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Distributionally robust optimization (DRO) is a powerful framework for training robust models against data distribution shifts. This paper focuses on constrained DRO, which has an explicit characterization of the robustness level. Existing studies on constrained DRO mostly focus on convex loss function, and exclude the practical and challenging case with non-convex loss function, e.g., neural network. This paper develops a stochastic algorithm and its performance analysis for non-convex constrained DRO. The computational complexity of our stochastic algorithm at each iteration is independent of the overall dataset size, and thus is suitable for large-scale applications. We focus on the general Cressie-Read family divergence defined uncertainty set which includes chi^2-divergences as a special case. We prove that our algorithm finds an epsilon-stationary point with an improved computational complexity than existing methods. Our method also applies to the smoothed conditional value at risk (CVaR) DRO.
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A Reduced-Complexity Trajectory Generation Algorithm for Three-Body Regimes With Minimum Predefined Data
Computational limitations and Big Data analysis pose challenges in seeking efficient techniques to predict trajectories in three-body dynamics. Thus, a reduced-complexity classical algorithm is proposed utilizing predefined spacecraft's position and velocity data to achieve precise and accurate orbital trajectories of the spacecraft within three-body dynamics. The proposed algorithm seamlessly solves polynomial interpolation along with the boundary and interior conditions without the need for the spacecraft's acceleration data. Once the algorithm is derived, it will be tested across a diverse variety of periodic trajectories in the Earth-Moon system. Moreover, a comparative analysis is performed to evaluate the time complexity of the proposed algorithm compared with conventional orbit propagators. Finally, the proposed algorithm will be utilized and extended to learn and update distant retrograde orbits (DRO) while training a neural network with several initial conditions composing minimum predefined data. After the training is done, the neural network is used to accurately predict DRO trajectories for a given initial condition, demonstrating the exceptional accuracy and effectiveness of the proposed learning process.
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- Award ID(s):
- 2229473
- PAR ID:
- 10556161
- Publisher / Repository:
- IEEE Transactions on Aerospace and Electronic Systems
- Date Published:
- Journal Name:
- IEEE Transactions on Aerospace and Electronic Systems
- ISSN:
- 0018-9251
- Page Range / eLocation ID:
- 1 to 15
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1109/TAES.2024.3465502
