The first International Workshop on Verification and Validation of Cyber-Physical Systems (V2CPS-16) was held in conjunction with the 12th International Conference on integration of Formal Methods (iFM 2016) in Reykjavik, Iceland. The purpose of V2CPS-16 was to bring together researchers and experts of the fields of formal verification and cyber-physical systems (CPS) to cover the theme of this workshop, namely a wide spectrum of verification and validation methods including (but not limited to) control, simulation, formal methods, etc. A CPS is an integration of networked computational and physical processes with meaningful inter-effects; the former monitors, controls, and affects the latter, while the latter also impacts the former. CPSs have applications in a wide-range of systems spanning robotics, transportation, communication, infrastructure, energy, and manufacturing. Many safety-critical systems such as chemical processes, medical devices, aircraft flight control, and automotive systems, are indeed CPS. The advanced capabilities of CPS require complex software and synthesis algorithms, which are hard to verify. In fact, many problems in this area are undecidable. Thus, a major step is to find particular abstractions of such systems which might be algorithmically verifiable regarding specific properties of such systems, describing the partial/overall behaviors of CPSs.

Designing a neural network processor is an end-to-end co-design problem: network architecture and training budget determine the inference workload; hardware mapping decisions determine chip area, latency, and energy; and these characteristics govern fabrication yield and manufacturing cost. In practice, these decisions are made in separate stages, and existing co-design methodologies are tightly coupled to specific algorithms, making it difficult to improve one component without reworking the entire pipeline. This paper presents a unified framework, grounded in monotone co-design theory, that composes four interoperable design blocks spanning network training, chip mapping, wafer-level fabrication, and compute resource allocation. Each block exposes only a functionality-resource interface to the rest of the system, so any block can be refined without structural changes elsewhere. A central contribution is the treatment of uncertainty: rather than collapsing stochastic outcomes into point estimates, the framework introduces Confidence, the inverse of success probability, as an explicit and optimizable resource alongside cost, time, and power. Three case studies validate the approach. The first recovers Pareto-optimal implementations across heterogeneous application scenarios. The second confirms that Confidence functions as a continuously tunable design knob rather than a post-hoc diagnostic. The third demonstrates that improving a single block's implementation set automatically propagates to the global Pareto front, without modifying the co-design diagram.

Correspondence pruning aims to identify inliers from an initial set of correspondences. Most existing Graph Neural Network (GNN)-based methods rely on geometric features mapped from coarse Euclidean coordinates, which struggle to capture the subtle geometric consistencies presented by inliers. While Mamba-based methods possess global receptive fields and long sequence modeling capabilities, they tend to accumulate substantial inconsistent features within the hidden state space, making it difficult to distinguish inliers from outliers. In this paper, we integrate frequency domain perception into this task for the first time and propose SFMambaNet, a novel Spectral-Frequency enhanced Mamba-based two-view correspondence pruning network. Our method is collaboratively composed of two components: First, we design a Local Spectral-Geometric Attention (LSGA) block. LSGA incorporates spectral positional encoding into local graph interactions and introduces multi-scale Mamba processing to enhance the capture of subtle geometric consistencies and improve local feature discriminability. Building upon this, we design a Spectral-Integrated Global Mamba (SIGM) block. SIGM embeds a frequency gating mechanism within the state space, utilizing the frequency information provided by LSGA to explicitly suppress high-frequency noise accumulation within hidden states and mitigate the propagation of inconsistent features. This enhances inlier-outlier separability and achieves robust global context modeling capabilities with nearly linear complexity. Extensive experiments demonstrate that SFMambaNet outperforms current state-of-the-art methods on several challenging tasks. The code is available at https://github.com/Kirito14IT/SFMambaNet.

This article situates large language models (LLMs) within the longer history of computational approaches to concept analysis in the history, philosophy, and sociology of science (HPSS). We examine what LLMs add to existing methods, how they inherit longstanding problems, and review recent case studies that employ them. In the first part, we reconstruct computational conceptual history before LLMs by bringing together three strands of work: early digital methods in HPSS, distributional approaches from digital history and related research, and lexical semantic change detection. We provide an overview of the main challenges and opportunities, focusing on corpus construction, operationalization and modelling choices, and evaluation and interpretation. In the second part, we turn to the era of LLMs, starting with a short introduction to LLMs before reviewing LLM-based work on lexical semantic change detection and relevant case studies in HPSS. We then revisit the earlier methodological questions, showing how issues of corpus construction, model choice and training data, operationalization trade-offs, and evaluation and interpretation play out in LLM-based workflows.

The emergence of large language model agents capable of invoking external tools has created urgent need for formal verification of agent protocols. Two paradigms dominate this space: Schema-Guided Dialogue (SGD), a research framework for zero-shot API generalization, and the Model Context Protocol (MCP), an industry standard for agent-tool integration. While both enable dynamic service discovery through schema descriptions, their formal relationship remains unexplored. Building on prior work establishing the conceptual convergence of these paradigms, we present the first process calculus formalization of SGD and MCP, proving they are structurally bisimilar under a well-defined mapping Phi. However, we demonstrate that the reverse mapping Phi^{-1} is partial and lossy, revealing critical gaps in MCP's expressivity. Through bidirectional analysis, we identify five principles -- semantic completeness, explicit action boundaries, failure mode documentation, progressive disclosure compatibility, and inter-tool relationship declaration -- as necessary and sufficient conditions for full behavioral equivalence. We formalize these principles as type-system extensions MCP+, proving MCP+ is isomorphic to SGD. Our work provides the first formal foundation for verified agent systems and establishes schema quality as a provable safety property.

We present Unified Latent Dynamics (ULD), a novel reinforcement learning algorithm that unifies the efficiency of model-free methods with the representational strengths of model-based approaches, without incurring planning overhead. By embedding state-action pairs into a latent space in which the true value function is approximately linear, our method supports a single set of hyperparameters across diverse domains -- from continuous control with low-dimensional and pixel inputs to high-dimensional Atari games. We prove that, under mild conditions, the fixed point of our embedding-based temporal-difference updates coincides with that of a corresponding linear model-based value expansion, and we derive explicit error bounds relating embedding fidelity to value approximation quality. In practice, ULD employs synchronized updates of encoder, value, and policy networks, auxiliary losses for short-horizon predictive dynamics, and reward-scale normalization to ensure stable learning under sparse rewards. Evaluated on 80 environments spanning Gym locomotion, DeepMind Control (proprioceptive and visual), and Atari, our approach matches or exceeds the performance of specialized model-free and general model-based baselines -- achieving cross-domain competence with minimal tuning and a fraction of the parameter footprint. These results indicate that value-aligned latent representations alone can deliver the adaptability and sample efficiency traditionally attributed to full model-based planning.

To precisely reach for an object with a humanoid robot, it is of central importance to have good knowledge of both end-effector, object pose and shape. In this work we propose a framework for markerless visual servoing on unknown objects, which is divided in four main parts: I) a least-squares minimization problem is formulated to find the volume of the object graspable by the robot's hand using its stereo vision; II) a recursive Bayesian filtering technique, based on Sequential Monte Carlo (SMC) filtering, estimates the 6D pose (position and orientation) of the robot's end-effector without the use of markers; III) a nonlinear constrained optimization problem is formulated to compute the desired graspable pose about the object; IV) an image-based visual servo control commands the robot's end-effector toward the desired pose. We demonstrate effectiveness and robustness of our approach with extensive experiments on the iCub humanoid robot platform, achieving real-time computation, smooth trajectories and sub-pixel precisions.

This paper addresses the problem of Multi-robot Coverage Path Planning (MCPP) for unknown environments in the presence of robot failures. Unexpected robot failures can seriously degrade the performance of a robot team and in extreme cases jeopardize the overall operation. Therefore, this paper presents a distributed algorithm, called Cooperative Autonomy for Resilience and Efficiency (CARE), which not only provides resilience to the robot team against failures of individual robots, but also improves the overall efficiency of operation via event-driven replanning. The algorithm uses distributed Discrete Event Supervisors (DESs), which trigger games between a set of feasible players in the event of a robot failure or idling, to make collaborative decisions for task reallocations. The game-theoretic structure is built using Potential Games, where the utility of each player is aligned with a shared objective function for all players. The algorithm has been validated in various complex scenarios on a high-fidelity robotic simulator, and the results demonstrate that the team achieves complete coverage under failures, reduced coverage time, and faster target discovery as compared to three alternative methods.

In this paper, we propose several dictionary learning algorithms for sparse representations that also impose specific structures on the learned dictionaries such that they are numerically efficient to use: reduced number of addition/multiplications and even avoiding multiplications altogether. We base our work on factorizations of the dictionary in highly structured basic building blocks (binary orthonormal, scaling and shear transformations) for which we can write closed-form solutions to the optimization problems that we consider. We show the effectiveness of our methods on image data where we can compare against well-known numerically efficient transforms such as the fast Fourier and the fast discrete cosine transforms.

Metrics on the space of sets of trajectories are important for scientists in the field of computer vision, machine learning, robotics, and general artificial intelligence. However, existing notions of closeness between sets of trajectories are either mathematically inconsistent or of limited practical use. In this paper, we outline the limitations in the current mathematically-consistent metrics, which are based on OSPA (Schuhmacher et al. 2008); and the inconsistencies in the heuristic notions of closeness used in practice, whose main ideas are common to the CLEAR MOT measures (Keni and Rainer 2008) widely used in computer vision. In two steps, we then propose a new intuitive metric between sets of trajectories and address these limitations. First, we explain a solution that leads to a metric that is hard to compute. Then we modify this formulation to obtain a metric that is easy to compute while keeping the useful properties of the previous metric. Our notion of closeness is the first demonstrating the following three features: the metric 1) can be quickly computed, 2) incorporates confusion of trajectories' identity in an optimal way, and 3) is a metric in the mathematical sense.

This work investigates the design of risk-perception-aware motion-planning strategies that incorporate non-rational perception of risks associated with uncertain spatial costs. Our proposed method employs the Cumulative Prospect Theory (CPT) to generate a perceived risk map over a given environment. CPT-like perceived risks and path-length metrics are then combined to define a cost function that is compliant with the requirements of asymptotic optimality of sampling-based motion planners (RRT*). The modeling power of CPT is illustrated in theory and in simulation, along with a comparison to other risk perception models like Conditional Value at Risk (CVaR). Theoretically, we define a notion of expressiveness for a risk perception model and show that CPT's is higher than that of CVaR and expected risk. We then show that this expressiveness translates to our path planning setting, where we observe that a planner equipped with CPT together with a simultaneous perturbation stochastic approximation (SPSA) method can better approximate arbitrary paths in an environment. Additionally, we show in simulation that our planner captures a rich set of meaningful paths, representative of different risk perceptions in a custom environment. We then compare the performance of our planner with T-RRT* (a planner for continuous cost spaces) and Risk-RRT* (a risk-aware planner for dynamic human obstacles) through simulations in cluttered and dynamic environments respectively, showing the advantage of our proposed planner.

Autonomous unmanned aerial vehicles (UAVs) that can execute aggressive (i.e., high-speed and high-acceleration) maneuvers have attracted significant attention in the past few years. This paper focuses on accurate tracking of aggressive quadcopter trajectories. We propose a novel control law for tracking of position and yaw angle and their derivatives of up to fourth order, specifically, velocity, acceleration, jerk, and snap along with yaw rate and yaw acceleration. Jerk and snap are tracked using feedforward inputs for angular rate and angular acceleration based on the differential flatness of the quadcopter dynamics. Snap tracking requires direct control of body torque, which we achieve using closed-loop motor speed control based on measurements from optical encoders attached to the motors. The controller utilizes incremental nonlinear dynamic inversion (INDI) for robust tracking of linear and angular accelerations despite external disturbances, such as aerodynamic drag forces. Hence, prior modeling of aerodynamic effects is not required. We rigorously analyze the proposed control law through response analysis, and we demonstrate it in experiments. The controller enables a quadcopter UAV to track complex 3D trajectories, reaching speeds up to 12.9 m/s and accelerations up to 2.1g, while keeping the root-mean-square tracking error down to 6.6 cm, in a flight volume that is roughly 18 m by 7 m and 3 m tall. We also demonstrate the robustness of the controller by attaching a drag plate to the UAV in flight tests and by pulling on the UAV with a rope during hover.

A robot making contact with an environment or human presents potential safety risks, including excessive collision force. While experiments on the effect of robot inertia, relative velocity, and interface stiffness on collision are in literature, analytical models for maximum collision force are limited to a simplified mass-spring robot model. This simplified model limits the analysis of control (force/torque, impedance, or admittance) or compliant robots (joint and end-effector compliance). Here, the Sobolev norm is adapted to be a system norm, giving rigorous bounds on the maximum force on a stiffness element in a general dynamic system, allowing the study of collision with more accurate models and feedback control. The Sobolev norm can be found through the $\mathcal{H}_2$ norm of a transformed system, allowing efficient computation, connection with existing control theory, and controller synthesis to minimize collision force. The Sobolev norm is validated, first experimentally with an admittance-controlled robot, then in simulation with a linear flexible-joint robot. It is then used to investigate the impact of control, joint flexibility and end-effector compliance on collision, and a trade-off between collision performance and environmental estimation uncertainty is shown.

In this paper, we introduce a novel data-driven inverse dynamics estimator based on Gaussian Process Regression. Driven by the fact that the inverse dynamics can be described as a polynomial function on a suitable input space, we propose the use of a novel kernel, called Geometrically Inspired Polynomial Kernel (GIP). The resulting estimator behaves similarly to model-based approaches as concerns data efficiency. Indeed, we proved that the GIP kernel defines a finite-dimensional Reproducing Kernel Hilbert Space that contains the inverse dynamics function computed through the Rigid Body Dynamics. The proposed kernel is based on the recently introduced Multiplicative Polynomial Kernel, a redefinition of the classical polynomial kernel equipped with a set of parameters that allows for a higher regularization. We tested the proposed approach in a simulated environment, and also in real experiments with a UR10 robot. The obtained results confirm that, compared to other data-driven estimators, the proposed approach is more data-efficient and exhibits better generalization properties. Instead, with respect to model-based estimators, our approach requires less prior information and is not affected by model bias.

Deep neural networks can be powerful tools, but require careful application-specific design to ensure that the most informative relationships in the data are learnable. In this paper, we apply deep neural networks to the nonlinear spatiotemporal physics problem of vehicle traffic dynamics. We consider problems of estimating macroscopic quantities (e.g., the queue at an intersection) at a lane level. First-principles modeling at the lane scale has been a challenge due to complexities in modeling social behaviors like lane changes, and those behaviors' resultant macro-scale effects. Following domain knowledge that upstream/downstream lanes and neighboring lanes affect each others' traffic flows in distinct ways, we apply a form of neural attention that allows the neural network layers to aggregate information from different lanes in different manners. Using a microscopic traffic simulator as a testbed, we obtain results showing that an attentional neural network model can use information from nearby lanes to improve predictions, and, that explicitly encoding the lane-to-lane relationship types significantly improves performance. We also demonstrate the transfer of our learned neural network to a more complex road network, discuss how its performance degradation may be attributable to new traffic behaviors induced by increased topological complexity, and motivate learning dynamics models from many road network topologies.

In this paper, we present a mesh-based approach to analyze stability and robustness of the policies obtained via deep reinforcement learning for various biped gaits of a five-link planar model. Intuitively, one would expect that including perturbations and/or other types of noise during training would likely result in more robustness of the resulting control policy. However, one would also like to have a quantitative and computationally-efficient means of evaluating the degree to which this might be so. Rather than relying on Monte Carlo simulations, which can become quite computationally burdensome in quantifying performance metrics, our goal is to provide more sophisticated tools to assess robustness properties of such policies. Our work is motivated by the twin hypotheses that contraction of dynamics, when achievable, can simplify the required complexity of a control policy and that control policies obtained via deep learning may therefore exhibit tendency to contract to lower-dimensional manifolds within the full state space, as a result. The tractability of our mesh-based tools in this work provides some evidence that this may be so.

Partial differential equations (PDEs) are commonly derived based on empirical observations. However, recent advances of technology enable us to collect and store massive amount of data, which offers new opportunities for data-driven discovery of PDEs. In this paper, we propose a new deep neural network, called PDE-Net 2.0, to discover (time-dependent) PDEs from observed dynamic data with minor prior knowledge on the underlying mechanism that drives the dynamics. The design of PDE-Net 2.0 is based on our earlier work \cite{Long2018PDE} where the original version of PDE-Net was proposed. PDE-Net 2.0 is a combination of numerical approximation of differential operators by convolutions and a symbolic multi-layer neural network for model recovery. Comparing with existing approaches, PDE-Net 2.0 has the most flexibility and expressive power by learning both differential operators and the nonlinear response function of the underlying PDE model. Numerical experiments show that the PDE-Net 2.0 has the potential to uncover the hidden PDE of the observed dynamics, and predict the dynamical behavior for a relatively long time, even in a noisy environment.

This paper investigates a hybrid compositional approach to optimal mission planning for multi-rotor Unmanned Aerial Vehicles (UAVs). We consider a time critical search and rescue scenario with two quadrotors in a constrained environment. Metric Temporal Logic (MTL) is used to formally describe the task specifications. In order to capture the various modes of UAV operation, we utilize a hybrid model for the system with linearized dynamics around different operating points. We divide the mission into several sub-tasks by exploiting the invariant nature of various task specifications i.e., the mutual independence of safety and timing constraints along the way, and the different modes (i,e., dynamics) of the robot. For each sub-task, we translate the MTL formulae into linear constraints, and solve the associated optimal control problem for desired path using a Mixed Integer Linear Program (MILP) solver. The complete path is constructed by the composition of individual optimal sub-paths. We show that the resulting trajectory satisfies the task specifications, and the proposed approach leads to significant reduction in computational complexity of the problem, making it possible to implement in real-time.

This work develops novel strategies for optimal planning with semantic observations using continuous state partially observable markov decision processes (CPOMDPs). Two major innovations are presented in relation to Gaussian mixture (GM) CPOMDP policy approximation methods. While existing methods have many desirable theoretical properties, they are unable to efficiently represent and reason over hybrid continuous-discrete probabilistic models. The first major innovation is the derivation of closed-form variational Bayes GM approximations of Point-Based Value Iteration Bellman policy backups, using softmax models of continuous-discrete semantic observation probabilities. A key benefit of this approach is that dynamic decision-making tasks can be performed with complex non-Gaussian uncertainties, while also exploiting continuous dynamic state space models (thus avoiding cumbersome and costly discretization). The second major innovation is a new clustering-based technique for mixture condensation that scales well to very large GM policy functions and belief functions. Simulation results for a target search and interception task with semantic observations show that the GM policies resulting from these innovations are more effective than those produced by other state of the art policy approximations, but require significantly less modeling overhead and online runtime cost. Additional results show the robustness of this approach to model errors and scaling to higher dimensions.

We investigate a classification problem using multiple mobile agents capable of collecting (partial) pose-dependent observations of an unknown environment. The objective is to classify an image over a finite time horizon. We propose a network architecture on how agents should form a local belief, take local actions, and extract relevant features from their raw partial observations. Agents are allowed to exchange information with their neighboring agents to update their own beliefs. It is shown how reinforcement learning techniques can be utilized to achieve decentralized implementation of the classification problem by running a decentralized consensus protocol. Our experimental results on the MNIST handwritten digit dataset demonstrates the effectiveness of our proposed framework.

Time Optimal Path Parametrization is the problem of minimizing the time interval during which an actuation constrained agent can traverse a given path. Recently, an efficient linear-time algorithm for solving this problem was proposed. However, its optimality was proved for only a strict subclass of problems solved optimally by more computationally intensive approaches based on convex programming. In this paper, we prove that the same linear-time algorithm is asymptotically optimal for all problems solved optimally by convex optimization approaches. We also characterize the optimum of the Time Optimal Path Parametrization Problem, which may be of independent interest.

We present a reusable formally verified safety net that provides end-to-end safety and liveness guarantees for 2D waypoint-following of Dubins-type ground robots with tolerances and acceleration. We: i) Model a robot in differential dynamic logic (dL), and specify assumptions on the controller and robot kinematics, ii) Prove formal safety and liveness properties for waypoint-following with speed limits, iii) Synthesize a monitor, which is automatically proven to enforce model compliance at runtime, and iv) Our use of the VeriPhy toolchain makes these guarantees carry over down to the level of machine code with untrusted controllers, environments, and plans. The guarantees for the safety net apply to any robot as long as the waypoints are chosen safely and the physical assumptions in its model hold. Experiments show these assumptions hold in practice, with an inherent trade-off between compliance and performance.

Control of robot orientation in Cartesian space implicates some difficulties, because the rotation group SO(3) is not contractible, and only globally contractible state spaces support continuous and globally asymptotically stable feedback control systems. In this paper, unit quaternions are used to represent orientations, and it is first shown that the unit quaternion set minus one single point is contractible. This is used to design a control system for temporally coupled dynamical movement primitives (DMPs) in Cartesian space. The functionality of the control system is verified experimentally on an industrial robot.

We propose a high-level planner for a multirotor to chase a ground vehicle, while simultaneously respecting various state and input constraints. Assuming a minimal kinematic model for the ground vehicle, we use data collected online to generate predictions for our planner within a model predictive control framework. Our solution is demonstrated, both via simulations and experiments on a stable quadcopter platform.

This paper presents a vision-based methodology which makes use of a stereo camera rig and a one dimension LiDAR to estimate free obstacle areas for quadrotor navigation. The presented approach fuses information provided by a depth map from a stereo camera rig, and the sensing distance of the 1D-LiDAR. Once the depth map is filtered with a Weighted Least Squares filter (WLS), the information is fused through a Kalman filter algorithm. To determine if there is a free space large enough for the quadrotor to pass through, our approach marks an area inside the disparity map by using the Kalman Filter output information. The whole process is implemented in an embedded computer Jetson TX2 and coded in the Robotic Operating System (ROS). Experiments demonstrate the effectiveness of our approach.

We present a novel application of robust control and online learning for the balancing of a n Degree of Freedom (DoF), Wheeled Inverted Pendulum (WIP) humanoid robot. Our technique condenses the inaccuracies of a mass model into a Center of Mass (CoM) error, balances despite this error, and uses online learning to update the mass model for a better CoM estimate. Using a simulated model of our robot, we meta-learn a set of excitory joint poses that makes our gradient descent algorithm quickly converge to an accurate (CoM) estimate. This simulated pipeline executes in a fully online fashion, using active disturbance rejection to address the mass errors that result from a steadily evolving mass model. Experiments were performed on a 19 DoF WIP, in which we manually acquired the data for the learned set of poses and show that the mass model produced by a gradient descent produces a CoM estimate that improves overall control and efficiency. This work contributes to a greater corpus of whole body control on the Golem Krang humanoid robot.

This paper presents a vision-based Unscented FastSLAM (UFastSLAM) algorithm combing the Rao-Blackwellized particle filter and Unscented Kalman filte(UKF). The landmarks are detected by a binocular vision to integrate localization and mapping. Since such binocular vision system generally inherits larger measurement errors, it is suitable to adopt Unscented FastSLAM to improve the performance of localization and mapping. Unscented FastSLAM takes advantage of UKF instead of the linear approximations of the nonlinear function where the effective number of particles is used as the criteria to reduce the particle degeneration. Simulations and experiments are carried out to demonstrate that the Unscented FastSLAM algorithm can achieve much better performance in the vision-based system than FastSLAM2.0 algorithm on the accuracy and robustness.

In recent years, Signal Temporal Logic (STL) has gained traction as a practical and expressive means of encoding control objectives for robotic and cyber-physical systems. The state-of-the-art in STL trajectory synthesis is to formulate the problem as a Mixed Integer Linear Program (MILP). The MILP approach is sound and complete for bounded specifications, but such strong correctness guarantees come at the price of exponential complexity in the number of predicates and the time bound of the specification. In this work, we propose an alternative synthesis paradigm that relies on Bayesian optimization rather than mixed integer programming. This relaxes the completeness guarantee to probabilistic completeness, but is significantly more efficient: our approach scales polynomially in the STL time-bound and linearly in the number of predicates. We prove that our approach is sound and probabilistically complete, and demonstrate its scalability with a nontrivial example.

Driving in urban environments often presents difficult situations that require expert maneuvering of a vehicle. These situations become even more challenging when considering large vehicles, such as buses. We present a path planning framework that addresses the demanding driving task of buses in urban areas. The approach is formulated as an optimization problem using the road-aligned vehicle model. The road-aligned frame introduces a distortion on the vehicle body and obstacles, motivating the development of novel approximations that capture this distortion. These approximations allow for the formulation of safe and non-conservative collision avoidance constraints. Unlike other path planning approaches, our method exploits curbs and other sweepable regions, which a bus must often sweep over in order to manage certain maneuvers. Furthermore, it takes full advantage of the particular characteristics of buses, namely the overhangs, an elevated part of the vehicle chassis, that can sweep over curbs. Simulations are presented, showing the applicability and benefits of the proposed method.

In decision making problems for continuous state and action spaces, linear dynamical models are widely employed. Specifically, policies for stochastic linear systems subject to quadratic cost functions capture a large number of applications in reinforcement learning. Selected randomized policies have been studied in the literature recently that address the trade-off between identification and control. However, little is known about policies based on bootstrapping observed states and actions. In this work, we show that bootstrap-based policies achieve a square root scaling of regret with respect to time. We also obtain results on the accuracy of learning the model's dynamics. Corroborative numerical analysis that illustrates the technical results is also provided.