Differentially Private Regularized Stochastic Convex Optimization with Heavy-Tailed Data
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Bibliographic record
Abstract
Existing privacy guarantees for convex optimization algorithms do not apply to heavy-tailed data with regularized estimation.This is a notable gap in the differential privacy (DP) literature, given the broad prevalence of non-Gaussian data and penalized optimization problems.In this work, we propose three (ϵ, δ)-DP methods for regularized convex optimization and derive bounds on their population excess risks in a framework that accommodates heavy-tailed data with fewer assumptions (relative to previous works).This work is the first to address DP in generic regularized convex optimization problems with heavy-tailed responses.Two of our methods augment a basic (ϵ, δ)-DP algorithm with robust procedures for privately estimating minibatch gradients.Our numerical analyses highlight the performance of our methods relative to data dimensionality, batch size, and privacy budget, and suggest settings where each approach is favorable.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.005 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.002 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it