Navigation in dynamic environments requires autonomous systems to reason about uncertainties in the behavior of other agents. In this paper, we introduce a unified framework that combines trajectory planning with multimodal predictions and active probing to enhance decision-making under uncertainty. We develop a novel risk metric that seamlessly integrates multimodal prediction uncertainties through mixture models. When these uncertainties follow a Gaussian mixture distribution, we prove that our risk metric admits a closed-form solution, and is always finite, thus ensuring analytical tractability. To reduce prediction ambiguity, we incorporate an active probing mechanism that strategically selects actions to improve its estimates of behavioral parameters of other agents, while simultaneously handling multimodal uncertainties. We extensively evaluate our framework in autonomous navigation scenarios using the MetaDrive simulation environment. Results demonstrate that our active probing approach successfully navigates complex traffic scenarios with uncertain predictions. Additionally, our framework shows robust performance across diverse traffic agent behavior models, indicating its broad applicability to real-world autonomous navigation challenges.

Score matching based diffusion has shown to achieve the state of art results in generation modeling. In the original score matching based diffusion algorithm, the forward equation is a differential equation for which the probability density equation evolves according to a linear partial differential equation, the Fokker-Planck equation. A drawback of this approach is that one needs the data distribution to have a Lipschitz logarithmic gradient. This excludes a large class of data distributions that have a compact support. We present a deterministic diffusion process for which the vector fields are always Lipschitz and hence the score does not explode for probability measures with compact support. This deterministic diffusion process can be seen as a regularization of the porous media equation equation, which enables one to guarantee long term convergence of the forward process to the noise distribution. Though the porous media equation is itself not always guaranteed to have a Lipschitz vector field, it can be used to understand the closeness of the output of the algorithm to the data distribution as a function of the the time horizon and score matching error. This analysis enables us to show that the algorithm has better dependence on the score matching error than approaches based on stochastic diffusions. Using numerical experiments we verify our theoretical results on example one and two dimensional data distributions which are compactly supported. Additionally, we validate the approach on a modified MNIST data set for which the distribution is concentrated on a compact set. In each of the experiments, the approach using deterministic diffusion performs better that the diffusion algorithm with stochastic forward process, when considering the FID scores of the generated samples.

Astrocytes are a ubiquitous and enigmatic type of non-neuronal cell and are found in the brain of all vertebrates. While traditionally viewed as being supportive of neurons, it is increasingly recognized that astrocytes play a more direct and active role in brain function and neural computation. On account of their sensitivity to a host of physiological covariates and ability to modulate neuronal activity and connectivity on slower time scales, astrocytes may be particularly well poised to modulate the dynamics of neural circuits in functionally salient ways. In the current paper, we seek to capture these features via actionable abstractions within computational models of neuron-astrocyte interaction. Specifically, we engage how nested feedback loops of neuron-astrocyte interaction, acting over separated time-scales, may endow astrocytes with the capability to enable learning in context-dependent settings, where fluctuations in task parameters may occur much more slowly than within-task requirements. We pose a general model of neuron-synapse-astrocyte interaction and use formal analysis to characterize how astrocytic modulation may constitute a form of meta-plasticity, altering the ways in which synapses and neurons adapt as a function of time. We then embed this model in a bandit-based reinforcement learning task environment, and show how the presence of time-scale separated astrocytic modulation enables learning over multiple fluctuating contexts. Indeed, these networks learn far more reliably compared to dynamically homogeneous networks and conventional non-network-based bandit algorithms. Our results fuel the notion that neuron-astrocyte interactions in the brain benefit learning over different time-scales and the conveyance of task-relevant contextual information onto circuit dynamics.

The growing interest in complex decision-making and language modeling problems highlights the importance of sample-efficient learning over very long horizons. This work takes a step in this direction by investigating contextual linear bandits where the current reward depends on at most s prior actions and contexts (not necessarily consecutive), up to a time horizon of h. In order to avoid polynomial dependence on h, we propose new algorithms that leverage sparsity to discover the dependence pattern and arm parameters jointly. We consider both the data-poor (T= h) regimes and derive respective regret upper bounds O(d square-root(sT) +min(q, T) and O( square-root(sdT) ), with sparsity s, feature dimension d, total time horizon T, and q that is adaptive to the reward dependence pattern. Complementing upper bounds, we also show that learning over a single trajectory brings inherent challenges: While the dependence pattern and arm parameters form a rank-1 matrix, circulant matrices are not isometric over rank-1 manifolds and sample complexity indeed benefits from the sparse reward dependence structure. Our results necessitate a new analysis to address long-range temporal dependencies across data and avoid polynomial dependence on the reward horizon h. Specifically, we utilize connections to the restricted isometry property of circulant matrices formed by dependent sub-Gaussian vectors and establish new guarantees that are also of independent interest.

In this work we propose a graph-based learning framework to train models with provable robustness to adversarial perturbations. In contrast to regularization-based approaches, we formulate the adversarially robust learning problem as one of loss minimization with a Lipschitz constraint, and show that the saddle point of the associated Lagrangian is characterized by a Poisson equation with weighted Laplace operator. Further, the weighting for the Laplace operator is given by the Lagrange multiplier for the Lipschitz constraint, which modulates the sensitivity of the minimizer to perturbations. We then design a provably robust training scheme using graph-based discretization of the input space and a primal-dual algorithm to converge to the Lagrangian's saddle point. Our analysis establishes a novel connection between elliptic operators with constraint-enforced weighting and adversarial learning. We also study the complementary problem of improving the robustness of minimizers with a margin on their loss, formulated as a loss-constrained minimization problem of the Lipschitz constant. We propose a technique to obtain robustified minimizers, and evaluate fundamental Lipschitz lower bounds by approaching Lipschitz constant minimization via a sequence of gradient $p$-norm minimization problems. Ultimately, our results show that, for a desired nominal performance, there exists a fundamental lower bound on the sensitivity to adversarial perturbations that depends only on the loss function and the data distribution, and that improvements in robustness beyond this bound can only be made at the expense of nominal performance. Our training schemes provably achieve these bounds both under constraints on performance and~robustness.

This paper proposes a simplified version of classical models for urban traffic networks and studies the problem of optimizing the network overall efficiency by controlling the signalized intersections. Differently from traditional approaches to control traffic signaling, the tractability of our framework allows us to effectively model large-scale interconnections and enables the design of critical parameters while considering network-wide measures of efficiency. Motivated by the increasing availability of real-time high-resolution traffic data, we cast an optimization problem that formalizes the goal of optimizing vehicle evacuation by controlling the durations of green lights at the intersections under the current congestion conditions. Our framework allows us to relate efficiency objectives with the optimization of a metric of controllability of the associated dynamical network. We then provide a technique to efficiently solve the optimization by parallelizing the computation among a group of distributed agents. Last, we assess the benefits of the proposed modeling and optimization framework through macroscopic and microscopic simulations on daily commute scenarios for the urban interconnection of Manhattan, NY, USA.

The ability to modulate brain states using targeted stimulation is increasingly being employed to treat neurological disorders and to enhance human performance. Despite the growing interest in brain stimulation as a form of neuromodulation, much remains unknown about the network-level impact of these focal perturbations. To study the system wide impact of regional stimulation, we employ a data-driven computational model of nonlinear brain dynamics to systematically explore the effects of targeted stimulation. Validating predictions from network control theory, we uncover the relationship between regional controllability and the focal versus global impact of stimulation, and we relate these findings to differences in the underlying network architecture. Finally, by mapping brain regions to cognitive systems, we observe that the default mode system imparts large global change despite being highly constrained by structural connectivity. This work forms an important step towards the development of personalized stimulation protocols for medical treatment or performance enhancement.

Security attacks may have disruptive consequences on cyber-physical systems, and lead to significant social and economic losses. Building secure cyber-physical systems is particularly challenging due to the variety of attack surfaces from the cyber and physical components, and often to limited computation and communication resources. In this paper, we propose a cross-layer design framework for resource-constrained cyber-physical systems. The framework combines control-theoretic methods at the functional layer and cybersecurity techniques at the embedded platform layer, and addresses security together with other design metrics such as control performance under resource and real-time constraints. We use the concept of interface variables to capture the interactions between control and platform layers, and quantitatively model the relation among system security, performance, and schedulability via interface variables. The general codesign framework is customized and refined to the automotive domain, and its effectiveness is demonstrated through an industrial case study and a set of synthetic examples.

This paper focuses on the problem of patrolling an environment with a team of autonomous agents. Given a set of strategically important locations (viewpoints) with different priorities, our patrolling strategy consists of 1) constructing a tour through the viewpoints, and 2) driving the robots along the tour in a coordinated way. As performance criteria, we consider the weighted refresh time, i.e., the longest time interval between any two visits of a viewpoint, weighted by the viewpoint's priority. We consider the design of both optimal trajectories and distributed control laws for the robots to converge to optimal trajectories. First, we propose a patrolling strategy and we characterize its performance as a function of the environment and the viewpoints priorities. Second, we restrict our attention to the problem of patrolling a nonintersecting tour, and we describe a team trajectory with minimum weighted refresh time. Third, for the tour patrolling problem and for two distinct communication scenarios, namely the Passing and the Neighbor-Broadcast communication models, we develop distributed algorithms to steer the robots toward a minimum weighted refresh time team trajectory. Finally, we show the effectiveness and robustness of our control algorithms via simulations and experiments.

The subject of this paper is the patrolling of an environment with the aid of a team of autonomous agents. We consider both the design of open-loop trajectories with optimal properties and of distributed control laws converging to optimal trajectories. As performance criteria, the refresh time and the latency are considered, i.e., respectively, time gap between any two visits of the same region and the time necessary to inform every agent about an event occurred in the environment. We associate a graph with the environment, and we study separately the case of a chain, tree, and cyclic graph. For the case of chain graph, we first describe a minimum refresh time and latency team trajectory and propose a polynomial time algorithm for its computation. Then, we describe a distributed procedure that steers the robots toward an optimal trajectory. For the case of tree graph, a polynomial time algorithm is developed for the minimum refresh time problem, under the technical assumption of a constant number of robots involved in the patrolling task. Finally, we show that the design of a minimum refresh time trajectory for a cyclic graph is NP-hard, and we develop a constant factor approximation algorithm.