Multi-Agent Path Finding (MAPF) is an important optimization problem underlying the deployment of robots in automated warehouses and factories. Despite the large body of work on this topic, most approaches make heavy simplifications, both on the environment and the agents, which make the resulting algorithms impractical for real-life scenarios. In this paper, we consider a realistic problem of online order delivery in a warehouse, where a fleet of robots bring the products belonging to each order from shelves to workstations. This creates a stream of inter-dependent pickup and delivery tasks and the associated MAPF problem consists of computing realistic collision-free robot trajectories fulfilling these tasks. To solve this MAPF problem, we propose an extension of the standard Prioritized Planning algorithm to deal with the inter-dependent tasks (Interleaved Prioritized Planning) and a novel Via-Point Star (VP*) algorithm to compute an optimal dynamics-compliant robot trajectory to visit a sequence of goal locations while avoiding moving obstacles. We prove the completeness of our approach and evaluate it in simulation as well as in a real warehouse.

Quadruped robots require robust and general locomotion skills to exploit their mobility potential in complex and challenging environments. In this work, we present the first implementation of a robust end-to-end learning-based controller on the Solo12 quadruped. Our method is based on deep reinforcement learning of joint impedance references. The resulting control policies follow a commanded velocity reference while being efficient in its energy consumption, robust and easy to deploy. We detail the learning procedure and method for transfer on the real robot. In our experiments, we show that the Solo12 robot is a suitable open-source platform for research combining learning and control because of the easiness in transferring and deploying learned controllers.

Autonomous navigation consists in an agent being able to navigate without human intervention or supervision, it affects both high level planning and low level control. Navigation is at the crossroad of multiple disciplines, it combines notions of computer vision, robotics and control. This work aimed at creating, in a simulation, a navigation pipeline whose transfer to the real world could be done with as few efforts as possible. Given the limited time and the wide range of problematic to be tackled, absolute navigation performances while important was not the main objective. The emphasis was rather put on studying the sim2real gap which is one the major bottlenecks of modern robotics and autonomous navigation. To design the navigation pipeline four main challenges arise; environment, localization, navigation and planning. The iGibson simulator is picked for its photo-realistic textures and physics engine. A topological approach to tackle space representation was picked over metric approaches because they generalize better to new environments and are less sensitive to change of conditions. The navigation pipeline is decomposed as a localization module, a planning module and a local navigation module. These modules utilize three different networks, an image representation extractor, a passage detector and a local policy. The laters are trained on specifically tailored tasks with some associated datasets created for those specific tasks. Localization is the ability for the agent to localize itself against a specific space representation. It must be reliable, repeatable and robust to a wide variety of transformations. Localization is tackled as an image retrieval task using a deep neural network trained on an auxiliary task as a feature descriptor extractor. The local policy is trained with behavioral cloning from expert trajectories gathered with ROS navigation stack.

Partially observable environments present an important open challenge in the domain of sequential control learning with delayed rewards. Despite numerous attempts during the two last decades, the majority of reinforcement learning algorithms and associated approximate models, applied to this context, still assume Markovian state transitions. In this paper, we explore the use of a recently proposed attention-based model, the Gated End-to-End Memory Network, for sequential control. We call the resulting model the Gated End-to-End Memory Policy Network. More precisely, we use a model-free value-based algorithm to learn policies for partially observed domains using this memory-enhanced neural network. This model is end-to-end learnable and it features unbounded memory. Indeed, because of its attention mechanism and associated non-parametric memory, the proposed model allows us to define an attention mechanism over the observation stream unlike recurrent models. We show encouraging results that illustrate the capability of our attention-based model in the context of the continuous-state non-stationary control problem of stock trading. We also present an OpenAI Gym environment for simulated stock exchange and explain its relevance as a benchmark for the field of non-Markovian decision process learning.

The trade-off between the cost of acquiring and processing data, and uncertainty due to a lack of data is fundamental in machine learning. A basic instance of this trade-off is the problem of deciding when to make noisy and costly observations of a discrete-time Gaussian random walk, so as to minimise the posterior variance plus observation costs. We present the first proof that a simple policy, which observes when the posterior variance exceeds a threshold, is optimal for this problem. The proof generalises to a wide range of cost functions other than the posterior variance. This result implies that optimal policies for linear-quadratic-Gaussian control with costly observations have a threshold structure. It also implies that the restless bandit problem of observing multiple such time series, has a well-defined Whittle index. We discuss computation of that index, give closed-form formulae for it, and compare the performance of the associated index policy with heuristic policies. The proof is based on a new verification theorem that demonstrates threshold structure for Markov decision processes, and on the relation between binary sequences known as mechanical words and the dynamics of discontinuous nonlinear maps, which frequently arise in physics, control and biology.

We study the restless bandit associated with an extremely simple scalar Kalman filter model in discrete time. Under certain assumptions, we prove that the problem is {\it indexable} in the sense that the {\it Whittle index} is a non-decreasing function of the relevant belief state. In spite of the long history of this problem, this appears to be the first such proof. We use results about {\it Schur-convexity} and {\it mechanical words}, which are particularbinary strings intimately related to {\it palindromes}.

We study the restless bandit associated with an extremely simple scalar Kalman filter model in discrete time. Under certain assumptions, we prove that the problem is indexable in the sense that the Whittle index is a non-decreasing function of the relevant belief state. In spite of the long history of this problem, this appears to be the first such proof. We use results about Schur-convexity and mechanical words, which are particular binary strings intimately related to palindromes.

Finding optimal policies for Markov Decision Processes with large state spaces is in general intractable. Nonetheless, simulation-based algorithms inspired by Sparse Sampling (SS) such as Upper Confidence Bound applied in Trees (UCT) and Forward Search Sparse Sampling (FSSS) have been shown to perform reasonably well in both theory and practice, despite the high computational demand. To improve the efficiency of these algorithms, we adopt a simple enhancement technique with a heuristic policy to speed up the selection of optimal actions. The general method, called Aux, augments the look-ahead tree with auxiliary arms that are evaluated by the heuristic policy. In this paper, we provide theoretical justification for the method and demonstrate its effectiveness in two experimental benchmarks that showcase the faster convergence to a near optimal policy for both SS and FSSS. Moreover, to further speed up the convergence of these algorithms at the early stage, we present a novel mechanism to combine them with UCT so that the resulting hybrid algorithm is superior to both of its components.

We analyze differences between two information-theoretically motivated approaches to statistical inference and model selection: the Minimum Description Length (MDL) principle, and the Minimum Message Length (MML) principle. Based on this analysis, we present two revised versions of MML: a pointwise estimator which gives the MML-optimal single parameter model, and a volumewise estimator which gives the MML-optimal region in the parameter space. Our empirical results suggest that with small data sets, the MDL approach yields more accurate predictions than the MML estimators. The empirical results also demonstrate that the revised MML estimators introduced here perform better than the original MML estimator suggested by Wallace and Freeman.

Given a set of possible models (e.g., Bayesian network structures) and a data sample, in the unsupervised model selection problem the task is to choose the most accurate model with respect to the domain joint probability distribution. In contrast to this, in supervised model selection it is a priori known that the chosen model will be used in the future for prediction tasks involving more ``focused' predictive distributions. Although focused predictive distributions can be produced from the joint probability distribution by marginalization, in practice the best model in the unsupervised sense does not necessarily perform well in supervised domains. In particular, the standard marginal likelihood score is a criterion for the unsupervised task, and, although frequently used for supervised model selection also, does not perform well in such tasks. In this paper we study the performance of the marginal likelihood score empirically in supervised Bayesian network selection tasks by using a large number of publicly available classification data sets, and compare the results to those obtained by alternative model selection criteria, including empirical crossvalidation methods, an approximation of a supervised marginal likelihood measure, and a supervised version of Dawids prequential(predictive sequential) principle.The results demonstrate that the marginal likelihood score does NOT perform well FOR supervised model selection, WHILE the best results are obtained BY using Dawids prequential r napproach.