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Tag: penalty

  • Efficient Penalty-Based Bilevel Methods: Improved Analysis, Novel Updates, and Flatness Condition

    Efficient Penalty-Based Bilevel Methods: Improved Analysis, Novel Updates, and Flatness Condition arXiv:2511.16796v1 Announce Type: cross Abstract: Penalty-based methods have become popular for solving bilevel optimization (BLO) problems, thanks to their effective first-order nature. However, they often require inner-loop iterations to solve the lower-level (LL) problem and small outer-loop step sizes to handle the increased smoothness…

  • Proximal Iteration for Nonlinear Adaptive Lasso

    Proximal Iteration for Nonlinear Adaptive Lasso arXiv:2412.05726v1 Announce Type: new Abstract: Augmenting a smooth cost function with an $ell_1$ penalty allows analysts to efficiently conduct estimation and variable selection simultaneously in sophisticated models and can be efficiently implemented using proximal gradient methods. However, one drawback of the $ell_1$ penalty is bias: nonzero parameters are underestimated…