arXiv:2505.13299v2 Announce Type: replace-cross
Abstract: This paper considers the estimation of quantiles via a smoothed version of the stochastic gradient descent (SGD) algorithm. By smoothing the...
By Likai Chen, Georg Keilbar, Wei Biao Wu
Bilevel optimization (BLO) is fundamental to hierarchical decision-making but suffers from critical instability under heavy-tailed stochastic noise. Existing variance-reduction techniques typically rely on myopic magnitude checks, which fail to distinguish informative geometric signals from impulsive outliers.
Occupancy-based Quantile Risk Control (OQRC) is a new method that extends conformal risk control to quantile-based risk measures. It partitions the loss space using ordered calibration losses, estimates the distribution of test losses in each bin, and upper-bounds the risk by the maximum loss per bin. The approach guarantees finite-sample validity, achieving tight risk control bounds that converge at a rate of σ(n^{-1/2}) and reducing the risk gap by up to 78.64% in experiments.
By Zihao Shi, Huajun Xi, Bingyi Jing, Hongxin Wei
arXiv:2606. 28652v1 Announce Type: cross Abstract: Online high-dimensional regression requires algorithms that can update sequentially while preserving structural sparsity.
By Zitian Zhou, Nan Lin
The paper introduces a distributionally robust method for learning hyperparameters of first‑order convex optimization algorithms. By minimizing a Wasserstein‑robust performance estimation problem over a dataset of problem instances, the approach interpolates between classical learning‑to‑optimize (L2O) and worst‑case PEP design. The authors solve the resulting problem with stochastic gradient descent, provide high‑probability risk bounds, and demonstrate that the learned algorithms outperform both worst‑case optimal and vanilla L2O baselines on logistic regression, LASSO, and linear programming tasks.
By Vinit Ranjan, Jisun Park, Bartolomeo Stellato
Occupancy-based Quantile Risk Control (OQRC) is a new method that extends conformal risk control to quantile-based risk measures while avoiding excessive conservatism and providing rigorous finite-sample guarantees. It works by partitioning the loss space using ordered calibration losses, estimating the distribution of test losses in each bin, and bounding the risk by the maximum loss in each bin. The authors prove that OQRC achieves tight risk control bounds with a finite-sample guarantee that converges at a rate of π(n−½), and experiments show it can reduce the risk gap by up to 78.64% on common benchmarks.