OFDM-Assisted Over-the-Air Computation With Privacy Protection in Federated Learning

Abstract

Federated Learning (FL) is an emerging distributed machine learning paradigm that protects data privacy by performing iterative local training and gradient aggregation across multiple devices and a central server. Over-the-air computation enables fast aggregation when multiple devices need to upload their local gradients to the central server simultaneously. Orthogonal Frequency Division Modulation (OFDM) further accelerates this process by allowing concurrent symbol transmission over multiple fading channels. To address the challenge of non-linear distortion at the OFDM transmitter’s amplifier while ensuring privacy for each device, we propose a novel aggregation method: OFDM-assisted over-the-air computation for differential privacy (DP) in FL (OA2DPFL). This method first normalizes local gradients and then adds uniformly distributed artificial noise before uploading them to the central server. Our analysis demonstrates that the proposed approach effectively controls peak transmit power and establishes a quantitative relationship between the variance of artificial noise and the level of DP protection. Furthermore, we rigorously prove that OA2DPFL achieves a zero <italic>stationary</italic> optimality gap under general <inline-formula><tex-math notation="LaTeX">$\displaystyle L$</tex-math><alternatives><mml:math><mml:mstyle scriptlevel="0" displaystyle="true"><mml:mi>L</mml:mi></mml:mstyle></mml:math><inline-graphic xlink:href="fan-ieq1-3715532.gif"/></alternatives></inline-formula>-smooth (non-convex) loss functions, and a zero <italic>global</italic> optimality gap under <inline-formula><tex-math notation="LaTeX">$\displaystyle L$</tex-math><alternatives><mml:math><mml:mstyle scriptlevel="0" displaystyle="true"><mml:mi>L</mml:mi></mml:mstyle></mml:math><inline-graphic xlink:href="fan-ieq2-3715532.gif"/></alternatives></inline-formula>-smooth and strongly convex loss functions, both with a convergence rate of <inline-formula><tex-math notation="LaTeX">$\displaystyle \mathcal {O}(1/T^{1/2-\rho })$</tex-math><alternatives><mml:math><mml:mstyle scriptlevel="0" displaystyle="true"><mml:mrow><mml:mi mathvariant="script">O</mml:mi><mml:mo>(</mml:mo><mml:mn>1</mml:mn><mml:mo>/</mml:mo><mml:msup><mml:mi>T</mml:mi><mml:mrow><mml:mn>1</mml:mn><mml:mo>/</mml:mo><mml:mn>2</mml:mn><mml:mo>-</mml:mo><mml:mi>ρ</mml:mi></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:mstyle></mml:math><inline-graphic xlink:href="fan-ieq3-3715532.gif"/></alternatives></inline-formula>, where <inline-formula><tex-math notation="LaTeX">$\displaystyle T$</tex-math><alternatives><mml:math><mml:mstyle scriptlevel="0" displaystyle="true"><mml:mi>T</mml:mi></mml:mstyle></mml:math><inline-graphic xlink:href="fan-ieq4-3715532.gif"/></alternatives></inline-formula> is the iteration number and <inline-formula><tex-math notation="LaTeX">$\displaystyle \rho \in (0,1/2)$</tex-math><alternatives><mml:math><mml:mstyle scriptlevel="0" displaystyle="true"><mml:mrow><mml:mi>ρ</mml:mi><mml:mo>∈</mml:mo><mml:mo>(</mml:mo><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mn>1</mml:mn><mml:mo>/</mml:mo><mml:mn>2</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:mstyle></mml:math><inline-graphic xlink:href="fan-ieq5-3715532.gif"/></alternatives></inline-formula>. Experimental results validate the superiority of OA2DPFL in terms of peak power, convergence performance, and DP protection compared to baseline methods.