STL Robustness Risk over Discrete-Time Stochastic Processes

We present a framework to interpret signal temporal logic (STL) formulas over discrete-time stochastic processes in terms of the induced risk. Each realization of a stochastic process either satisfies or violates an STL formula. In fact, we can assign a robustness value to each realization that indicates how robustly this realization satisfies an STL formula. We then define the risk of a stochastic process not satisfying an STL formula robustly, referred to as the "STL robustness risk". In our definition, we permit general classes of risk measures such as, but not limited to, the value-at-risk. While in general hard to compute, we propose an approximation of the STL robustness risk. This approximation has the desirable property of being an upper bound of the STL robustness risk when the chosen risk measure is monotone, a property satisfied by most risk measures. Motivated by the interest in data-driven approaches, we present a sampling-based method for calculating an upper bound of the approximate STL robustness risk for the value-at-risk that holds with high probability. While we consider the case of the value-at-risk, we highlight that such sampling-based methods are viable for other risk measures.

Linear Systems can be Hard to Learn

In this paper, we investigate when system identification is statistically easy or hard, in the finite sample regime. Statistically easy to learn linear system classes have sample complexity that is polynomial with the system dimension. Most prior research in the finite sample regime falls in this category, focusing on systems that are directly excited by process noise. Statistically hard to learn linear system classes have worst-case sample complexity that is at least exponential with the system dimension, regardless of the identification algorithm. Using tools from minimax theory, we show that classes of linear systems can be hard to learn. Such classes include, for example, under-actuated or under-excited systems with weak coupling among the states. Having classified some systems as easy or hard to learn, a natural question arises as to what system properties fundamentally affect the hardness of system identifiability. Towards this direction, we characterize how the controllability index of linear systems affects the sample complexity of identification. More specifically, we show that the sample complexity of robustly controllable linear systems is upper bounded by an exponential function of the controllability index. This implies that identification is easy for classes of linear systems with small controllability index and potentially hard if the controllability index is large. Our analysis is based on recent statistical tools for finite sample analysis of system identification as well as a novel lower bound that relates controllability index with the least singular value of the controllability Gramian.

Resilient Active Information Acquisition with Teams of Robots

Emerging applications of collaborative autonomy, such as Multi-Target Tracking, Unknown Map Exploration, and Persistent Surveillance, require robots plan paths to navigate an environment while maximizing the information collected via on-board sensors. In this paper, we consider such information acquisition tasks but in adversarial environments, where attacks may temporarily disable the robots' sensors. We propose the first receding horizon algorithm, aiming for robust and adaptive multi-robot planning against any number of attacks, which we call Resilient Active Information acquisitioN (RAIN). RAIN calls, in an online fashion, a Robust Trajectory Planning (RTP) subroutine which plans attack-robust control inputs over a look-ahead planning horizon. We quantify RTP's performance by bounding its suboptimality. We base our theoretical analysis on notions of curvature introduced in combinatorial optimization. We evaluate RAIN in three information acquisition scenarios: Multi-Target Tracking, Occupancy Grid Mapping, and Persistent Surveillance. The scenarios are simulated in C++ and a Unity-based simulator. In all simulations, RAIN runs in real-time, and exhibits superior performance against a state-of-the-art baseline information acquisition algorithm, even in the presence of a high number of attacks. We also demonstrate RAIN's robustness and effectiveness against varying models of attacks (worst-case and random), as well as, varying replanning rates.

Technical Report: Scalable Active Information Acquisition for Multi-Robot Systems

This paper proposes a novel highly scalable non-myopic planning algorithm for multi-robot Active Information Acquisition (AIA) tasks. AIA scenarios include target localization and tracking, active SLAM, surveillance, environmental monitoring and others. The objective is to compute control policies for multiple robots which minimize the accumulated uncertainty of a static hidden state over an a priori unknown horizon. The majority of existing AIA approaches are centralized and, therefore, face scaling challenges. To mitigate this issue, we propose an online algorithm that relies on decomposing the AIA task into local tasks via a dynamic space-partitioning method. The local subtasks are formulated online and require the robots to switch between exploration and active information gathering roles depending on their functionality in the environment. The switching process is tightly integrated with optimizing information gathering giving rise to a hybrid control approach. We show that the proposed decomposition-based algorithm is probabilistically complete for homogeneous sensor teams and under linearity and Gaussian assumptions. We provide extensive simulation results that show that the proposed algorithm can address large-scale estimation tasks that are computationally challenging to solve using existing centralized approaches.

Model-Based Domain Generalization

We consider the problem of domain generalization, in which a predictor is trained on data drawn from a family of related training domains and tested on a distinct and unseen test domain. While a variety of approaches have been proposed for this setting, it was recently shown that no existing algorithm can consistently outperform empirical risk minimization (ERM) over the training domains. To this end, in this paper we propose a novel approach for the domain generalization problem called Model-Based Domain Generalization. In our approach, we first use unlabeled data from the training domains to learn multi-modal domain transformation models that map data from one training domain to any other domain. Next, we propose a constrained optimization-based formulation for domain generalization which enforces that a trained predictor be invariant to distributional shifts under the underlying domain transformation model. Finally, we propose a novel algorithmic framework for efficiently solving this constrained optimization problem. In our experiments, we show that this approach outperforms both ERM and domain generalization algorithms on numerous well-known, challenging datasets, including WILDS, PACS, and ImageNet. In particular, our algorithms beat the current state-of-the-art methods on the very-recently-proposed WILDS benchmark by up to 20 percentage points.

Achieving Linear Convergence in Federated Learning under Objective and Systems Heterogeneity

We consider a standard federated learning architecture where a group of clients periodically coordinate with a central server to train a statistical model. We tackle two major challenges in federated learning: (i) objective heterogeneity, which stems from differences in the clients' local loss functions, and (ii) systems heterogeneity, which leads to slow and straggling client devices. Due to such client heterogeneity, we show that existing federated learning algorithms suffer from a fundamental speed-accuracy conflict: they either guarantee linear convergence but to an incorrect point, or convergence to the global minimum but at a sub-linear rate, i.e., fast convergence comes at the expense of accuracy. To address the above limitation, we propose FedLin - a simple, new algorithm that exploits past gradients and employs client-specific learning rates. When the clients' local loss functions are smooth and strongly convex, we show that FedLin guarantees linear convergence to the global minimum. We then establish matching upper and lower bounds on the convergence rate of FedLin that highlight the trade-offs associated with infrequent, periodic communication. Notably, FedLin is the only approach that is able to match centralized convergence rates (up to constants) for smooth strongly convex, convex, and non-convex loss functions despite arbitrary objective and systems heterogeneity. We further show that FedLin preserves linear convergence rates under aggressive gradient sparsification, and quantify the effect of the compression level on the convergence rate.

Non-Monotone Energy-Aware Information Gathering for Heterogeneous Robot Teams

This paper considers the problem of planning trajectories for a team of sensor-equipped robots to reduce uncertainty about a dynamical process. Optimizing the trade-off between information gain and energy cost (e.g., control effort, energy expenditure, distance travelled) is desirable but leads to a non-monotone objective function in the set of robot trajectories. Therefore, common multi-robot planning algorithms based on techniques such as coordinate descent lose their performance guarantees. Methods based on local search provide performance guarantees for optimizing a non-monotone submodular function, but require access to all robots' trajectories, making it not suitable for distributed execution. This work proposes a distributed planning approach based on local search, and shows how to reduce its computation and communication requirements without sacrificing algorithm performance. We demonstrate the efficacy of our proposed method by coordinating robot teams composed of both ground and aerial vehicles with different sensing and control profiles, and evaluate the algorithm's performance in two target tracking scenarios. Our results show up to 60% communication reduction and 80-92% computation reduction on average when coordinating up to 10 robots, while outperforming the coordinate descent based algorithm in achieving a desirable trade-off between sensing and energy expenditure.

Is the brain macroscopically linear? A system identification of resting state dynamics

A central challenge in the computational modeling of neural dynamics is the trade-off between accuracy and simplicity. At the level of individual neurons, nonlinear dynamics are both experimentally established and essential for neuronal functioning. An implicit assumption has thus formed that an accurate computational model of whole-brain dynamics must also be highly nonlinear, whereas linear models may provide a first-order approximation. Here, we provide a rigorous and data-driven investigation of this hypothesis at the level of whole-brain blood-oxygen-level-dependent (BOLD) and macroscopic field potential dynamics by leveraging the theory of system identification. Using functional MRI (fMRI) and intracranial EEG (iEEG), we model the resting state activity of 700 subjects in the Human Connectome Project (HCP) and 122 subjects from the Restoring Active Memory (RAM) project using state-of-the-art linear and nonlinear model families. We assess relative model fit using predictive power, computational complexity, and the extent of residual dynamics unexplained by the model. Contrary to our expectations, linear auto-regressive models achieve the best measures across all three metrics, eliminating the trade-off between accuracy and simplicity. To understand and explain this linearity, we highlight four properties of macroscopic neurodynamics which can counteract or mask microscopic nonlinear dynamics: averaging over space, averaging over time, observation noise, and limited data samples. Whereas the latter two are technological limitations and can improve in the future, the former two are inherent to aggregated macroscopic brain activity. Our results, together with the unparalleled interpretability of linear models, can greatly facilitate our understanding of macroscopic neural dynamics and the principled design of model-based interventions for the treatment of neuropsychiatric disorders.

Sensor-Based Temporal Logic Planning in Uncertain Semantic Maps

This paper addresses a multi-robot mission planning problem in uncertain semantic environments. The environment is modeled by static labeled landmarks with uncertain positions and classes giving rise to an uncertain semantic map generated by semantic SLAM algorithms. Our goal is to design control policies for sensing robots so that they can accomplish complex collaborative high level tasks captured by global temporal logic specifications. To account for environmental and sensing uncertainty, we extend Linear Temporal Logic (LTL) by including sensor-based predicates allowing us to incorporate uncertainty and probabilistic satisfaction requirements directly into the task specification. The sensor-based LTL planning problem gives rise to an optimal control problem, solved by a novel sampling-based algorithm, that generates open-loop control policies that can be updated online to adapt to the map that is continuously learned by existing semantic SLAM methods. We provide extensive experiments that corroborate the theoretical analysis and show that the proposed algorithm can address large-scale planning tasks in the presence of uncertainty.