Randomized Exploration in Cooperative Multi-Agent Reinforcement Learning

We present the first study on provably efficient randomized exploration in cooperative multi-agent reinforcement learning (MARL). We propose a unified algorithm framework for randomized exploration in parallel Markov Decision Processes (MDPs), and two Thompson Sampling (TS)-type algorithms, CoopTS-PHE and CoopTS-LMC, incorporating the perturbed-history exploration (PHE) strategy and the Langevin Monte Carlo exploration (LMC) strategy respectively, which are flexible in design and easy to implement in practice. For a special class of parallel MDPs where the transition is (approximately) linear, we theoretically prove that both CoopTS-PHE and CoopTS-LMC achieve a $\widetilde{\mathcal{O}}(d^{3/2}H^2\sqrt{MK})$ regret bound with communication complexity $\widetilde{\mathcal{O}}(dHM^2)$, where $d$ is the feature dimension, $H$ is the horizon length, $M$ is the number of agents, and $K$ is the number of episodes. This is the first theoretical result for randomized exploration in cooperative MARL. We evaluate our proposed method on multiple parallel RL environments, including a deep exploration problem (\textit{i.e.,} $N$-chain), a video game, and a real-world problem in energy systems. Our experimental results support that our framework can achieve better performance, even under conditions of misspecified transition models. Additionally, we establish a connection between our unified framework and the practical application of federated learning.

On the Uniqueness of Solution for the Bellman Equation of LTL Objectives

Surrogate rewards for linear temporal logic (LTL) objectives are commonly utilized in planning problems for LTL objectives. In a widely-adopted surrogate reward approach, two discount factors are used to ensure that the expected return approximates the satisfaction probability of the LTL objective. The expected return then can be estimated by methods using the Bellman updates such as reinforcement learning. However, the uniqueness of the solution to the Bellman equation with two discount factors has not been explicitly discussed. We demonstrate with an example that when one of the discount factors is set to one, as allowed in many previous works, the Bellman equation may have multiple solutions, leading to inaccurate evaluation of the expected return. We then propose a condition for the Bellman equation to have the expected return as the unique solution, requiring the solutions for states inside a rejecting bottom strongly connected component (BSCC) to be 0. We prove this condition is sufficient by showing that the solutions for the states with discounting can be separated from those for the states without discounting under this condition

Bayesian Methods for Trust in Collaborative Multi-Agent Autonomy

Multi-agent, collaborative sensor fusion is a vital component of a multi-national intelligence toolkit. In safety-critical and/or contested environments, adversaries may infiltrate and compromise a number of agents. We analyze state of the art multi-target tracking algorithms under this compromised agent threat model. We prove that the track existence probability test ("track score") is significantly vulnerable to even small numbers of adversaries. To add security awareness, we design a trust estimation framework using hierarchical Bayesian updating. Our framework builds beliefs of trust on tracks and agents by mapping sensor measurements to trust pseudomeasurements (PSMs) and incorporating prior trust beliefs in a Bayesian context. In case studies, our trust estimation algorithm accurately estimates the trustworthiness of tracks/agents, subject to observability limitations.

ε-Neural Thompson Sampling of Deep Brain Stimulation for Parkinson Disease Treatment

Deep Brain Stimulation (DBS) stands as an effective intervention for alleviating the motor symptoms of Parkinson's disease (PD). Traditional commercial DBS devices are only able to deliver fixed-frequency periodic pulses to the basal ganglia (BG) regions of the brain, i.e., continuous DBS (cDBS). However, they in general suffer from energy inefficiency and side effects, such as speech impairment. Recent research has focused on adaptive DBS (aDBS) to resolve the limitations of cDBS. Specifically, reinforcement learning (RL) based approaches have been developed to adapt the frequencies of the stimuli in order to achieve both energy efficiency and treatment efficacy. However, RL approaches in general require significant amount of training data and computational resources, making it intractable to integrate RL policies into real-time embedded systems as needed in aDBS. In contrast, contextual multi-armed bandits (CMAB) in general lead to better sample efficiency compared to RL. In this study, we propose a CMAB solution for aDBS. Specifically, we define the context as the signals capturing irregular neuronal firing activities in the BG regions (i.e., beta-band power spectral density), while each arm signifies the (discretized) pulse frequency of the stimulation. Moreover, an {\epsilon}-exploring strategy is introduced on top of the classic Thompson sampling method, leading to an algorithm called {\epsilon}-Neural Thompson sampling ({\epsilon}-NeuralTS), such that the learned CMAB policy can better balance exploration and exploitation of the BG environment. The {\epsilon}-NeuralTS algorithm is evaluated using a computation BG model that captures the neuronal activities in PD patients' brains. The results show that our method outperforms both existing cDBS methods and CMAB baselines.

RadCloud: Real-Time High-Resolution Point Cloud Generation Using Low-Cost Radars for Aerial and Ground Vehicles

In this work, we present RadCloud, a novel real time framework for directly obtaining higher-resolution lidar-like 2D point clouds from low-resolution radar frames on resource-constrained platforms commonly used in unmanned aerial and ground vehicles (UAVs and UGVs, respectively); such point clouds can then be used for accurate environmental mapping, navigating unknown environments, and other robotics tasks. While high-resolution sensing using radar data has been previously reported, existing methods cannot be used on most UAVs, which have limited computational power and energy; thus, existing demonstrations focus on offline radar processing. RadCloud overcomes these challenges by using a radar configuration with 1/4th of the range resolution and employing a deep learning model with 2.25x fewer parameters. Additionally, RadCloud utilizes a novel chirp-based approach that makes obtained point clouds resilient to rapid movements (e.g., aggressive turns or spins), which commonly occur during UAV flights. In real-world experiments, we demonstrate the accuracy and applicability of RadCloud on commercially available UAVs and UGVs, with off-the-shelf radar platforms on-board.

A Multi-Agent Security Testbed for the Analysis of Attacks and Defenses in Collaborative Sensor Fusion

The performance and safety of autonomous vehicles (AVs) deteriorates under adverse environments and adversarial actors. The investment in multi-sensor, multi-agent (MSMA) AVs is meant to promote improved efficiency of travel and mitigate safety risks. Unfortunately, minimal investment has been made to develop security-aware MSMA sensor fusion pipelines leaving them vulnerable to adversaries. To advance security analysis of AVs, we develop the Multi-Agent Security Testbed, MAST, in the Robot Operating System (ROS2). Our framework is scalable for general AV scenarios and is integrated with recent multi-agent datasets. We construct the first bridge between AVstack and ROS and develop automated AV pipeline builds to enable rapid AV prototyping. We tackle the challenge of deploying variable numbers of agent/adversary nodes at launch-time with dynamic topic remapping. Using this testbed, we motivate the need for security-aware AV architectures by exposing the vulnerability of centralized multi-agent fusion pipelines to (un)coordinated adversary models in case studies and Monte Carlo analysis.

Spectral Statistics of the Sample Covariance Matrix for High Dimensional Linear Gaussians

Performance of ordinary least squares(OLS) method for the \emph{estimation of high dimensional stable state transition matrix} $A$(i.e., spectral radius $\rho(A)<1$) from a single noisy observed trajectory of the linear time invariant(LTI)\footnote{Linear Gaussian (LG) in Markov chain literature} system $X_{-}:(x_0,x_1, \ldots,x_{N-1})$ satisfying \begin{equation} x_{t+1}=Ax_{t}+w_{t}, \hspace{10pt} \text{ where } w_{t} \thicksim N(0,I_{n}), \end{equation} heavily rely on negative moments of the sample covariance matrix: $(X_{-}X_{-}^{*})=\sum_{i=0}^{N-1}x_{i}x_{i}^{*}$ and singular values of $EX_{-}^{*}$, where $E$ is a rectangular Gaussian ensemble $E=[w_0, \ldots, w_{N-1}]$. Negative moments requires sharp estimates on all the eigenvalues $\lambda_{1}\big(X_{-}X_{-}^{*}\big) \geq \ldots \geq \lambda_{n}\big(X_{-}X_{-}^{*}\big) \geq 0$. Leveraging upon recent results on spectral theorem for non-Hermitian operators in \cite{naeem2023spectral}, along with concentration of measure phenomenon and perturbation theory(Gershgorins' and Cauchys' interlacing theorem) we show that only when $A=A^{*}$, typical order of $\lambda_{j}\big(X_{-}X_{-}^{*}\big) \in \big[N-n\sqrt{N}, N+n\sqrt{N}\big]$ for all $j \in [n]$. However, in \emph{high dimensions} when $A$ has only one distinct eigenvalue $\lambda$ with geometric multiplicity of one, then as soon as eigenvalue leaves \emph{complex half unit disc}, largest eigenvalue suffers from curse of dimensionality: $\lambda_{1}\big(X_{-}X_{-}^{*}\big)=\Omega\big( \lfloor\frac{N}{n}\rfloor e^{\alpha_{\lambda}n} \big)$, while smallest eigenvalue $\lambda_{n}\big(X_{-}X_{-}^{*}\big) \in (0, N+\sqrt{N}]$. Consequently, OLS estimator incurs a \emph{phase transition} and becomes \emph{transient: increasing iteration only worsens estimation error}, all of this happening when the dynamics are generated from stable systems.

Datasets, Models, and Algorithms for Multi-Sensor, Multi-agent Autonomy Using AVstack

Recent advancements in assured autonomy have brought autonomous vehicles (AVs) closer to fruition. Despite strong evidence that multi-sensor, multi-agent (MSMA) systems can yield substantial improvements in the safety and security of AVs, there exists no unified framework for developing and testing representative MSMA configurations. Using the recently-released autonomy platform, AVstack, this work proposes a new framework for datasets, models, and algorithms in MSMA autonomy. Instead of releasing a single dataset, we deploy a dataset generation pipeline capable of generating unlimited volumes of ground-truth-labeled MSMA perception data. The data derive from cameras (semantic segmentation, RGB, depth), LiDAR, and radar, and are sourced from ground-vehicles and, for the first time, infrastructure platforms. Pipelining generating labeled MSMA data along with AVstack's third-party integrations defines a model training framework that allows training multi-sensor perception for vehicle and infrastructure applications. We provide the framework and pretrained models open-source. Finally, the dataset and model training pipelines culminate in insightful multi-agent case studies. While previous works used specific ego-centric multi-agent designs, our framework considers the collaborative autonomy space as a network of noisy, time-correlated sensors. Within this environment, we quantify the impact of the network topology and data fusion pipeline on an agent's situational awareness.

MadRadar: A Black-Box Physical Layer Attack Framework on mmWave Automotive FMCW Radars

Frequency modulated continuous wave (FMCW) millimeter-wave (mmWave) radars play a critical role in many of the advanced driver assistance systems (ADAS) featured on today's vehicles. While previous works have demonstrated (only) successful false-positive spoofing attacks against these sensors, all but one assumed that an attacker had the runtime knowledge of the victim radar's configuration. In this work, we introduce MadRadar, a general black-box radar attack framework for automotive mmWave FMCW radars capable of estimating the victim radar's configuration in real-time, and then executing an attack based on the estimates. We evaluate the impact of such attacks maliciously manipulating a victim radar's point cloud, and show the novel ability to effectively `add' (i.e., false positive attacks), `remove' (i.e., false negative attacks), or `move' (i.e., translation attacks) object detections from a victim vehicle's scene. Finally, we experimentally demonstrate the feasibility of our attacks on real-world case studies performed using a real-time physical prototype on a software-defined radio platform.

From Spectral Theorem to Statistical Independence with Application to System Identification

High dimensional random dynamical systems are ubiquitous, including -- but not limited to -- cyber-physical systems, daily return on different stocks of S&P 1500 and velocity profile of interacting particle systems around McKeanVlasov limit. Mathematically, underlying phenomenon can be captured via a stable $n$-dimensional linear transformation `$A$' and additive randomness. System identification aims at extracting useful information about underlying dynamical system, given a length $N$ trajectory from it (corresponds to an $n \times N$ dimensional data matrix). We use spectral theorem for non-Hermitian operators to show that spatio-temperal correlations are dictated by the discrepancy between algebraic and geometric multiplicity of distinct eigenvalues corresponding to state transition matrix. Small discrepancies imply that original trajectory essentially comprises of multiple lower dimensional random dynamical systems living on $A$ invariant subspaces and are statistically independent of each other. In the process, we provide first quantitative handle on decay rate of finite powers of state transition matrix $\|A^{k}\|$ . It is shown that when a stable dynamical system has only one distinct eigenvalue and discrepancy of $n-1$: $\|A\|$ has a dependence on $n$, resulting dynamics are spatially inseparable and consequently there exist at least one row with covariates of typical size $\Theta\big(\sqrt{N-n+1}$ $e^{n}\big)$ i.e., even under stability assumption, covariates can suffer from curse of dimensionality. In the light of these findings we set the stage for non-asymptotic error analysis in estimation of state transition matrix $A$ via least squares regression on observed trajectory by showing that element-wise error is essentially a variant of well-know Littlewood-Offord problem.