Enrique Mallada

3 papers accepted to CDC

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Our papers on Dissipative Gradient Descent-Ascent algorithms for min-max problems [1], Accelerated saddle flow dynamics [2], and invertibility of sparse linear dynamical systems [3] have been accepted to the 63rd IEEE Conference on Decision and Control. Congrats to the leading students Tianqi, Yingzhu, Kyle, and to all the rest of the team!

[1] T. Zheng, N. Loizou, P. You, and E. Mallada, “Dissipative Gradient Descent Ascent Method: A Control Theory Inspired Algorithm for Min-max Optimization,” in 63rd IEEE Conference on Decision and Control (CDC), 2024.
[Bibtex] [Abstract] [Download PDF]

Gradient Descent Ascent (GDA) methods for min-max optimization problems typically produce oscillatory behavior that can lead to instability, e.g., in bilinear settings. To address this problem, we introduce a dissipation term into the GDA updates to dampen these oscillations. The proposed Dissipative GDA (DGDA) method can be seen as performing standard GDA on a state-augmented and regularized saddle function that does not strictly introduce additional convexity/concavity. We theoretically show the linear convergence of DGDA in the bilinear and strongly convex-strongly concave settings and assess its performance by comparing DGDA with other methods such as GDA, Extra-Gradient (EG), and Optimistic GDA. Our findings demonstrate that DGDA surpasses these methods, achieving superior convergence rates. We support our claims with two numerical examples that showcase DGDA’s effectiveness in solving saddle point problems.

@inproceedings{zlym2024cdc,
  abstract = {Gradient Descent Ascent (GDA) methods for min-max optimization problems typically produce oscillatory behavior that can lead to instability, e.g., in bilinear settings.
To address this problem, we introduce a dissipation term into the GDA updates to dampen these oscillations. The proposed Dissipative GDA (DGDA) method can be seen as performing standard GDA on a state-augmented and regularized saddle function that does not strictly introduce additional convexity/concavity. We theoretically show the linear convergence of DGDA in the bilinear and strongly convex-strongly concave settings and assess its performance by comparing DGDA with other methods such as GDA, Extra-Gradient (EG), and Optimistic GDA.
Our findings demonstrate that DGDA surpasses these methods, achieving superior convergence rates. We support our claims with two numerical examples that showcase DGDA's effectiveness in solving saddle point problems.},
  author = {Zheng, Tianqi and Loizou, Nicolas and You, Pengcheng and Mallada, Enrique},
  booktitle = {63rd IEEE Conference on Decision and Control (CDC)},
  grants = {CPS-2136324, Global-Centers-2330450},
  month = {07},
  note = {also in L-CSS},
  pubstate = {accepted, submitted Mar 2024},
  title = {Dissipative Gradient Descent Ascent Method: A Control Theory Inspired Algorithm for Min-max Optimization},
  url = {https://mallada.ece.jhu.edu/pubs/2024-LCSS-ZLYM.pdf},
  year = {2024}
}
[2] Y. Liu, E. Mallada, Z. Li, and P. You, “Accelerated Saddle Flow Dynamics for Bilinearly Coupled Minimax Problems,” in 63rd IEEE Conference on Decision and Control (CDC), 2024.
[Bibtex] [Abstract] [Download PDF]

Minimax problems have attracted much attention due to various applications in constrained optimization problems and zero-sum games. Identifying saddle points within these problems is crucial, and saddle flow dynamics offer a straightforward yet useful approach. This study focuses on a class of bilinearly coupled minimax problems and designs an accelerated algorithm based on saddle flow dynamics that achieves a convergence rate beyond stereotype limits. The algorithm is derived based on a sequential two-step transformation of the objective function. First, a change of variable is aimed at a better-conditioned saddle function. Second, a proximal regularization, when staggered with the first step, guarantees strong convexity-strong concavity of the objective function that can be tuned for accelerated exponential convergence. Besides, such an approach can be extended to a class of weakly convex-weakly concave functions and still achieve exponential convergence to one stationary point. The theory is verified by a numerical test on an affine equality-constrained convex optimization problem.

@inproceedings{lmly2024cdc,
  abstract = {Minimax problems have attracted much attention due to various applications in constrained optimization problems and zero-sum games. Identifying saddle points within these problems is crucial, and saddle flow dynamics offer a straightforward yet useful approach. This study focuses on a class of bilinearly coupled minimax problems and designs an accelerated algorithm based on saddle flow dynamics that achieves a convergence rate beyond stereotype limits.  The algorithm is derived based on a sequential two-step transformation of the objective function. First, a change of variable is aimed at a better-conditioned saddle function. Second, a proximal regularization, when staggered with the first step, guarantees strong convexity-strong concavity of the objective function that can be tuned for accelerated exponential convergence.
Besides, such an approach can be extended to a class of weakly convex-weakly concave functions and still achieve exponential convergence to one stationary point. The theory is verified by a numerical test on an affine equality-constrained convex optimization problem.},
  author = {Liu, Yingzhu and Mallada, Enrique and Li, Zhongkui and You, Pengcheng},
  booktitle = {63rd IEEE Conference on Decision and Control (CDC)},
  grants = {CPS-2136324, Global-Centers-2330450},
  month = {07},
  pubstate = {accepted, submitted Mar 2024},
  title = {Accelerated Saddle Flow Dynamics for Bilinearly Coupled Minimax Problems},
  url = {https://mallada.ece.jhu.edu/pubs/2024-Preprint-LMLY.pdf},
  year = {2024}
}
[3] K. Poe, E. Mallada, and R. Vidal, “Invertibility of Discrete-Time Linear Systems with Sparse Inputs,” in 63rd IEEE Conference on Decision and Control (CDC), 2024.
[Bibtex] [Abstract] [Download PDF]

One of the fundamental problems of interest for discrete-time linear systems is whether its input sequence may be recovered given its output sequence, a.k.a. the left inversion problem. Many conditions on the state space geometry, dynamics, and spectral structure of a system have been used to characterize the well-posedness of this problem, without assumptions on the inputs. However, certain structural assumptions, such as input sparsity, have been shown to translate to practical gains in the performance of inversion algorithms, surpassing classical guarantees. Establishing necessary and sufficient conditions for left invertibility of systems with sparse inputs is therefore a crucial step toward understanding the performance limits of system inversion under structured input assumptions. In this work, we provide the first necessary and sufficient characterizations of left invertibility for linear systems with sparse inputs, echoing classic characterizations for standard linear systems. The key insight in deriving these results is in establishing the existence of two novel geometric invariants unique to the sparse-input setting, the weakly unobservable and strongly reachable subspace arrangements. By means of a concrete example, we demonstrate the utility of these characterizations. We conclude by discussing extensions and applications of this framework to several related problems in sparse control.

@inproceedings{pmv2024cdc,
  abstract = {One of the fundamental problems of interest for discrete-time linear systems is whether its input sequence may be recovered given its output sequence, a.k.a. the left inversion problem. Many conditions on the state space geometry, dynamics, and spectral structure of a system have been used to characterize the well-posedness of this problem, without assumptions on the inputs. However, certain structural assumptions, such as input sparsity, have been shown to translate to practical gains in the performance of inversion algorithms, surpassing classical guarantees. Establishing necessary and sufficient conditions for left invertibility of systems with sparse inputs is therefore a crucial step toward understanding the performance limits of system inversion under structured input assumptions. In this work, we provide the first necessary and sufficient characterizations of left invertibility for linear systems with sparse inputs,  echoing classic characterizations for standard linear systems. The key insight in deriving these results is in establishing the existence of two novel geometric invariants unique to the sparse-input setting, the weakly unobservable and strongly reachable subspace arrangements. By means of a concrete example, we demonstrate the utility of these characterizations. We conclude by discussing extensions and applications of this framework to several related problems in sparse control.},
  author = {Poe, Kyle and Mallada, Enrique and Vidal, Rene},
  booktitle = {63rd IEEE Conference on Decision and Control (CDC)},
  grants = {CPS-2136324, Global-Centers-2330450},
  month = {07},
  pubstate = {accepted, submitted Mar 2024},
  title = {Invertibility of Discrete-Time Linear Systems with Sparse Inputs},
  url = {https://mallada.ece.jhu.edu/pubs/2024-Preprint-PMV.pdf},
  year = {2024}
}

1 paper accepted to L-CSS

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Our paper on Dissipative Gradient Descent-Ascent algorithms for min-max problems [1] has been accepted to the IEEE Control Systems Letters. Congrats Tianqi!

[1] [doi] T. Zheng, N. Loizou, P. You, and E. Mallada, “Dissipative Gradient Descent Ascent Method: A Control Theory Inspired Algorithm for Min-max Optimization,” IEEE Control Systems Letters (L-CSS), 2024.
[Bibtex] [Abstract] [Download PDF]

Gradient Descent Ascent (GDA) methods for min-max optimization problems typically produce oscillatory behavior that can lead to instability, e.g., in bilinear settings. To address this problem, we introduce a dissipation term into the GDA updates to dampen these oscillations. The proposed Dissipative GDA (DGDA) method can be seen as performing standard GDA on a state-augmented and regularized saddle function that does not strictly introduce additional convexity/concavity. We theoretically show the linear convergence of DGDA in the bilinear and strongly convex-strongly concave settings and assess its performance by comparing DGDA with other methods such as GDA, Extra-Gradient (EG), and Optimistic GDA. Our findings demonstrate that DGDA surpasses these methods, achieving superior convergence rates. We support our claims with two numerical examples that showcase DGDA’s effectiveness in solving saddle point problems.

@article{zlym2024lcss,
  abstract = {Gradient Descent Ascent (GDA) methods for min-max optimization problems typically produce oscillatory behavior that can lead to instability, e.g., in bilinear settings.
To address this problem, we introduce a dissipation term into the GDA updates to dampen these oscillations. The proposed Dissipative GDA (DGDA) method can be seen as performing standard GDA on a state-augmented and regularized saddle function that does not strictly introduce additional convexity/concavity. We theoretically show the linear convergence of DGDA in the bilinear and strongly convex-strongly concave settings and assess its performance by comparing DGDA with other methods such as GDA, Extra-Gradient (EG), and Optimistic GDA.
Our findings demonstrate that DGDA surpasses these methods, achieving superior convergence rates. We support our claims with two numerical examples that showcase DGDA's effectiveness in solving saddle point problems.},
  author = {Zheng, Tianqi and Loizou, Nicolas and You, Pengcheng and Mallada, Enrique},
  doi = {10.1109/LCSYS.2024.3413004},
  grants = {CPS-2136324, Global-Centers-2330450},
  journal = {IEEE Control Systems Letters (L-CSS)},
  month = {06},
  record = {published, accepted May 2024, submitted Mar 2024},
  title = {Dissipative Gradient Descent Ascent Method: A Control Theory Inspired Algorithm for Min-max Optimization},
  url = {https://mallada.ece.jhu.edu/pubs/2024-LCSS-ZLYM.pdf},
  year = {2024}
}

2 papers accepted to PES General Meeting

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Our papers on decentralized stability analysis for grid forming control [1] and on grid forming based grid shaping [2] have been accepted to PES General Meeting!

[1] Z. Siahaan, E. Mallada, and S. Geng, “Decentralized Stability Criteria for Grid-Forming Control in Inverter-Based Power Systems,” in PES General Meeting, 2024, pp. 1-5.
[Bibtex] [Abstract] [Download PDF]

This paper presents a decentralized stability analysis of power systems comprising grid-forming (GFM) inverters. We leverage a decentralized stability framework capable of ensuring the stability of the entire interconnection through individual assessments at each bus. The key novelty lies in incorporating voltage dynamics and their coupling with reactive power, in addition to the angle dynamics and their coupling with active power. We perform loop transformation to address the challenge posed by the non-Laplacian nature of the network Jacobian matrix in this case. This methodology is applied to characterize conditions on the droop gains of GFM controllers that can preserve system-wide stability. Our proposed stability criteria exhibit scalability and robustness, and can be extended to accommodate delays, variations in network conditions, and plug-and-play of new components in the network.

@inproceedings{smg2024pesgm,
  abstract = {This paper presents a decentralized stability analysis of power systems comprising grid-forming (GFM) inverters. We leverage a decentralized stability framework capable of ensuring the stability of the entire interconnection through individual assessments at each bus. The key novelty lies in incorporating voltage dynamics and their coupling with reactive power, in addition to the angle dynamics and their coupling with active power. We perform loop transformation to address the challenge posed by the non-Laplacian nature of the network Jacobian matrix in this case. This methodology is applied to characterize conditions on the droop gains of GFM controllers that can preserve system-wide stability. Our proposed stability criteria exhibit scalability and robustness, and can be extended to accommodate delays, variations in network conditions, and plug-and-play of new components in the network.},
  author = {Siahaan, Zudika and Mallada, Enrique and Geng, Sijia},
  booktitle = {PES General Meeting},
  month = {06},
  pages = {1-5},
  pubstate = {presented},
  record = {accepted Mar. 2024, submitted Nov. 2023},
  title = {Decentralized Stability Criteria for Grid-Forming Control in Inverter-Based Power Systems},
  url = {https://mallada.ece.jhu.edu/pubs/2024-PESGM-SMG.pdf},
  year = {2024}
}
[2] B. K. Poolla, Y. Lin, A. Bernstein, E. Mallada, and D. Groß, “Dynamic Shaping of Grid Response of Multi-Machine Multi-Inverter Systems Through Grid-Forming IBRs,” in PES General Meeting, 2024, pp. 1-5.
[Bibtex] [Abstract] [Download PDF]

We consider the problem of controlling the frequency response of weakly-coupled multi-machine multi-inverter low-inertia power systems via grid-forming inverter-based resources (IBRs). In contrast to existing methods, our approach relies on dividing the larger system into multiple strongly-coupled subsystems, without ignoring either the underlying network or approximating the subsystem response as an aggregate harmonic mean model. Rather, through a structured clustering and recursive dynamic shaping approach, the frequency response of the overall system to load perturbations is shaped appropriately. We demonstrate the proposed approach for a three-node triangular configuration and a small-scale radial network. Furthermore, previous synchronization analysis for heterogeneous systems requires the machines to satisfy certain proportionality property. In our approach, the effective transfer functions for each cluster can be tuned by the IBRs to satisfy such property, enabling us to apply the shaping control to systems with a wider range of heterogeneous machines.

@inproceedings{plbmg2024pesgm,
  abstract = {We consider the problem of controlling the frequency response of weakly-coupled multi-machine multi-inverter low-inertia power systems via grid-forming inverter-based resources (IBRs). In contrast to existing methods, our approach relies on dividing the larger system into multiple strongly-coupled subsystems, without ignoring either the underlying network or approximating the subsystem response as an aggregate harmonic mean model. Rather, through a structured clustering and recursive dynamic shaping approach, the frequency response of the overall system to load perturbations is shaped appropriately. We demonstrate the proposed approach for a three-node triangular configuration and a small-scale radial network. Furthermore, previous synchronization analysis for heterogeneous systems requires the machines to satisfy certain proportionality property. In our approach, the effective transfer functions for each cluster can be tuned by the IBRs to satisfy such property, enabling us to apply the shaping control to systems with a wider range of heterogeneous machines.},
  author = {Poolla, Bala Kameshwar and Lin, Yashen and Bernstein, Andrey and Mallada, Enrique and Groß, Dominic},
  booktitle = {PES General Meeting},
  month = {06},
  pages = {1-5},
  pubstate = {presented},
  record = {accepted Mar. 2024, submitted Nov. 2023},
  title = {Dynamic Shaping of Grid Response of Multi-Machine Multi-Inverter Systems Through Grid-Forming IBRs},
  url = {https://mallada.ece.jhu.edu/pubs/2024-PESGM-PLBMG.pdf},
  year = {2024}
}

1 paper accepted to ICLR

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Our paper on Early Neuron Alignment in Two-layer ReLU Networks [1] has been accepted to the International Conference on Representation Learning. Congrats Hancheng!

[1] H. Min, R. Vidal, and E. Mallada, “Early Neuron Alignment in Two-layer ReLU Networks with Small Initialization,” in International Conference on Representation Learning (ICLR), 2024.
[Bibtex] [Abstract] [Download PDF]

This paper studies the problem of training a two-layer ReLU network for binary classification using gradient flow with small initialization. We consider a training dataset with well-separated input vectors: Any pair of input data with the same label are positively correlated, and any pair with different labels are negatively correlated. Our analysis shows that, during the early phase of training, neurons in the first layer try to align with either the positive data or the negative data, depending on its corresponding weight on the second layer. A careful analysis of the neurons’ directional dynamics allows us to provide an $\mathcalO(\fracłog n\sqrtμ)$ upper bound on the time it takes for all neurons to achieve good alignment with the input data, where $n$ is the number of data points and $μ$ measures how well the data are separated. After the early alignment phase, the loss converges to zero at a $\mathcalO(\frac1t)$ rate, and the weight matrix on the first layer is approximately low-rank. Numerical experiments on the MNIST dataset illustrate our theoretical findings.

@inproceedings{mvm2024iclr,
  abstract = {This paper studies the problem of training a two-layer ReLU network for binary classification using gradient flow with small initialization. We consider a training dataset with well-separated input vectors: Any pair of input data with the same label are positively correlated, and any pair with different labels are negatively correlated. Our analysis shows that, during the early phase of training, neurons in the first layer try to align with either the positive data or the negative data, depending on its corresponding weight on the second layer. A careful analysis of the neurons' directional dynamics allows us to provide an $\mathcalO(\fracłog n\sqrtμ)$ upper bound on the time it takes for all neurons to achieve good alignment with the input data, where $n$ is the number of data points and $μ$ measures how well the data are separated. After the early alignment phase, the loss converges to zero at a $\mathcalO(\frac1t)$ rate, and the weight matrix on the first layer is approximately low-rank. Numerical experiments on the MNIST dataset illustrate our theoretical findings.},
  author = {Min, Hancheng and Vidal, Rene and Mallada, Enrique},
  booktitle = {International Conference on Representation Learning (ICLR)},
  grants = {CAREER-1752362},
  month = {05},
  record = {published, accepted Jan 2024, submitted Sep 2023},
  title = {Early Neuron Alignment in Two-layer ReLU Networks with Small Initialization},
  url = {https://mallada.ece.jhu.edu/pubs/2024-ICLR-MVM.pdf},
  year = {2024}
}

1 paper accepted to IEEE TEMPR

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Our paper on market power mitigation in two-stage markets [1] has been accepted to Transactions on Energy Markets, Policy, and Regulation!

[1] [doi] R. K. Bansal, Y. Chen, P. You, and E. Mallada, “Market Power Mitigation in Two-stage Electricity Market with Supply Function and Quantity Bidding,” IEEE Transactions on Energy Markets, Policy and Regulation, vol. 1, iss. 4, pp. 512-522, 2023.
[Bibtex] [Abstract] [Download PDF]

The main goal of a sequential two-stage electricity market—e.g., day-ahead and real-time markets—is to operate efficiently. However, the price difference across stages due to inadequate competition and unforeseen circumstances leads to undesirable price manipulation. To mitigate this, some Inde- pendent System Operators (ISOs) proposed system-level market power mitigation (MPM) policies in addition to existing local policies. These policies aim to substitute noncompetitive bids with a default bid based on estimated generator costs. However, these policies may lead to unintended consequences when implemented without accounting for the conflicting interest of participants. In this paper, we model the competition between generators (bidding supply functions) and loads (bidding quantity) in a two-stage market with a stage-wise MPM policy. An equilibrium analysis shows that a real-time MPM policy leads to equilibrium loss, meaning no stable market outcome (Nash equilibrium) exists. A day-ahead MPM policy, besides, leads to a Stackelberg-Nash game with loads acting as leaders and generators as followers. In this setting, loads become winners, i.e., their aggregate payment is always less than competitive payments. Moreover, comparison with standard market equilibrium highlights that markets are better off without such policies. Finally, numerical studies highlight the impact of heterogeneity and load size on market equilibrium.

@article{bcym2023tempr,
  abstract = {The main goal of a sequential two-stage electricity market---e.g., day-ahead and real-time markets---is to operate efficiently. However, the price difference across stages due to inadequate competition and unforeseen circumstances leads to undesirable price manipulation. To mitigate this, some Inde- pendent System Operators (ISOs) proposed system-level market power mitigation (MPM) policies in addition to existing local policies. These policies aim to substitute noncompetitive bids with a default bid based on estimated generator costs. However, these policies may lead to unintended consequences when implemented without accounting for the conflicting interest of participants. In this paper, we model the competition between generators (bidding supply functions) and loads (bidding quantity) in a two-stage market with a stage-wise MPM policy. An equilibrium analysis shows that a real-time MPM policy leads to equilibrium loss, meaning no stable market outcome (Nash equilibrium) exists. A day-ahead MPM policy, besides, leads to a Stackelberg-Nash game with loads acting as leaders and generators as followers. In this setting, loads become winners, i.e., their aggregate payment is always less than competitive payments. Moreover, comparison with standard market equilibrium highlights that markets are better off without such policies. Finally, numerical studies highlight the impact of heterogeneity and load size on market equilibrium.},
  author = {Bansal, Rajni Kant and Chen, Yue and You, Pengcheng and Mallada, Enrique},
  doi = {10.1109/TEMPR.2023.3318149},
  grants = {CAREER-1752362, CPS-2136324, EPICS-2330450},
  journal = {IEEE Transactions on Energy Markets, Policy and Regulation},
  month = {12},
  number = {4},
  pages = {512-522},
  record = {published, online Sep 2023, revised July 2023, under revision May 2023, submitted Jan 2023},
  title = {Market Power Mitigation in Two-stage Electricity Market with Supply Function and Quantity Bidding},
  url = {https://mallada.ece.jhu.edu/pubs/2023-TEMPR-BCYM.pdf},
  volume = {1},
  year = {2023}
}

Tianqi defended his dissertation

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Tianqi Zheng, an ECE Ph.D. student in our lab, defended his dissertation entitled “Online decision-making for dynamical systems: Model-based and data-driven approaches” on Tuesday, September 5th. Congratulations!

Rajni defended his dissertation

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Rajni Kant Bansal, a MechE Ph.D. student in our lab, defended his dissertation entitled “Efficiency and Market Power in Electricity Markets with Inelastic Demand, Energy Storage, and Hybrid Energy Resources” on Wednesday, August 30th. Congratulations!