Navid Azizan

Contacts:

Email: azizan at stanford dot edu

Navid Azizan


Dr. Navid Azizan is a Postdoctoral Scholar in ASL at Stanford, and an incoming Assistant Professor at MIT with dual appointments in the Department of Mechanical Engineering and the Institute for Data, Systems, and Society (IDSS).

Navid received his PhD in Computing and Mathematical Sciences (CMS) from the California Institute of Technology (Caltech) in 2020. Additionally, he was a research scientist intern at Google DeepMind in 2019. His research interests broadly lie in machine learning, control theory, mathematical optimization, and network science. He has made fundamental contributions to various aspects of intelligent systems, including the design and analysis of optimization algorithms for nonconvex and networked problems with applications to the smart grid, distributed computation, epidemics, and autonomy.

Navid’s work has been recognized by several awards including the 2020 Information Theory and Applications (ITA) Graduation-Day Gold Award. He was named an Amazon Fellow in Artificial Intelligence in 2017 and a PIMCO Fellow in Data Science in 2018. His research on smart grids received the ACM GREENMETRICS Best Student Paper Award in 2016. He was also the first-place winner and a gold medalist at the 2008 National Physics Olympiad in Iran. He co-organizes the popular “Control meets Learning” virtual seminar series.


Currently at Massachusetts Institute of Technology

ASL Publications

  1. S. M. Richards, J.-J. Slotine, N. Azizan, and M. Pavone, “Learning Control-Oriented Dynamical Structure from Data,” in Int. Conf. on Machine Learning, Honolulu, Hawaii, 2023.

    Abstract: Even for known nonlinear dynamical systems, feedback controller synthesis is a difficult problem that often requires leveraging the particular structure of the dynamics to induce a stable closed-loop system. For general nonlinear models, including those fit to data, there may not be enough known structure to reliably synthesize a stabilizing feedback controller. In this paper, we discuss a state-dependent nonlinear tracking controller formulation based on a state-dependent Riccati equation for general nonlinear control-affine systems. This formulation depends on a nonlinear factorization of the system of vector fields defining the control-affine dynamics, which always exists under mild smoothness assumptions. We propose a method for learning this factorization from a finite set of data. On a variety of simulated nonlinear dynamical systems, we empirically demonstrate the efficacy of learned versions of this controller in stable trajectory tracking. Alongside our learning method, we evaluate recent ideas in jointly learning a controller and stabilizability certificate for known dynamical systems; we show experimentally that such methods can be frail in comparison.

    @inproceedings{RichardsSlotineEtAl2023,
      author = {Richards, S. M. and Slotine, J.-J. and Azizan, N. and Pavone, M.},
      title = {Learning Control-Oriented Dynamical Structure from Data},
      year = {2023},
      booktitle = {{Int. Conf. on Machine Learning}},
      note = {In press},
      owner = {spenrich},
      timestamp = {2023-07-17},
      url = {https://arxiv.org/abs/2302.02529},
      address = {Honolulu, Hawaii},
      month = jul,
      keywords = {}
    }
    
  2. S. M. Richards, N. Azizan, J.-J. Slotine, and M. Pavone, “Control-Oriented Meta-Learning,” Int. Journal of Robotics Research, 2023. (In Press)

    Abstract: Real-time adaptation is imperative to the control of robots operating in complex, dynamic environments. Adaptive control laws can endow even nonlinear systems with good trajectory tracking performance, provided that any uncertain dynamics terms are linearly parameterizable with known nonlinear features. However, it is often difficult to specify such features a priori, such as for aerodynamic disturbances on rotorcraft or interaction forces between a manipulator arm and various objects. In this paper, we turn to data-driven modeling with neural networks to learn, offline from past data, an adaptive controller with an internal parametric model of these nonlinear features. Our key insight is that we can better prepare the controller for deployment with control-oriented meta-learning of features in closed-loop simulation, rather than regression-oriented meta-learning of features to fit input-output data. Specifically, we meta-learn the adaptive controller with closed-loop tracking simulation as the base-learner and the average tracking error as the meta-objective. With both fully-actuated and underactuated nonlinear planar rotorcraft subject to wind, we demonstrate that our adaptive controller outperforms other controllers trained with regression-oriented meta-learning when deployed in closed-loop for trajectory tracking control.

    @article{RichardsAzizanEtAl2023,
      author = {Richards, S. M. and Azizan, N. and Slotine, J.-J. and Pavone, M.},
      title = {Control-Oriented Meta-Learning},
      year = {2023},
      journal = {{Int. Journal of Robotics Research}},
      volume = {},
      number = {},
      pages = {},
      note = {In press},
      owner = {spenrich},
      timestamp = {2023-02-03},
      url = {https://arxiv.org/abs/2204.06716},
      keywords = {press}
    }
    
  3. D. Jalota, K. Gopalakrishnan, N. Azizan, R. Johari, and M. Pavone, “Online Learning for Traffic Routing under Unknown Preferences,” in Int. Conf. on Artificial Intelligence and Statistics, 2023.

    Abstract: In transportation networks, users typically choose routes in a decentralized and self-interested manner to minimize their individual travel costs, which, in practice, often results in inefficient overall outcomes for society. As a result, there has been a growing interest in designing road tolling schemes to cope with these efficiency losses and steer users toward a system-efficient traffic pattern. However, the efficacy of road tolling schemes often relies on having access to complete information on users’ trip attributes, such as their origin-destination (O-D) travel information and their values of time, which may not be available in practice. Motivated by this practical consideration, we propose an online learning approach to set tolls in a traffic network to drive heterogeneous users with different values of time toward a system-efficient traffic pattern. In particular, we develop a simple yet effective algorithm that adjusts tolls at each time period solely based on the observed aggregate flows on the roads of the network without relying on any additional trip attributes of users, thereby preserving user privacy. In the setting where the O-D pairs and values of time of users are drawn i.i.d. at each period, we show that our approach obtains an expected regret and road capacity violation of O(\sqrtT), where T is the number of periods over which tolls are updated. Our regret guarantee is relative to an offline oracle that has complete information on users’ trip attributes. We further establish a Ω(\sqrtT) lower bound on the regret of any algorithm, which establishes that our algorithm is optimal up to constants. Finally, we demonstrate the superior performance of our approach relative to several benchmarks on a real-world transportation network, thereby highlighting its practical applicability.

    @inproceedings{JalotaEtAl2022,
      author = {Jalota, D. and Gopalakrishnan, K. and Azizan, N. and Johari, R. and Pavone, M.},
      title = {Online Learning for Traffic Routing under Unknown Preferences},
      booktitle = {{Int. Conf. on Artificial Intelligence and Statistics}},
      year = {2023},
      keywords = {pub},
      owner = {devanshjalota},
      timestamp = {2022-05-03},
      url = {https://arxiv.org/abs/2203.17150}
    }
    
  4. R. Brown, E. Schmerling, N. Azizan, and M. Pavone, “A Unified View of SDP-based Neural Network Verification through Completely Positive Programming,” in Int. Conf. on Artificial Intelligence and Statistics, 2022.

    Abstract: Verifying that input-output relationships of a neural network conform to prescribed operational specifications is a key enabler towards deploying these networks in safety-critical applications. Semidefinite programming (SDP)-based approaches to Rectified Linear Unit (ReLU) network verification transcribe this problem into an optimization problem, where the accuracy of any such formulation reflects the level of fidelity in how the neural network computation is represented, as well as the relaxations of intractable constraints. While the literature contains much progress on improving the tightness of SDP formulations while maintaining tractability, comparatively little work has been devoted to the other extreme, i.e., how to most accurately capture the original verification problem before SDP relaxation. In this work, we develop an exact, convex formulation of verification as a completely positive program (CPP), and provide analysis showing that our formulation is minimal—the removal of any constraint fundamentally misrepresents the neural network computation. We leverage our formulation to provide a unifying view of existing approaches, and give insight into the source of large relaxation gaps observed in some cases.

    @inproceedings{BrownSchmerlingEtAl2022,
      author = {Brown, R. and Schmerling, E. and Azizan, N. and Pavone, M.},
      title = {A Unified View of SDP-based Neural Network Verification through Completely Positive Programming},
      booktitle = {{Int. Conf. on Artificial Intelligence and Statistics}},
      year = {2022},
      owner = {rabrown1},
      timestamp = {2022-02-17}
    }
    
  5. A. Sharma, N. Azizan, and M. Pavone, “Sketching Curvature for Efficient Out-of-Distribution Detection for Deep Neural Networks,” in Proc. Conf. on Uncertainty in Artificial Intelligence, 2021.

    Abstract: In order to safely deploy Deep Neural Networks (DNNs) within the perception pipelines of real-time decision making systems, there is a need for safeguards that can detect out-of-training-distribution (OoD) inputs both efficiently and accurately. Building on recent work leveraging the local curvature of DNNs to reason about epistemic uncertainty, we propose Sketching Curvature of OoD Detection (SCOD), an architecture-agnostic framework for equipping any trained DNN with a task-relevant epistemic uncertainty estimate. Offline, given a trained model and its training data, SCOD employs tools from matrix sketching to tractably compute a low-rank approximation of the Fisher information matrix, which characterizes which directions in the weight space are most influential on the predictions over the training data. Online, we estimate uncertainty by measuring how much perturbations orthogonal to these directions can alter predictions at a new test input. We apply SCOD to pre-trained networks of varying architectures on several tasks, ranging from regression to classification. We demonstrate that SCOD achieves comparable or better OoD detection performance with lower computational burden relative to existing baselines.

    @inproceedings{SharmaAzizanEtAl2021,
      author = {Sharma, A. and Azizan, N. and Pavone, M.},
      title = {Sketching Curvature for Efficient Out-of-Distribution Detection for Deep Neural Networks},
      booktitle = {{Proc. Conf. on Uncertainty in Artificial Intelligence}},
      year = {2021},
      month = jul,
      url = {https://arxiv.org/abs/2102.12567},
      owner = {apoorva},
      timestamp = {2021-05-24}
    }
    
  6. S. M. Richards, N. Azizan, J.-J. Slotine, and M. Pavone, “Adaptive-Control-Oriented Meta-Learning for Nonlinear Systems,” in Robotics: Science and Systems, Virtual, 2021.

    Abstract: Real-time adaptation is imperative to the control of robots operating in complex, dynamic environments. Adaptive control laws can endow even nonlinear systems with good trajectory tracking performance, provided that any uncertain dynamics terms are linearly parameterizable with known nonlinear features. However, it is often difficult to specify such features a priori, such as for aerodynamic disturbances on rotorcraft or interaction forces between a manipulator arm and various objects. In this paper, we turn to data-driven modeling with neural networks to learn, offline from past data, an adaptive controller with an internal parametric model of these nonlinear features. Our key insight is that we can better prepare the controller for deployment with control-oriented meta-learning of features in closed-loop simulation, rather than regression-oriented meta-learning of features to fit input-output data. Specifically, we meta-learn the adaptive controller with closed-loop tracking simulation as the base-learner and the average tracking error as the meta-objective. With a nonlinear planar rotorcraft subject to wind, we demonstrate that our adaptive controller outperforms other controllers trained with regression-oriented meta-learning when deployed in closed-loop for trajectory tracking control.

    @inproceedings{RichardsAzizanEtAl2021,
      author = {Richards, S. M. and Azizan, N. and Slotine, J.-J. and Pavone, M.},
      title = {Adaptive-Control-Oriented Meta-Learning for Nonlinear Systems},
      year = {2021},
      booktitle = {{Robotics: Science and Systems}},
      note = {},
      owner = {spenrich},
      timestamp = {2023-01-30},
      url = {https://arxiv.org/abs/2103.04490},
      address = {Virtual},
      month = jul,
      keywords = {}
    }