AI 中文总结
该研究针对在线差分隐私查询回答问题，提出带加权稀缺性分配的剩余隐私预算规划方法，利用QIF处理查询稀缺性，在可行机制下实现与离线最优的1-竞争性，为在线差分隐私查询提供解决方案。
AI 中文摘要
在差分隐私的许多实际部署中，查询并非全部同时到达。我们研究在有限零集中差分隐私（zCDP）合约下的在线差分隐私查询回答问题。在此设定中，查询按顺序到达，带有不同的精度阈值，且可能与已发布的信息重叠。我们将此设定形式化为剩余隐私预算规划：对于每个到达的查询，机制首先从先前的差分隐私输出中计入可重复使用的支持，然后仅在满足当前阈值所需的剩余支持上消耗新预算。控制器将可行情况（即最小剩余支持被精确分配）与稀缺情况（即加权短缺守恒优化器根据查询难度分配有限支持）分开。我们使用查询影响因子（QIF）定义权重，QIF是用于衡量查询难度和不稳定性而非查询重要性的诊断信号。对于标量高斯精确复用，逆方差融合证明了加性支持的合理性。我们证明了zCDP组合性、剩余最小性、在可行机制下相对于离线最优的1-竞争性，以及忽略已发布历史的分配器可避免的支出。稀缺性不可能性结果表明，没有在线分配器能在阈值满足方面保证优于1/n的竞争比率，这将QIF稀缺层定位为固有困难的在线问题的一种设计选择。
英文摘要
In many practical deployments of differential privacy, queries do not arrive all at once. We study online differentially private query answering under a finite zero-concentrated differential privacy (zCDP) contract. In this setting, queries arrive sequentially, carry different accuracy thresholds, and may overlap with information already released. We formulate this setting as residual privacy budgeting: for each arriving query, the mechanism first credits reusable support from previous DP outputs and then spends new budget only on the remaining support required to satisfy the current threshold. The controller separates feasible cases, where the minimal residual support is allocated exactly, from scarcity cases, where a weighted shortfall-conservation optimiser assigns limited support according to query difficulty. We define the weight using the Query Influence Factor (QIF), a diagnostic signal for query difficulty and instability rather than query importance. For scalar Gaussian exact reuse, inverse-variance fusion justifies additive support. We prove zCDP composition, residual minimality, 1-competitiveness against the offline optimum in the feasible regime, and avoidable expenditure for allocators that ignore released history. A scarcity impossibility result shows that no online allocator can guarantee a competitive ratio better than 1/n in threshold satisfaction, contextualising the QIF scarcity layer as a design choice for an inherently hard online problem.
Comments13 pages. Presented as a poster at the Learning Theory Workshop, University of Copenhagen, June 2026
