DP-EGGROLL: Centered Fitness-Vector Privatization for Backprop-Free Differentially Private Optimization

Evolution strategies optimize through fitness evaluations, but standard ES exposes data-dependent fitness values. We introduce DP-EGGROLL, a central-DP mechanism for EGGROLL-style population optimization with decomposable supervised losses. Each private step forms per-example candidate-loss vectors, mean-centers each row across candidates, clips the centered row, averages with a fixed nominal denominator, and adds calibrated Gaussian noise; reward shaping and the ES update are post-processing. Clipping gives the $C/m$ add/remove sensitivity bound, while centering removes common-mode loss before clipping. We evaluate 10 public tabular benchmarks across five privacy budgets, using 10 final seeds and equal 32-configuration HPO budgets for fast DP-AdamW, scalar DP-ZO, centered DP-EGGROLL, and independently tuned uncentered DP-EGGROLL. Each selected final run is accounted as an individual $(\varepsilon,10^{-5})$-DP run; multi-configuration HPO is a benchmark protocol, not a single-run deployment guarantee. On tabular classification, centered DP-EGGROLL is practically non-inferior to fast DP-AdamW on 22/25 AUROC endpoints and is faster per step in all 25 classification settings. Centering improves over tuned uncentered DP-EGGROLL on all 25 classification AUROC endpoints. Neural experiments include end-to-end small MLPs and a low-rank adapter stress test; both reinforce that centered population-vector privatization carries more signal than scalar DP-ZO. Regression is more heterogeneous, with centered DP-EGGROLL practically non-inferior on 14/25 RMSE endpoints.