News

1 paper accepted to CDC 21

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Our paper on tight inner approximation of the positive-semidefinite cone [1] have been accepted to IEEE Conference on Decision and Control!

[1] [doi] T. Zheng, J. Guthrie, and E. Mallada, “Inner Approximations of the Positive-Semidefinite Cone via Grassmannian Packings,” in 60th IEEE Conference on Decision and Control (CDC), 2021, pp. 981-986.
[Bibtex] [Abstract] [Download PDF]

We investigate the problem of finding tight inner approximations of large dimensional positive semidefinite (PSD) cones. To solve this problem, we develop a novel decomposition framework of the PSD cone by means of conical combinations of smaller dimensional sub-cones. We show that many inner approximation techniques could be summarized within this framework, including the set of (scaled) diagonally dominant matrices, Factor-width k matrices, and Chordal Sparse matrices. Furthermore, we provide a more flexible family of inner approximations of the PSD cone, where we aim to arrange the sub-cones so that they are maximally separated from each other. In doing so, these approximations tend to occupy large fractions of the volume of the PSD cone. The proposed approach is connected to a classical packing problem in Riemannian Geometry. Precisely, we show that the problem of finding maximally distant sub-cones in an ambient PSD cone is equivalent to the problem of packing sub-spaces in a Grassmannian Manifold. We further leverage the existing computational methods for constructing packings in Grassmannian manifolds to build tighter approximations of the PSD cone. Numerical experiments show how the proposed framework can balance accuracy and computational complexity, to efficiently solve positive-semidefinite programs.

@inproceedings{zgm2021cdc,
  abstract = {We investigate the problem of finding tight inner approximations of large dimensional positive semidefinite (PSD) cones. To solve this problem, we develop a novel decomposition framework of the PSD cone by means of conical combinations of smaller dimensional sub-cones. We show that many inner approximation techniques could be summarized within this framework, including the set of (scaled) diagonally dominant matrices, Factor-width k matrices, and Chordal Sparse matrices. Furthermore, we provide a more flexible family of inner approximations of the PSD cone, where we aim to arrange the sub-cones so that they are maximally separated from each other. In doing so, these approximations tend to occupy large fractions of the volume of the PSD cone. The proposed approach is connected to a classical packing problem in Riemannian Geometry. Precisely, we show that the problem of finding maximally distant sub-cones in an ambient PSD cone is equivalent to the problem of packing sub-spaces in a Grassmannian Manifold. We further leverage the existing computational methods for constructing packings in Grassmannian manifolds to build tighter approximations of the PSD cone. Numerical experiments show how the proposed framework can balance accuracy and computational complexity, to efficiently solve positive-semidefinite programs.},
  author = {Zheng, Tianqi and Guthrie, James and Mallada, Enrique},
  booktitle = {60th IEEE Conference on Decision and Control (CDC)},
  doi = {10.1109/CDC45484.2021.9682923},
  grants = {EPCN-1711188, CAREER-1752362, AMPS-1736448, TRIPODS-1934979},
  month = {12},
  pages = {981-986},
  record = {presented Dec. 2022, accepted Jul. 2021, submitted Mar. 2021},
  title = {Inner Approximations of the Positive-Semidefinite Cone via Grassmannian Packings},
  url = {https://mallada.ece.jhu.edu/pubs/2021-CDC-ZGM.pdf},
  year = {2021}
}

Yan and Charalampos defended their dissertations

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Yan has defended her dissertation entitled “Leveraging Inverter-Interfaced Energy Storage for Frequency Control in Low-Inertia Power Systems” on Tuesday, June 29th!

Charalampos has defended his dissertation entitled “Designing resilient interdependent infrastructures across spatial and temporal scales” on Wednesday, June 30th!

Congratulations, Yan and Charalampos!

2 papers accepted to ICML’21

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Our papers on nullspace property for subspace-preserving recovery[1], and on convergence and implicit bias of overparametrized linear networks [2] have been accepted to the International Conference of Machine Learning (ICML), 2021.

[1] M. D. Kaba, C. You, D. R. Robinson, E. Mallada, and R. Vidal, “Characterization of Subspace-Preserving Recovery by a Nullspace Property,” in International Conference on Machine Learning (ICML), 2021, pp. 5180-5188.
[Bibtex] [Abstract] [Download PDF]

Economic dispatch and frequency regulation are typically viewed as fundamentally different problems in power systems and, hence, are typically studied separately. In this paper, we frame and study a joint problem that co-optimizes both slow timescale economic dispatch resources and fast timescale frequency regulation resources. We show how the joint problem can be decomposed without loss of optimality into slow and fast timescale sub-problems that have appealing interpretations as the economic dispatch and frequency regulation problems respectively. We solve the fast timescale sub-problem using a distributed frequency control algorithm that preserves the stability of the network during transients. We solve the slow timescale sub-problem using an efficient market mechanism that coordinates with the fast timescale sub-problem. We investigate the performance of the decomposition on the IEEE 24-bus reliability test system.

@inproceedings{kcrmv2021icml,
  abstract = {Economic dispatch and frequency regulation are typically viewed as fundamentally different problems in power systems and, hence, are typically studied separately. In this paper, we frame and study a joint problem that co-optimizes both slow timescale economic dispatch resources and fast timescale frequency regulation resources. We show how the joint problem can be decomposed without loss of optimality into slow and fast timescale sub-problems that have appealing interpretations as the economic dispatch and frequency regulation problems respectively. We solve the fast timescale sub-problem using a distributed frequency control algorithm that preserves the stability of the network during transients. We solve the slow timescale sub-problem using an efficient market mechanism that coordinates with the fast timescale sub-problem. We investigate the performance of the decomposition on the IEEE
24-bus reliability test system.},
  author = {Kaba, Mustafa Devrim and You, Chong and Robinson, Daniel R. and Mallada, Enrique and Vidal, Rene},
  booktitle = {International Conference on Machine Learning (ICML)},
  grants = {CAREER-1752362;TRIPODS-1934979;CPS-2136324},
  month = {11},
  note = {(21.5$%$ acceptance)},
  pages = {5180--5188},
  publisher = {PMLR},
  record = {accepted May 2021},
  series = {Proceedings of Machine Learning Research},
  title = {Characterization of Subspace-Preserving Recovery by a Nullspace Property},
  url = {https://mallada.ece.jhu.edu/pubs/2021-ICML-KCRMV.pdf},
  volume = {139},
  year = {2021}
}
[2] H. Min, S. Tarmoun, R. Vidal, and E. Mallada, “On the Explicit Role of Initialization on the Convergence and Implicit Bias of Overparametrized Linear Networks,” in International Conference on Machine Learning (ICML), 2021, pp. 7760-7768.
[Bibtex] [Abstract] [Download PDF]

Neural networks trained via gradient descent with random initialization and without any regularization enjoy good generalization performance in practice despite being highly overparametrized. A promising direction to explain this phenomenon is to study how initialization and overparametrization affect convergence and implicit bias of training algorithms. In this paper, we present a novel analysis of single-hidden-layer linear networks trained under gradient flow, which connects initialization, optimization, and overparametrization. Firstly, we show that the squared loss converges exponentially to its optimum at a rate that depends on the level of imbalance of the initialization. Secondly, we show that proper initialization constrains the dynamics of the network parameters to lie within an invariant set. In turn, minimizing the loss over this set leads to the min-norm solution. Finally, we show that large hidden layer width, together with (properly scaled) random initialization, ensures proximity to such an invariant set during training, allowing us to derive a novel non-asymptotic upper-bound on the distance between the trained network and the min-norm solution. 

@inproceedings{mtvm2021icml,
  abstract = {Neural networks trained via gradient descent with random initialization and without any regularization enjoy good generalization performance in practice despite being highly overparametrized. A promising direction to explain this phenomenon is to study how initialization and overparametrization affect convergence and implicit bias of training algorithms. In this paper, we present a novel analysis of single-hidden-layer linear networks trained under gradient flow, which connects initialization, optimization, and overparametrization. Firstly, we show that the squared loss converges exponentially to its optimum at a rate that depends on the level of imbalance of the initialization. Secondly, we show that proper initialization constrains the dynamics of the network parameters to lie within an invariant set. In turn, minimizing the loss over this set leads to the min-norm solution. Finally, we show that large hidden layer width, together with (properly scaled) random initialization, ensures proximity to such an invariant set during training, allowing us to derive a novel non-asymptotic upper-bound on the distance between the trained network and the min-norm solution.        },
  author = {Min, Hancheng and Tarmoun, Salma and Vidal, Rene and Mallada, Enrique},
  booktitle = {International Conference on Machine Learning (ICML)},
  grants = {TRIPODS-1934979, CAREER-1752362, AMPS-1736448},
  month = {7},
  note = {(21.5$%$ acceptance)},
  pages = {7760--7768},
  publisher = {PMLR},
  record = {accepted May 2021},
  series = {Proceedings of Machine Learning Research},
  title = {On the Explicit Role of Initialization on the Convergence and Implicit Bias of Overparametrized Linear Networks},
  url = {https://mallada.ece.jhu.edu/pubs/2021-ICML-MTVM.pdf},
  volume = {139},
  year = {2021}
}

Excellence in Teaching Award

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I received the Johns Hopkins Alumni Association Excellence in Teaching Award. https://engineering.jhu.edu/ece/2021/05/07/ece-2021-convocation-award-recipients-announced/

Epstein Institute Seminar @ USC

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I gave a talk on “Incentive Analysis and Coordination Design for Multi-timescale Electricity Markets” at Epstein Institute Seminar, USC (Hosts: Jong-Shi Pang, Suvrajeet Sen). Related publications include [1]

[1] [doi] D. Cai, E. Mallada, and A. Wierman, “Distributed optimization decomposition for joint economic dispatch and frequency regulation,” IEEE Transactions on Power Systems, vol. 32, iss. 6, pp. 4370-4385, 2017.
[Bibtex] [Abstract] [Download PDF]

Economic dispatch and frequency regulation are typically viewed as fundamentally different problems in power systems and, hence, are typically studied separately. In this paper, we frame and study a joint problem that co-optimizes both slow timescale economic dispatch resources and fast timescale frequency regulation resources. We show how the joint problem can be decomposed without loss of optimality into slow and fast timescale sub-problems that have appealing interpretations as the economic dispatch and frequency regulation problems respectively. We solve the fast timescale sub-problem using a distributed frequency control algorithm that preserves the stability of the network during transients. We solve the slow timescale sub-problem using an efficient market mechanism that coordinates with the fast timescale sub-problem. We investigate the performance of the decomposition on the IEEE 24-bus reliability test system.

@article{cmw2017tps,
  abstract = {Economic dispatch and frequency regulation are typically viewed as fundamentally different problems in power systems and, hence, are typically studied separately. In this paper, we frame and study a joint problem that co-optimizes both slow timescale economic dispatch resources and fast timescale frequency regulation resources. We show how the joint problem can be decomposed without loss of optimality into slow and fast timescale sub-problems that have appealing interpretations as the economic dispatch and frequency regulation problems respectively. We solve the fast timescale sub-problem using a distributed frequency control algorithm that preserves the stability of the network during transients. We solve the slow timescale sub-problem using an efficient market mechanism that coordinates with the fast timescale sub-problem. We investigate the performance of the decomposition on the IEEE
24-bus reliability test system.},
  author = {Cai, Desmond and Mallada, Enrique and Wierman, Adam},
  doi = {10.1109/TPWRS.2017.2682235},
  grants = {1544771},
  journal = {IEEE Transactions on Power Systems},
  keywords = {Power Networks; Markets},
  month = {11},
  number = {6},
  pages = {4370-4385},
  title = {Distributed optimization decomposition for joint economic dispatch and frequency regulation},
  url = {https://mallada.ece.jhu.edu/pubs/2017-TPS-CMW.pdf},
  volume = {32},
  year = {2017}
}