arXiv subjects

Alejandro Ribeiro

Publications and source records attributed to Alejandro Ribeiro.

At least 145 records · Page 8Linked to original sources

arXiv2022

Graph Neural Networks for Decentralized Multi-Robot Submodular Action Selection

The problem of decentralized multi-robot target tracking asks for jointly selecting actions, e.g., motion primitives, for the robots to maximize target tracking performance with local communications. One major challenge for practical implementations is to make target tracking approaches scalable for large-scale problem instances. In this work, we propose a general-purpose learning architecture toward collaborative target tracking at scale, with decentralized communications. Particularly, our learning architecture leverages a graph neural network (GNN) to capture local interactions of the robots and learns decentralized decision-making for the robots. We train the learning model by imitating an expert solution and implement the resulting model for decentralized action selection involving local observations and communications only. We demonstrate the performance of our GNN-based learning approach in a scenario of active target tracking with large networks of robots. The simulation results show our approach nearly matches the tracking performance of the expert algorithm, and yet runs several orders faster with up to 100 robots. Moreover, it slightly outperforms a decentralized greedy algorithm but runs faster (especially with more than 20 robots). The results also exhibit our approach's generalization capability in previously unseen scenarios, e.g., larger environments and larger networks of robots.

cs.RO↗

arXiv2022

Navigation of a Quadratic Potential with Ellipsoidal Obstacles

Given a convex quadratic potential of which its minimum is the agent's goal and a Euclidean space populated with ellipsoidal obstacles, one can construct a Rimon-Koditschek (RK) artificial potential to navigate. Its negative gradient attracts the agent toward the goal and repels the agent away from the boundary of the obstacles. This is a popular approach to navigation problems since it can be implemented with local spatial information that is acquired during operation time. However, navigation is only successful in situations where the obstacles are not too eccentric (flat). This paper proposes a modification to gradient dynamics that allows successful navigation of an environment with a quadratic cost and ellipsoidal obstacles regardless of their eccentricity. This is accomplished by altering gradient dynamics with a Hessian correction that is intended to imitate worlds with spherical obstacles in which RK potentials are known to work. The resulting dynamics simplify by the quadratic form of the obstacles. Convergence to the goal and obstacle avoidance is established from almost every initial position (up to a set of measure one) in the free space, with mild conditions on the location of the target. Results are corroborated empirically with numerical simulations.

math.OC↗

arXiv2022

Learning Connectivity-Maximizing Network Configurations

In this letter we propose a data-driven approach to optimizing the algebraic connectivity of a team of robots. While a considerable amount of research has been devoted to this problem, we lack a method that scales in a manner suitable for online applications for more than a handful of agents. To that end, we propose a supervised learning approach with a convolutional neural network (CNN) that learns to place communication agents from an expert that uses an optimization-based strategy. We demonstrate the performance of our CNN on canonical line and ring topologies, 105k randomly generated test cases, and larger teams not seen during training. We also show how our system can be applied to dynamic robot teams through a Unity-based simulation. After training, our system produces connected configurations over an order of magnitude faster than the optimization-based scheme for teams of 10-20 agents.

cs.RO↗

arXiv2022

Learning by Transference: Training Graph Neural Networks on Growing Graphs

Graph neural networks (GNNs) use graph convolutions to exploit network invariances and learn meaningful feature representations from network data. However, on large-scale graphs convolutions incur in high computational cost, leading to scalability limitations. Leveraging the graphon -- the limit object of a graph -- in this paper we consider the problem of learning a graphon neural network (WNN) -- the limit object of a GNN -- by training GNNs on graphs sampled from the graphon. Under smoothness conditions, we show that: (i) the expected distance between the learning steps on the GNN and on the WNN decreases asymptotically with the size of the graph, and (ii) when training on a sequence of growing graphs, gradient descent follows the learning direction of the WNN. Inspired by these results, we propose a novel algorithm to learn GNNs on large-scale graphs that, starting from a moderate number of nodes, successively increases the size of the graph during training. This algorithm is further benchmarked on a decentralized control problem, where it retains comparable performance to its large-scale counterpart at a reduced computational cost.

cs.LG↗

arXiv2022

Self-Consistency of the Fokker-Planck Equation

The Fokker-Planck equation (FPE) is the partial differential equation that governs the density evolution of the Itô process and is of great importance to the literature of statistical physics and machine learning. The FPE can be regarded as a continuity equation where the change of the density is completely determined by a time varying velocity field. Importantly, this velocity field also depends on the current density function. As a result, the ground-truth velocity field can be shown to be the solution of a fixed-point equation, a property that we call self-consistency. In this paper, we exploit this concept to design a potential function of the hypothesis velocity fields, and prove that, if such a function diminishes to zero during the training procedure, the trajectory of the densities generated by the hypothesis velocity fields converges to the solution of the FPE in the Wasserstein-2 sense. The proposed potential function is amenable to neural-network based parameterization as the stochastic gradient with respect to the parameter can be efficiently computed. Once a parameterized model, such as Neural Ordinary Differential Equation is trained, we can generate the entire trajectory to the FPE.

cs.LG↗

arXiv2022

Learning Graph Structure from Convolutional Mixtures

Machine learning frameworks such as graph neural networks typically rely on a given, fixed graph to exploit relational inductive biases and thus effectively learn from network data. However, when said graphs are (partially) unobserved, noisy, or dynamic, the problem of inferring graph structure from data becomes relevant. In this paper, we postulate a graph convolutional relationship between the observed and latent graphs, and formulate the graph learning task as a network inverse (deconvolution) problem. In lieu of eigendecomposition-based spectral methods or iterative optimization solutions, we unroll and truncate proximal gradient iterations to arrive at a parameterized neural network architecture that we call a Graph Deconvolution Network (GDN). GDNs can learn a distribution of graphs in a supervised fashion, perform link prediction or edge-weight regression tasks by adapting the loss function, and they are inherently inductive. We corroborate GDN's superior graph recovery performance and its generalization to larger graphs using synthetic data in supervised settings. Furthermore, we demonstrate the robustness and representation power of GDNs on real world neuroimaging and social network datasets.

cs.LG↗

arXiv2022

Large-Scale Graph Reinforcement Learning in Wireless Control Systems

Modern control systems routinely employ wireless networks to exchange information between spatially distributed plants, actuators and sensors. With wireless networks defined by random, rapidly changing transmission conditions that challenge assumptions commonly held in the design of control systems, proper allocation of communication resources is essential to achieve reliable operation. Designing resource allocation policies, however, is challenging, motivating recent works to successfully exploit deep learning and deep reinforcement learning techniques to design resource allocation and scheduling policies for wireless control systems (WCSs). As the number of learnable parameters in a neural network grows with the size of the input signal, deep reinforcement learning may fail to scale, limiting the immediate generalization of such scheduling and resource allocation policies to large-scale systems. The interference and fading patterns among plants and controllers in the network, however, induce a time-varying graph that can be used to construct policy representations based on graph neural networks (GNNs), with the number of learnable parameters now independent of the number of plants in the network. We further establish in the context of WCSs that, due to inherent invariance to graph permutations, the GNN is able to model scalable and transferable resource allocation policies, which are subsequently trained with primal-dual reinforcement learning. Numerical experiments show that the proposed graph reinforcement learning approach yields policies that not only outperform baseline solutions and deep reinforcement learning based policies in large-scale systems, but that can also be transferred across networks of varying size.

eess.SP↗

arXiv2022

Model-Free Design of Control Systems over Wireless Fading Channels

Wireless control systems replace traditional wired communication with wireless networks to exchange information between actuators, plants and sensors in a control system. The noise in wireless channels renders ideal control policies suboptimal, and their performance is moreover directly dependent on the way in which wireless resources are allocated between control loops. Proper design of the control policy and the resource allocation policy based on both plant states and wireless fading states is then critical to achieve good performance. The resulting problem of co-designing control-aware resource allocation policies and communication-aware controllers, however, is challenging due to its infinite dimensionality, existence of system constraints and need for explicit knowledge of the plants and wireless network models. To overcome those challenges, we rely on constrained reinforcement learning algorithms to propose a model-free approach to the design of wireless control systems. We demonstrate the near optimality of control system performance and stability using near-universal policy parametrizations and present a practical model-free algorithm to learn the co-design policy. Numerical experiments show the strong performance of learned policies over baseline solutions.

eess.SP↗

arXiv2022

Learning Decentralized Wireless Resource Allocations with Graph Neural Networks

We consider the broad class of decentralized optimal resource allocation problems in wireless networks, which can be formulated as a constrained statistical learning problems with a localized information structure. We develop the use of Aggregation Graph Neural Networks (Agg-GNNs), which process a sequence of delayed and potentially asynchronous graph aggregated state information obtained locally at each transmitter from multi-hop neighbors. We further utilize model-free primal-dual learning methods to optimize performance subject to constraints in the presence of delay and asynchrony inherent to decentralized networks. We demonstrate a permutation equivariance property of the resulting resource allocation policy that can be shown to facilitate transference to dynamic network configurations. The proposed framework is validated with numerical simulations that exhibit superior performance to baseline strategies.

eess.SP↗

arXiv2022

Synthesizing Decentralized Controllers with Graph Neural Networks and Imitation Learning

Dynamical systems consisting of a set of autonomous agents face the challenge of having to accomplish a global task, relying only on local information. While centralized controllers are readily available, they face limitations in terms of scalability and implementation, as they do not respect the distributed information structure imposed by the network system of agents. Given the difficulties in finding optimal decentralized controllers, we propose a novel framework using graph neural networks (GNNs) to \emph{learn} these controllers. GNNs are well-suited for the task since they are naturally distributed architectures and exhibit good scalability and transferability properties. We show that GNNs learn appropriate decentralized controllers by means of imitation learning, leverage their permutation invariance properties to successfully scale to larger teams and transfer to unseen scenarios at deployment time. The problems of flocking and multi-agent path planning are explored to illustrate the potential of GNNs in learning decentralized controllers.

cs.LG↗

arXiv2022

Wide and Deep Graph Neural Network with Distributed Online Learning

Graph neural networks (GNNs) are naturally distributed architectures for learning representations from network data. This renders them suitable candidates for decentralized tasks. In these scenarios, the underlying graph often changes with time due to link failures or topology variations, creating a mismatch between the graphs on which GNNs were trained and the ones on which they are tested. Online learning can be leveraged to retrain GNNs at testing time to overcome this issue. However, most online algorithms are centralized and usually offer guarantees only on convex problems, which GNNs rarely lead to. This paper develops the Wide and Deep GNN (WD-GNN), a novel architecture that can be updated with distributed online learning mechanisms. The WD-GNN consists of two components: the wide part is a linear graph filter and the deep part is a nonlinear GNN. At training time, the joint wide and deep architecture learns nonlinear representations from data. At testing time, the wide, linear part is retrained, while the deep, nonlinear one remains fixed. This often leads to a convex formulation. We further propose a distributed online learning algorithm that can be implemented in a decentralized setting. We also show the stability of the WD-GNN to changes of the underlying graph and analyze the convergence of the proposed online learning procedure. Experiments on movie recommendation, source localization and robot swarm control corroborate theoretical findings and show the potential of the WD-GNN for distributed online learning.

cs.LG↗

arXiv2022

Training Stable Graph Neural Networks Through Constrained Learning

Graph Neural Networks (GNN) rely on graph convolutions to learn features from network data. GNNs are stable to different types of perturbations of the underlying graph, a property that they inherit from graph filters. In this paper we leverage the stability property of GNNs as a typing point in order to seek for representations that are stable within a distribution. We propose a novel constrained learning approach by imposing a constraint on the stability condition of the GNN within a perturbation of choice. We showcase our framework in real world data, corroborating that we are able to obtain more stable representations while not compromising the overall accuracy of the predictor.

cs.LG↗

arXiv2022

Learning Optimal Resource Allocations in Wireless Systems

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.

cs.LG↗

arXiv2022

Space-Time Graph Neural Networks

We introduce space-time graph neural network (ST-GNN), a novel GNN architecture, tailored to jointly process the underlying space-time topology of time-varying network data. The cornerstone of our proposed architecture is the composition of time and graph convolutional filters followed by pointwise nonlinear activation functions. We introduce a generic definition of convolution operators that mimic the diffusion process of signals over its underlying support. On top of this definition, we propose space-time graph convolutions that are built upon a composition of time and graph shift operators. We prove that ST-GNNs with multivariate integral Lipschitz filters are stable to small perturbations in the underlying graphs as well as small perturbations in the time domain caused by time warping. Our analysis shows that small variations in the network topology and time evolution of a system does not significantly affect the performance of ST-GNNs. Numerical experiments with decentralized control systems showcase the effectiveness and stability of the proposed ST-GNNs.

cs.LG↗

arXiv2022

Safe Policies for Reinforcement Learning via Primal-Dual Methods

In this paper, we study the learning of safe policies in the setting of reinforcement learning problems. This is, we aim to control a Markov Decision Process (MDP) of which we do not know the transition probabilities, but we have access to sample trajectories through experience. We define safety as the agent remaining in a desired safe set with high probability during the operation time. We therefore consider a constrained MDP where the constraints are probabilistic. Since there is no straightforward way to optimize the policy with respect to the probabilistic constraint in a reinforcement learning framework, we propose an ergodic relaxation of the problem. The advantages of the proposed relaxation are threefold. (i) The safety guarantees are maintained in the case of episodic tasks and they are kept up to a given time horizon for continuing tasks. (ii) The constrained optimization problem despite its non-convexity has arbitrarily small duality gap if the parametrization of the policy is rich enough. (iii) The gradients of the Lagrangian associated with the safe-learning problem can be easily computed using standard policy gradient results and stochastic approximation tools. Leveraging these advantages, we establish that primal-dual algorithms are able to find policies that are safe and optimal. We test the proposed approach in a navigation task in a continuous domain. The numerical results show that our algorithm is capable of dynamically adapting the policy to the environment and the required safety levels.

eess.SY↗

arXiv2021

Linear Quadratic Control with Risk Constraints

We propose a new risk-constrained formulation of the classical Linear Quadratic (LQ) stochastic control problem for general partially-observed systems. Our framework is motivated by the fact that the risk-neutral LQ controllers, although optimal in expectation, might be ineffective under relatively infrequent, yet statistically significant extreme events. To effectively trade between average and extreme event performance, we introduce a new risk constraint, which explicitly restricts the total expected predictive variance of the state penalty by a user-prescribed level. We show that, under certain conditions on the process noise, the optimal risk-aware controller can be evaluated explicitly and in closed form. In fact, it is affine relative to the minimum mean square error (mmse) state estimate. The affine term pushes the state away from directions where the noise exhibits heavy tails, by exploiting the third-order moment~(skewness) of the noise. The linear term regulates the state more strictly in riskier directions, where both the prediction error (conditional) covariance and the state penalty are simultaneously large; this is achieved by inflating the state penalty within a new filtered Riccati difference equation. We also prove that the new risk-aware controller is internally stable, regardless of parameter tuning, in the special cases of i) fully-observed systems, and ii) partially-observed systems with Gaussian noise. The properties of the proposed risk-aware LQ framework are lastly illustrated via indicative numerical examples.

math.OC↗

arXiv2021

Scalable Perception-Action-Communication Loops with Convolutional and Graph Neural Networks

In this paper, we present a perception-action-communication loop design using Vision-based Graph Aggregation and Inference (VGAI). This multi-agent decentralized learning-to-control framework maps raw visual observations to agent actions, aided by local communication among neighboring agents. Our framework is implemented by a cascade of a convolutional and a graph neural network (CNN / GNN), addressing agent-level visual perception and feature learning, as well as swarm-level communication, local information aggregation and agent action inference, respectively. By jointly training the CNN and GNN, image features and communication messages are learned in conjunction to better address the specific task. We use imitation learning to train the VGAI controller in an offline phase, relying on a centralized expert controller. This results in a learned VGAI controller that can be deployed in a distributed manner for online execution. Additionally, the controller exhibits good scaling properties, with training in smaller teams and application in larger teams. Through a multi-agent flocking application, we demonstrate that VGAI yields performance comparable to or better than other decentralized controllers, using only the visual input modality and without accessing precise location or motion state information.

cs.RO↗

arXiv2021

Adversarial Robustness with Semi-Infinite Constrained Learning

Despite strong performance in numerous applications, the fragility of deep learning to input perturbations has raised serious questions about its use in safety-critical domains. While adversarial training can mitigate this issue in practice, state-of-the-art methods are increasingly application-dependent, heuristic in nature, and suffer from fundamental trade-offs between nominal performance and robustness. Moreover, the problem of finding worst-case perturbations is non-convex and underparameterized, both of which engender a non-favorable optimization landscape. Thus, there is a gap between the theory and practice of adversarial training, particularly with respect to when and why adversarial training works. In this paper, we take a constrained learning approach to address these questions and to provide a theoretical foundation for robust learning. In particular, we leverage semi-infinite optimization and non-convex duality theory to show that adversarial training is equivalent to a statistical problem over perturbation distributions, which we characterize completely. Notably, we show that a myriad of previous robust training techniques can be recovered for particular, sub-optimal choices of these distributions. Using these insights, we then propose a hybrid Langevin Monte Carlo approach of which several common algorithms (e.g., PGD) are special cases. Finally, we show that our approach can mitigate the trade-off between nominal and robust performance, yielding state-of-the-art results on MNIST and CIFAR-10. Our code is available at: https://github.com/arobey1/advbench.

stat.ML↗