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Stochastic Gradient Descent (SGD) has played a central role in machine learning. However, it requires a carefully hand-picked stepsize for fast convergence, which is notoriously tedious and time-consuming to tune. Over the last several years, a plethora of adaptive gradient-based algorithms have emerged to ameliorate this problem. In this paper, we propose new surrogate losses to cast the problem of learning the optimal stepsizes for the stochastic optimization of a non-convex smooth objective function onto an online convex optimization problem. This allows the use of no-regret online algorithms to compute optimal stepsizes on the fly. In turn, this results in a SGD algorithm with self-tuned stepsizes that guarantees convergence rates that are automatically adaptive to the level of noise.
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This content will become publicly available on May 1, 2026
Efficient Reconstruction of Neural Mass Dynamics Modeled by Linear-Threshold Networks
This paper studies the data-driven reconstruction of firing rate dynamics of brain activity described by linear-threshold network models. Identifying the system parameters directly leads to a large number of variables and a highly non-convex objective function. Instead, our approach introduces a novel reformulation that incorporates biological organizational features and turns the identification problem into a scalar variable optimization of a discontinuous, non-convex objective function. We prove that the minimizer of the objective function is unique and establish that the solution of the optimization problem leads to the identification of all the desired system parameters. These results are the basis to introduce an algorithm to find the optimizer by searching the different regions corresponding to the domain of definition of the objective function. To deal with measurement noise in sampled data, we propose a modification of the original algorithm whose identification error is linearly bounded by the magnitude of the measurement noise. We demonstrate the effectiveness of the proposed algorithms through simulations on synthetic and experimental data.
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- Award ID(s):
- 2308640
- PAR ID:
- 10640828
- Publisher / Repository:
- IEEE
- Date Published:
- Journal Name:
- IEEE Transactions on Automatic Control
- Volume:
- 70
- Issue:
- 5
- ISSN:
- 0018-9286
- Page Range / eLocation ID:
- 2843 to 2858
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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