发表机构
MIT; Cornell University（麻省理工学院; 康奈尔大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文在Goldwasser等人的交互式学习证明框架基础上，定义公开可验证统计有效性证书（pvCSV），在自适应统计查询算法中构建pvCSV，认证k次自适应查询的SQ算法，样本复杂度为O(log k)，并研究了SQ模型中的学习证明系统。
AI 中文摘要
继Goldwasser、Rothblum、Shafer和Yehudayoff定义交互式学习证明框架后，本文开启非交互式学习证明研究。定义并研究公开可验证统计有效性证书（pvCSV），学习者发布假设h和对应证书π，用户据此高效判定假设有效性。在自适应统计查询（SQ）算法中构建pvCSV，认证k次自适应查询的SQ算法，其样本复杂度为O(log k)，而最佳学习算法为Õ(√k)。还研究了SQ模型中的学习证明系统，展示其优缺点。
英文摘要
Following Goldwasser, Rothblum, Shafer, and Yehudayoff, who defined a framework for interactive proofs of learning [ITCS'21], we initiate the study of non-interactive proofs of learning. We define and study a new notion: Publicly-Verifiable Certificates of Statistical Validity (pvCSVs), which allow for public, distributionally-robust certification that the result of a learning algorithm is valid. In a pvCSV, a learner publishes a hypothesis $h$ and corresponding certificate $π$; then, any user, who holds a user-specific distribution, can read the pair $(h,π)$ and determine efficiently whether the hypothesis is valid according to the user-specific distribution. We construct pvCSVs in the context of Adaptive Statistical Query (SQ) Algorithms. To certify SQ algorithms that makes $k$ adaptive queries, we construct pvCSVs where the sample complexity scales with $O(\log k)$, whereas the sample complexity of the best learning algorithms scale with $\tilde{O}(\sqrt{k})$. More generally, we study proof systems for learning in the SQ model, demonstrating the model's strengths as well as its limitations.
