Online Allocation with Differential Privacy

We study private online allocation problems, where allocation decisions must satisfy differential privacy (DP) to protect sensitive user information while optimizing performance under constrained resources. We first formalize differential privacy notions suited to different privacy requirements in online allocation and establish the fundamental performance limits of any algorithm under these definitions. Based on these insights, we propose PPOA, a privacy-preserving meta algorithm for online allocation, and establish sufficient conditions under which PPOA preserves Joint DP (JDP) or Local DP (LDP) while achieving asymptotically near-optimal performance. Building on these conditions, PPOA can be instantiated into a variety of concrete algorithms. In particular, we present the specific designs, which include PPOA-DMD that preserves JDP and LDP and PPOA-FTRL that preserves JDP. We analyze their performance under both adversarial and stochastic settings and characterize the fundamental trade-offs between DP and allocation performance. Finally, we demonstrate the superior performance of the proposed algorithms via numerical experiments on AI model routing in battery-powered edge systems.