Optimal Rates for Pure $\varepsilon$-Differentially Private Stochastic Convex Optimization with Heavy Tails
We study stochastic convex optimization (SCO) with heavy-tailed gradients under pure $\varepsilon$-differential privacy (DP). Instead of assuming a bound on the worst-case Lipschitz parameter of the loss, we assume only a bounded $k$-th moment. This assumption allows for unbounded, heavy-tailed stochastic gradient distributions, and can yield sharper excess risk bounds. Prior work characterized the minimax optimal rate for $ρ$-zero-concentrated DP SCO up to logarithmic factors in this setting, but the pure $\varepsilon$-DP case has remained open. We characterize the minimax optimal excess-risk rate for pure $\varepsilon$-DP heavy-tailed SCO up to logarithmic factors. Our algorithm achieve...
| Authors | Andrew Lowy |
|---|---|
| Primary category | cs.LG |
| Published | 7 April 2026 |
| Last updated at source | 5 May 2026 |
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