Privacy‐Preserving Finite‐Bit Distributed Optimisation via Difference‐Transferred Gradient Tracking

ABSTRACT

This paper develops a finite‐bit distributed optimisation algorithm based on Aug‐DGM. A difference‐transferred realisation allows arbitrary auxiliary‐variable initialisation, and a trajectory‐equivalent incremental implementation communicates two native increments using synchronised predictive quantisers. Fresh independent modular masks provide information‐theoretic secrecy of finite‐alphabet symbols against an external passive eavesdropper. A separate conservative perturbation makes the isolated native‐increment masking map locally non‐injective; no privacy guarantee against an honest‐but‐curious neighbour's complete observation history is asserted. Under explicit capacity and stability conditions, the quantisers do not saturate, the optimisation iterates converge exactly at a linear rate and the cumulative squared communication‐signal norms are finite. Additional post‐reconstruction errors of difference form telescope to their current error levels; exact convergence is preserved when those levels decay geometrically and nonsaturation holds. Numerical examples illustrate the finite‐horizon behaviour and evaluate a parameter choice certified by the sufficient capacity bound.