Optimal Rates for Pure {\varepsilon}-Differentially Private Stochastic Convex Optimization with Heavy Tails

ArXi:2604.06492v1 Announce Type: new We study stochastic convex optimization (SCO) with heavy-tailed gradients under pure epsilon-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. The minimax optimal rate for approximate (epsilon, delta)-DP SCO is known in this setting, but the pure epsilon-DP case has remained open.