no code implementations • 15 Oct 2024 • Thomas T. Zhang, Bruce D. Lee, Ingvar Ziemann, George J. Pappas, Nikolai Matni

We show that when $N \gtrsim C_{\mathrm{dep}} (\mathrm{dim}(\mathcal F) + \mathrm{C}(\mathcal G)/T)$, the excess risk of $\hat f^{(0)} \circ \hat g$ on the target task decays as $\nu_{\mathrm{div}} \big(\frac{\mathrm{dim}(\mathcal F)}{N'} + \frac{\mathrm{C}(\mathcal G)}{N T} \big)$, where $C_{\mathrm{dep}}$ denotes the effect of data dependency, $\nu_{\mathrm{div}}$ denotes an (estimatable) measure of $\textit{task-diversity}$ between the source and target tasks, and $\mathrm C(\mathcal G)$ denotes the complexity of the representation class $\mathcal G$.

no code implementations • 20 Sep 2024 • Ingvar Ziemann, Nikolai Matni, George J. Pappas

For this situation, we show that there exists no learner using a linear filter which can succesfully learn the random walk unless the filter length exceeds a certain threshold depending on the effective memory length and horizon of the problem.

1 code implementation • 3 Aug 2024 • Fengjun Yang, Nikolai Matni

We propose a reinforcement learning (RL)-based algorithm to jointly train (1) a trajectory planner and (2) a tracking controller in a layered control architecture.

no code implementations • 8 Jul 2024 • Bruce D. Lee, Leonardo F. Toso, Thomas T. Zhang, James Anderson, Nikolai Matni

Representation learning is a powerful tool that enables learning over large multitudes of agents or domains by enforcing that all agents operate on a shared set of learned features.

no code implementations • 3 Jun 2024 • Brian Lee, Nikolai Matni

We study the performance of risk-controlling prediction sets (RCPS), an empirical risk minimization-based formulation of conformal prediction, with a single trajectory of temporally correlated data from an unknown stochastic dynamical system.

no code implementations • 16 May 2024 • Anish Bhattacharya, Nishanth Rao, Dhruv Parikh, Pratik Kunapuli, Yuwei Wu, Yuezhan Tao, Nikolai Matni, Vijay Kumar

We demonstrate the capabilities of an attention-based end-to-end approach for high-speed vision-based quadrotor obstacle avoidance in dense, cluttered environments, with comparison to various state-of-the-art learning architectures.

no code implementations • 13 Apr 2024 • Bruce D. Lee, Ingvar Ziemann, George J. Pappas, Nikolai Matni

Model-based reinforcement learning is an effective approach for controlling an unknown system.

1 code implementation • 27 Mar 2024 • Bo Wu, Bruce D. Lee, Kostas Daniilidis, Bernadette Bucher, Nikolai Matni

Large-scale robotic policies trained on data from diverse tasks and robotic platforms hold great promise for enabling general-purpose robots; however, reliable generalization to new environment conditions remains a major challenge.

no code implementations • 8 Feb 2024 • Ingvar Ziemann, Stephen Tu, George J. Pappas, Nikolai Matni

In this work, we study statistical learning with dependent ($\beta$-mixing) data and square loss in a hypothesis class $\mathscr{F}\subset L_{\Psi_p}$ where $\Psi_p$ is the norm $\|f\|_{\Psi_p} \triangleq \sup_{m\geq 1} m^{-1/p} \|f\|_{L^m} $ for some $p\in [2,\infty]$.

no code implementations • 10 Jan 2024 • Hanli Zhang, Anusha Srikanthan, Spencer Folk, Vijay Kumar, Nikolai Matni

In this paper, we argue that adapting the trajectory generation component keeping the controller fixed can improve trajectory tracking for quadrotor systems experiencing drag forces.

no code implementations • 29 Dec 2023 • Bruce D. Lee, Anders Rantzer, Nikolai Matni

Toward concretely understanding the benefit of pre-training for adaptive control, we study the adaptive linear quadratic control problem in the setting where the learner has prior knowledge of a collection of basis matrices for the dynamics.

1 code implementation • 3 Oct 2023 • Anish Bhattacharya, Ratnesh Madaan, Fernando Cladera, Sai Vemprala, Rogerio Bonatti, Kostas Daniilidis, Ashish Kapoor, Vijay Kumar, Nikolai Matni, Jayesh K. Gupta

We present EvDNeRF, a pipeline for generating event data and training an event-based dynamic NeRF, for the purpose of faithfully reconstructing eventstreams on scenes with rigid and non-rigid deformations that may be too fast to capture with a standard camera.

no code implementations • 7 Sep 2023 • Ingvar Ziemann, Anastasios Tsiamis, Bruce Lee, Yassir Jedra, Nikolai Matni, George J. Pappas

This tutorial serves as an introduction to recently developed non-asymptotic methods in the theory of -- mainly linear -- system identification.

1 code implementation • 16 Aug 2023 • Shaoru Chen, Kong Yao Chee, Nikolai Matni, M. Ani Hsieh, George J. Pappas

With the increase in data availability, it has been widely demonstrated that neural networks (NN) can capture complex system dynamics precisely in a data-driven manner.

no code implementations • 25 May 2023 • Bruce D. Lee, Thomas T. C. K. Zhang, Hamed Hassani, Nikolai Matni

In these special cases, we demonstrate that the severity of the tradeoff depends in an interpretable manner upon system-theoretic properties such as the spectrum of the controllability gramian, the spectrum of the observability gramian, and the stability of the system.

no code implementations • 16 May 2023 • Daniel Pfrommer, Max Simchowitz, Tyler Westenbroek, Nikolai Matni, Stephen Tu

A common pipeline in learning-based control is to iteratively estimate a model of system dynamics, and apply a trajectory optimization algorithm - e. g.~$\mathtt{iLQR}$ - on the learned model to minimize a target cost.

no code implementations • 27 Mar 2023 • Bruce D. Lee, Ingvar Ziemann, Anastasios Tsiamis, Henrik Sandberg, Nikolai Matni

We present a local minimax lower bound on the excess cost of designing a linear-quadratic controller from offline data.

no code implementations • 1 Dec 2022 • Thomas T. Zhang, Katie Kang, Bruce D. Lee, Claire Tomlin, Sergey Levine, Stephen Tu, Nikolai Matni

In particular, we consider a setting where learning is split into two phases: (a) a pre-training step where a shared $k$-dimensional representation is learned from $H$ source policies, and (b) a target policy fine-tuning step where the learned representation is used to parameterize the policy class.

no code implementations • 24 Nov 2022 • Kong Yao Chee, M. Ani Hsieh, Nikolai Matni

We show that the KNODE ensemble provides more accurate predictions and illustrate the efficacy and closed-loop performance of the proposed nonlinear MPC framework using two case studies.

1 code implementation • 28 Oct 2022 • Fengjun Yang, Fernando Gama, Somayeh Sojoudi, Nikolai Matni

Designing distributed optimal controllers subject to communication constraints is a difficult problem unless structural assumptions are imposed on the underlying dynamics and information exchange structure, e. g., sparsity, delay, or spatial invariance.

no code implementations • 5 Oct 2022 • David Brandfonbrener, Stephen Tu, Avi Singh, Stefan Welker, Chad Boodoo, Nikolai Matni, Jake Varley

We find that by adjusting the data collection process we improve the quality of both the learned value functions and policies over a variety of baseline methods for data collection.

no code implementations • 23 Sep 2022 • Shaoru Chen, Ning-Yuan Li, Victor M. Preciado, Nikolai Matni

In the proposed method, a time-varying feedback control policy is optimized such that the robust satisfaction of all constraints for the closed-loop system is guaranteed.

no code implementations • 12 Sep 2022 • Anastasios Tsiamis, Ingvar Ziemann, Nikolai Matni, George J. Pappas

This tutorial survey provides an overview of recent non-asymptotic advances in statistical learning theory as relevant to control and system identification.

no code implementations • 14 Jun 2022 • Ingvar Ziemann, Anastasios Tsiamis, Henrik Sandberg, Nikolai Matni

We study stochastic policy gradient methods from the perspective of control-theoretic limitations.

1 code implementation • 8 Jun 2022 • Haoze Wu, Teruhiro Tagomori, Alexander Robey, Fengjun Yang, Nikolai Matni, George Pappas, Hamed Hassani, Corina Pasareanu, Clark Barrett

We consider the problem of certifying the robustness of deep neural networks against real-world distribution shifts.

1 code implementation • 30 May 2022 • Daniel Pfrommer, Thomas T. C. K. Zhang, Stephen Tu, Nikolai Matni

We propose Taylor Series Imitation Learning (TaSIL), a simple augmentation to standard behavior cloning losses in the context of continuous control.

no code implementations • 28 May 2022 • Lars Lindemann, Lejun Jiang, Nikolai Matni, George J. Pappas

For discrete-time stochastic processes, we show under which conditions the approximate STL robustness risk can even be computed exactly.

no code implementations • 27 May 2022 • Anastasios Tsiamis, Ingvar Ziemann, Manfred Morari, Nikolai Matni, George J. Pappas

In this paper, we study the statistical difficulty of learning to control linear systems.

2 code implementations • 21 Mar 2022 • Shaoru Chen, Victor M. Preciado, Manfred Morari, Nikolai Matni

However, it is challenging to design LTV state feedback controllers in the face of model uncertainty whose effects are difficult to bound.

no code implementations • 21 Mar 2022 • Bruce D. Lee, Thomas T. C. K. Zhang, Hamed Hassani, Nikolai Matni

Though this fundamental tradeoff between nominal performance and robustness is known to exist, it is not well-characterized in quantitative terms.

1 code implementation • 24 Feb 2022 • Georgios Georgakis, Bernadette Bucher, Anton Arapin, Karl Schmeckpeper, Nikolai Matni, Kostas Daniilidis

We consider the problems of exploration and point-goal navigation in previously unseen environments, where the spatial complexity of indoor scenes and partial observability constitute these tasks challenging.

no code implementations • 16 Feb 2022 • Ingvar Ziemann, Henrik Sandberg, Nikolai Matni

Given a single trajectory of a dynamical system, we analyze the performance of the nonparametric least squares estimator (LSE).

1 code implementation • 4 Jan 2022 • Daniel Pfrommer, Nikolai Matni

We introduce Variational State-Space Filters (VSSF), a new method for unsupervised learning, identification, and filtering of latent Markov state space models from raw pixels.

2 code implementations • 22 Dec 2021 • Carmen Amo Alonso, Fengjun Yang, Nikolai Matni

By imposing locality constraints on the system response, we show that the amount of data needed for our synthesis problem is independent of the size of the global system.

no code implementations • 20 Dec 2021 • Thomas T. C. K. Zhang, Stephen Tu, Nicholas M. Boffi, Jean-Jacques E. Slotine, Nikolai Matni

Motivated by bridging the simulation to reality gap in the context of safety-critical systems, we consider learning adversarially robust stability certificates for unknown nonlinear dynamical systems.

1 code implementation • 18 Nov 2021 • Lars Lindemann, Alexander Robey, Lejun Jiang, Satyajeet Das, Stephen Tu, Nikolai Matni

Along with the optimization problem, we provide verifiable conditions in terms of the density of the data, smoothness of the system model and state estimator, and the size of the error bounds that guarantee validity of the obtained ROCBF.

no code implementations • 17 Nov 2021 • Thomas T. C. K. Zhang, Bruce D. Lee, Hamed Hassani, Nikolai Matni

We provide an algorithm to find this perturbation given data realizations, and develop upper and lower bounds on the adversarial state estimation error in terms of the standard (non-adversarial) estimation error and the spectral properties of the resulting observer.

1 code implementation • 10 Nov 2021 • Shaoru Chen, Nikolai Matni, Manfred Morari, Victor M. Preciado

We propose a robust model predictive control (MPC) method for discrete-time linear time-invariant systems with norm-bounded additive disturbances and model uncertainty.

1 code implementation • 28 Apr 2021 • Fengjun Yang, Nikolai Matni

Our proposed parameterization enjoys a local and distributed architecture, similar to previous Graph Neural Network (GNN)-based parameterizations, while further naturally allowing for joint optimization of the distributed controller and communication topology needed to implement it.

no code implementations • 3 Apr 2021 • Lars Lindemann, Nikolai Matni, George J. Pappas

We then define the risk of a stochastic process not satisfying an STL formula robustly, referred to as the STL robustness risk.

1 code implementation • 2 Apr 2021 • Jingxi Xu, Bruce Lee, Nikolai Matni, Dinesh Jayaraman

The difficulty of optimal control problems has classically been characterized in terms of system properties such as minimum eigenvalues of controllability/observability gramians.

no code implementations • 18 Feb 2021 • Stephen Tu, Alexander Robey, Tingnan Zhang, Nikolai Matni

We study the following question in the context of imitation learning for continuous control: how are the underlying stability properties of an expert policy reflected in the sample-complexity of an imitation learning task?

1 code implementation • 16 Jan 2021 • Alexander Robey, Lars Lindemann, Stephen Tu, Nikolai Matni

We identify sufficient conditions on the data such that feasibility of the optimization problem ensures correctness of the learned robust hybrid control barrier functions.

1 code implementation • 20 Nov 2020 • Anton Xue, Nikolai Matni

We establish data-driven versions of the System Level Synthesis (SLS) parameterization of achievable closed-loop system responses for a linear-time-invariant system over a finite-horizon.

no code implementations • 8 Nov 2020 • Lars Lindemann, Haimin Hu, Alexander Robey, Hanwen Zhang, Dimos V. Dimarogonas, Stephen Tu, Nikolai Matni

Motivated by the lack of systematic tools to obtain safe control laws for hybrid systems, we propose an optimization-based framework for learning certifiably safe control laws from data.

no code implementations • 13 Aug 2020 • Nicholas M. Boffi, Stephen Tu, Nikolai Matni, Jean-Jacques E. Slotine, Vikas Sindhwani

Many existing tools in nonlinear control theory for establishing stability or safety of a dynamical system can be distilled to the construction of a certificate function that guarantees a desired property.

1 code implementation • 7 Apr 2020 • Alexander Robey, Haimin Hu, Lars Lindemann, Hanwen Zhang, Dimos V. Dimarogonas, Stephen Tu, Nikolai Matni

Furthermore, if the CBF parameterization is convex, then under mild assumptions, so is our learning process.

1 code implementation • 13 Mar 2020 • Bernadette Bucher, Karl Schmeckpeper, Nikolai Matni, Kostas Daniilidis

Model-based curiosity combines active learning approaches to optimal sampling with the information gain based incentives for exploration presented in the curiosity literature.

1 code implementation • ICLR 2020 • Sangdon Park, Osbert Bastani, Nikolai Matni, Insup Lee

We propose an algorithm combining calibrated prediction and generalization bounds from learning theory to construct confidence sets for deep neural networks with PAC guarantees---i. e., the confidence set for a given input contains the true label with high probability.

no code implementations • L4DC 2020 • Anastasios Tsiamis, Nikolai Matni, George J. Pappas

We show that when the system identification step produces sufficiently accurate estimates, or when the underlying true KF is sufficiently robust, that a Certainty Equivalent (CE) KF, i. e., one designed using the estimated parameters directly, enjoys provable sub-optimality guarantees.

no code implementations • 21 Sep 2019 • Salar Fattahi, Nikolai Matni, Somayeh Sojoudi

In this work, we propose a robust approach to design distributed controllers for unknown-but-sparse linear and time-invariant systems.

no code implementations • L4DC 2020 • Sarah Dean, Nikolai Matni, Benjamin Recht, Vickie Ye

Motivated by vision-based control of autonomous vehicles, we consider the problem of controlling a known linear dynamical system for which partial state information, such as vehicle position, is extracted from complex and nonlinear data, such as a camera image.

no code implementations • 27 Jun 2019 • Nikolai Matni, Stephen Tu

We provide a brief tutorial on the use of concentration inequalities as they apply to system identification of state-space parameters of linear time invariant systems, with a focus on the fully observed setting.

no code implementations • 27 Jun 2019 • Nikolai Matni, Alexandre Proutiere, Anders Rantzer, Stephen Tu

Machine and reinforcement learning (RL) are increasingly being applied to plan and control the behavior of autonomous systems interacting with the physical world.

no code implementations • 20 Apr 2019 • Salar Fattahi, Nikolai Matni, Somayeh Sojoudi

In particular, we show that the proposed estimator can correctly identify the sparsity pattern of the system matrices with high probability, provided that the length of the sample trajectory exceeds a threshold.

2 code implementations • 26 Sep 2018 • Sarah Dean, Stephen Tu, Nikolai Matni, Benjamin Recht

We study the constrained linear quadratic regulator with unknown dynamics, addressing the tension between safety and exploration in data-driven control techniques.

no code implementations • NeurIPS 2018 • Sarah Dean, Horia Mania, Nikolai Matni, Benjamin Recht, Stephen Tu

We consider adaptive control of the Linear Quadratic Regulator (LQR), where an unknown linear system is controlled subject to quadratic costs.

1 code implementation • 25 Mar 2018 • Ross Boczar, Nikolai Matni, Benjamin Recht

As the systems we control become more complex, first-principle modeling becomes either impossible or intractable, motivating the use of machine learning techniques for the control of systems with continuous action spaces.

no code implementations • 4 Oct 2017 • Sarah Dean, Horia Mania, Nikolai Matni, Benjamin Recht, Stephen Tu

This paper addresses the optimal control problem known as the Linear Quadratic Regulator in the case when the dynamics are unknown.

no code implementations • 15 Jan 2014 • Matanya B. Horowitz, Nikolai Matni, Joel W. Burdick

The method is a convex relaxation of the classical pose estimation problem, and is based on explicit linear matrix inequality (LMI) representations for the convex hulls of $SE(2)$ and $SE(3)$.

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