Quantile-based Loss Filtering for Outlier-Robust Stochastic Gradient Descent

We study loss-based filtering for finite-sum optimization with a subset of corrupted component functions whose gradients may be highly unreliable. Motivated by minimum-loss-based SGD (min-$k$-loss) and quantile-based methods for corrupted linear systems, we propose and analyze a general loss-filtering framework -- Quantile-\(k\)-Loss SGD (Q\(k\)L-SGD) -- that samples \(k\) component losses at each iteration and updates using an index chosen uniformly from the lower empirical \(q\)-quantile. We prove linear convergence of this family of methods under standard convexity assumptions, requiring the sample size to scale with the number of corruptions and a subset strong-convexity threshold. Fo...

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