Private Stochastic Convex Optimization and Sparse Learning with Heavy-tailed Data Revisited
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Bibliographic record
Abstract
In this paper, we revisit the problem of Differentially Private Stochastic Convex Optimization (DP-SCO) with heavy-tailed data, where the gradient of the loss function has bounded moments. Instead of the case where the loss function is Lipschitz or each coordinate of the gradient has bounded second moment studied previously, we consider a relaxed scenario where each coordinate of the gradient only has bounded (1+v)-th moment with some v∈(0, 1]. Firstly, we start from the one dimensional private mean estimation for heavy-tailed distributions. We propose a novel robust and private mean estimator which is optimal. Based on its idea, we then extend to the general d-dimensional space and study DP-SCO with general convex and strongly convex loss functions. We also provide lower bounds for these two classes of loss under our setting and show that our upper bounds are optimal up to a factor of O(Poly(d)). To address the high dimensionality issue, we also study DP-SCO with heavy-tailed gradient under some sparsity constraint (DP sparse learning). We propose a new method and show it is also optimal up to a factor of O(s*), where s* is the underlying sparsity of the constraint.
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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 | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.003 | 0.002 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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