribution, where nodes are random variables and edges represent the conditional dependence between the connected nodes. Since it is possible to learn the edge structure of Gaussian MRFs directly from data, Gaussian MRFs provide an excellent way to understand complex data by revealing the dependence structure among many inputs features, such as genes, sensors, users, documents, etc. In learning the graphical structure of Gaussian MRFs, it is desired to discover the actual edges of the underlying but unknown probabilistic graphical model-it becomes more complicated when the number of random variables (features) p increases, compared to the number of data points n. In particular, when p >> n, it is statistically unavoidable for any estimation procedure to include false edges. Therefore, there have been many trials to reduce the false detection of edges, in particular, using different types of regularization on the learning parameters. Our method makes use of the SL1 regularization, introduced recently for model selection in linear regression. We focus on the benefit of SL1 regularization that it can be used to control the FDR of detecting important random variables. Adapting SL1 for probabilistic graphical models, we show that SL1 can be used for the structure learning of Gaussian MRFs using our suggested procedure nsSLOPE (neighborhood selection Sorted L-One Penalized Estimation), controlling the FDR of detecting edges.

It is a significant challenge to design probabilistic programming systems that can accommodate a wide variety of inference strategies within a unified framework. Noting that the versatility of modern automatic differentiation frameworks is based in large part on the unifying concept of tensors, we describe a software abstraction --functional tensors-- that captures many of the benefits of tensors, while also being able to describe continuous probability distributions. Moreover, functional tensors are a natural candidate for generalized variable elimination and parallel-scan filtering algorithms that enable parallel exact inference for a large family of tractable modeling motifs. We demonstrate the versatility of functional tensors by integrating them into the modeling frontend and inference backend of the Pyro programming language. In experiments we show that the resulting framework enables a large variety of inference strategies, including those that mix exact and approximate inference.

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.

In typical reinforcement learning (RL), the environment is assumed given and the goal of the learning is to identify an optimal policy for the agent taking actions through its interactions with the environment. In this paper, we extend this setting by considering the environment is not given, but controllable and learnable through its interaction with the agent at the same time. This extension is motivated by environment design scenarios in the real-world, including game design, shopping space design and traffic signal design. Theoretically, we find a dual Markov decision process (MDP) w.r.t. the environment to that w.r.t. the agent, and derive a policy gradient solution to optimizing the parametrized environment. Furthermore, discontinuous environments are addressed by a proposed general generative framework. Our experiments on a Maze game design task show the effectiveness of the proposed algorithms in generating diverse and challenging Mazes against various agent settings.

-- Deep reinforcement learning has great potential to acquire complex, adaptive behaviors for autonomous agents automatically. However, the underlying neural network polices have not been widely deployed in real-world applications, especially in these safety-critical tasks (e.g., autonomous driving). One of the reasons is that the learned policy cannot perform flexible and resilient behaviors as traditional methods to adapt to diverse environments. In this paper, we consider the problem that a mobile robot learns adaptive and resilient behaviors for navigating in unseen uncertain environments while avoiding collisions. We present a novel approach for uncertainty-aware navigation by introducing an uncertainty-aware predictor to model the environmental uncertainty, and we propose a novel uncertainty-aware navigation network to learn resilient behaviors in the prior unknown environments. T o train the proposed uncertainty-aware network more stably and efficiently, we present the temperature decay training paradigm, which balances exploration and exploitation during the training process. Our experimental evaluation demonstrates that our approach can learn resilient behaviors in diverse environments and generate adaptive trajectories according to environmental uncertainties. Videos of the experiments are available at https://sites.google.com/view/resilient-nav/ . With the recent progress of machine learning techniques, deep reinforcement learning has been seen as a promising technique for autonomous systems to learn intelligent and complex behaviors in manipulation and motion planning tasks [1]-[3].

This paper presents an algorithm and regret analysis for the restless hidden Markov bandit problem with linear rewards. In this problem the reward received by the decision maker is a random linear function which depends on the arm selected and a hidden state. In contrast to previous works on Markovian bandits, we do not assume that the decision maker receives information regarding the state of the system, but has to infer it based on its actions and the received reward. Surprisingly, we can still maintain logarithmic regret in the case of polyhedral action set. Furthermore, the regret does not depend on the number of extreme points in the action space.

In this paper, we study the graph-based semi-supervised learning for classifying nodes in attributed networks, where the nodes and edges possess content information. Recent approaches like graph convolution networks and attention mechanisms have been proposed to ensemble the first-order neighbors and incorporate the relevant neighbors. However, it is costly (especially in memory) to consider all neighbors without a prior differentiation. We propose to explore the neighborhood in a reinforcement learning setting and find a walk path well-tuned for classifying the unlabelled target nodes. We let an agent (of node classification task) walk over the graph and decide where to direct to maximize classification accuracy. We define the graph walk as a partially observable Markov decision process (POMDP). The proposed method is flexible for working in both transductive and inductive setting. Extensive experiments on four datasets demonstrate that our proposed method outperforms several state-of-the-art methods. Several case studies also illustrate the meaningful movement trajectory made by the agent.

Markov chain Monte Carlo (MCMC) methods and neural networks are instrumental in tackling inferential and prediction problems. However, Bayesian inference based on joint use of MCMC methods and of neural networks is limited. This paper reviews the main challenges posed by neural networks to MCMC developments, including lack of parameter identifiability due to weight symmetries, prior specification effects, and consequently high computational cost and convergence failure. Population and manifold MCMC algorithms are combined to demonstrate these challenges via multilayer perceptron (MLP) examples and to develop case studies for assessing the capacity of approximate inference methods to uncover the posterior covariance of neural network parameters. Some of these challenges, such as high computational cost arising from the application of neural networks to big data and parameter identifiability arising from weight symmetries, stimulate research towards more scalable approximate MCMC methods or towards MCMC methods in reduced parameter spaces.