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Vision guided navigation requires processing complex visual information to inform task-orientated decisions. Applications include autonomous robots, self-driving cars, and assistive vision for humans. A key element is the extraction and selection of relevant features in pixel space upon which to base action choices, for which Machine Learning techniques are well suited. However, Deep Reinforcement Learning agents trained in simulation often exhibit unsatisfactory results when deployed in the real-world due to perceptual differences known as the $\textit{reality gap}$. An approach that is yet to be explored to bridge this gap is self-attention. In this paper we (1) perform a systematic exploration of the hyperparameter space for self-attention based navigation of 3D environments and qualitatively appraise behaviour observed from different hyperparameter sets, including their ability to generalise; (2) present strategies to improve the agents' generalisation abilities and navigation behaviour; and (3) show how models trained in simulation are capable of processing real world images meaningfully in real time. To our knowledge, this is the first demonstration of a self-attention based agent successfully trained in navigating a 3D action space, using less than 4000 parameters.

The computational prediction of wave propagation in dam-break floods is a long-standing problem in hydrodynamics and hydrology. Until now, conventional numerical models based on Saint-Venant equations are the dominant approaches. Here we show that a machine learning model that is well-trained on a minimal amount of data, can help predict the long-term dynamic behavior of a one-dimensional dam-break flood with satisfactory accuracy. For this purpose, we solve the Saint-Venant equations for a one-dimensional dam-break flood scenario using the Lax-Wendroff numerical scheme and train the reservoir computing echo state network (RC-ESN) with the dataset by the simulation results consisting of time-sequence flow depths. We demonstrate a good prediction ability of the RC-ESN model, which ahead predicts wave propagation behavior 286 time-steps in the dam-break flood with a root mean square error (RMSE) smaller than 0.01, outperforming the conventional long short-term memory (LSTM) model which reaches a comparable RMSE of only 81 time-steps ahead. To show the performance of the RC-ESN model, we also provide a sensitivity analysis of the prediction accuracy concerning the key parameters including training set size, reservoir size, and spectral radius. Results indicate that the RC-ESN are less dependent on the training set size, a medium reservoir size K=1200~2600 is sufficient. We confirm that the spectral radius \r{ho} shows a complex influence on the prediction accuracy and suggest a smaller spectral radius \r{ho} currently. By changing the initial flow depth of the dam break, we also obtained the conclusion that the prediction horizon of RC-ESN is larger than that of LSTM.

Indoor motion planning focuses on solving the problem of navigating an agent through a cluttered environment. To date, quite a lot of work has been done in this field, but these methods often fail to find the optimal balance between computationally inexpensive online path planning, and optimality of the path. Along with this, these works often prove optimality for single-start single-goal worlds. To address these challenges, we present a multiple waypoint path planner and controller stack for navigation in unknown indoor environments where waypoints include the goal along with the intermediary points that the robot must traverse before reaching the goal. Our approach makes use of a global planner (to find the next best waypoint at any instant), a local planner (to plan the path to a specific waypoint), and an adaptive Model Predictive Control strategy (for robust system control and faster maneuvers). We evaluate our algorithm on a set of randomly generated obstacle maps, intermediate waypoints, and start-goal pairs, with results indicating a significant reduction in computational costs, with high accuracies and robust control.

Safe navigation is a fundamental challenge in multi-robot systems due to the uncertainty surrounding the future trajectory of the robots that act as obstacles for each other. In this work, we propose a principled data-driven approach where each robot repeatedly solves a finite horizon optimization problem subject to collision avoidance constraints with latter being formulated as distributionally robust conditional value-at-risk (CVaR) of the distance between the agent and a polyhedral obstacle geometry. Specifically, the CVaR constraints are required to hold for all distributions that are close to the empirical distribution constructed from observed samples of prediction error collected during execution. The generality of the approach allows us to robustify against prediction errors that arise under commonly imposed assumptions in both distributed and decentralized settings. We derive tractable finite-dimensional approximations of this class of constraints by leveraging convex and minmax duality results for Wasserstein distributionally robust optimization problems. The effectiveness of the proposed approach is illustrated in a multi-drone navigation setting implemented in Gazebo platform.

We develop a new formulation of deep learning based on the Mori-Zwanzig (MZ) formalism of irreversible statistical mechanics. The new formulation is built upon the well-known duality between deep neural networks and discrete stochastic dynamical systems, and it allows us to directly propagate quantities of interest (conditional expectations and probability density functions) forward and backward through the network by means of exact linear operator equations. Such new equations can be used as a starting point to develop new effective parameterizations of deep neural networks, and provide a new framework to study deep-learning via operator theoretic methods. The proposed MZ formulation of deep learning naturally introduces a new concept, i.e., the memory of the neural network, which plays a fundamental role in low-dimensional modeling and parameterization. By using the theory of contraction mappings, we develop sufficient conditions for the memory of the neural network to decay with the number of layers. This allows us to rigorously transform deep networks into shallow ones, e.g., by reducing the number of neurons per layer (using projection operators), or by reducing the total number of layers (using the decay property of the memory operator).

This paper provides a theoretical study of deep neural function approximation in reinforcement learning (RL) with the $\epsilon$-greedy exploration under the online setting. This problem setting is motivated by the successful deep Q-networks (DQN) framework that falls in this regime. In this work, we provide an initial attempt on theoretical understanding deep RL from the perspective of function class and neural networks architectures (e.g., width and depth) beyond the "linear" regime. To be specific, we focus on the value based algorithm with the $\epsilon$-greedy exploration via deep (and two-layer) neural networks endowed by Besov (and Barron) function spaces, respectively, which aims at approximating an $\alpha$-smooth Q-function in a $d$-dimensional feature space. We prove that, with $T$ episodes, scaling the width $m = \widetilde{\mathcal{O}}(T^{\frac{d}{2\alpha + d}})$ and the depth $L=\mathcal{O}(\log T)$ of the neural network for deep RL is sufficient for learning with sublinear regret in Besov spaces. Moreover, for a two layer neural network endowed by the Barron space, scaling the width $\Omega(\sqrt{T})$ is sufficient. To achieve this, the key issue in our analysis is how to estimate the temporal difference error under deep neural function approximation as the $\epsilon$-greedy exploration is not enough to ensure "optimism". Our analysis reformulates the temporal difference error in an $L^2(\mathrm{d}\mu)$-integrable space over a certain averaged measure $\mu$, and transforms it to a generalization problem under the non-iid setting. This might have its own interest in RL theory for better understanding $\epsilon$-greedy exploration in deep RL.

This paper develops a novel control-theoretic framework to analyze the non-asymptotic convergence of Q-learning. We show that the dynamics of asynchronous Q-learning with a constant step-size can be naturally formulated as a discrete-time stochastic affine switching system. Moreover, the evolution of the Q-learning estimation error is over- and underestimated by trajectories of two simpler dynamical systems. Based on these two systems, we derive a new finite-time error bound of asynchronous Q-learning when a constant stepsize is used. Our analysis also sheds light on the overestimation phenomenon of Q-learning. We further illustrate and validate the analysis through numerical simulations.

Vision-based navigation requires processing complex information to make task-orientated decisions. Applications include autonomous robots, self-driving cars, and assistive vision for humans. One of the key elements in the process is the extraction and selection of relevant features in pixel space upon which to base action choices, for which Machine Learning techniques are well suited. However, Deep Reinforcement Learning agents trained in simulation often exhibit unsatisfactory results when deployed in the real-world due to perceptual differences known as the $\textit{reality gap}$. An approach that is yet to be explored to bridge this gap is self-attention. In this paper we (1) perform a systematic exploration of the hyperparameter space for self-attention based navigation of 3D environments and qualitatively appraise behaviour observed from different hyperparameter sets, including their ability to generalise; (2) present strategies to improve the agents' generalisation abilities and navigation behaviour; and (3) show how models trained in simulation are capable of processing real world images meaningfully in real time. To our knowledge, this is the first demonstration of a self-attention based agent successfully trained in navigating a 3D action space, using less than 4000 parameters.

Breakthroughs in machine learning in the last decade have led to `digital intelligence', i.e. machine learning models capable of learning from vast amounts of labeled data to perform several digital tasks such as speech recognition, face recognition, machine translation and so on. The goal of this thesis is to make progress towards designing algorithms capable of `physical intelligence', i.e. building intelligent autonomous navigation agents capable of learning to perform complex navigation tasks in the physical world involving visual perception, natural language understanding, reasoning, planning, and sequential decision making. Despite several advances in classical navigation methods in the last few decades, current navigation agents struggle at long-term semantic navigation tasks. In the first part of the thesis, we discuss our work on short-term navigation using end-to-end reinforcement learning to tackle challenges such as obstacle avoidance, semantic perception, language grounding, and reasoning. In the second part, we present a new class of navigation methods based on modular learning and structured explicit map representations, which leverage the strengths of both classical and end-to-end learning methods, to tackle long-term navigation tasks. We show that these methods are able to effectively tackle challenges such as localization, mapping, long-term planning, exploration and learning semantic priors. These modular learning methods are capable of long-term spatial and semantic understanding and achieve state-of-the-art results on various navigation tasks.

In this monograph, I introduce the basic concepts of Online Learning through a modern view of Online Convex Optimization. Here, online learning refers to the framework of regret minimization under worst-case assumptions. I present first-order and second-order algorithms for online learning with convex losses, in Euclidean and non-Euclidean settings. All the algorithms are clearly presented as instantiation of Online Mirror Descent or Follow-The-Regularized-Leader and their variants. Particular attention is given to the issue of tuning the parameters of the algorithms and learning in unbounded domains, through adaptive and parameter-free online learning algorithms. Non-convex losses are dealt through convex surrogate losses and through randomization. The bandit setting is also briefly discussed, touching on the problem of adversarial and stochastic multi-armed bandits. These notes do not require prior knowledge of convex analysis and all the required mathematical tools are rigorously explained. Moreover, all the proofs have been carefully chosen to be as simple and as short as possible.