Querying complex models for precise information (e.g. traffic models, database systems, large ML models) often entails intense computations and results in long response times. Thus, weaker models which give imprecise results quickly can be advantageous, provided inaccuracies can be resolved using few queries to a stronger model. In the fundamental problem of computing a maximum-weight basis of a matroid, a well-known generalization of many combinatorial optimization problems, algorithms have access to a clean oracle to query matroid information. We additionally equip algorithms with a fast but dirty oracle modelling an unknown, potentially different matroid. We design and analyze practical algorithms which only use few clean queries w.r.t. the quality of the dirty oracle, while maintaining robustness against arbitrarily poor dirty matroids, approaching the performance of classic algorithms for the given problem. Notably, we prove that our algorithms are, in many respects, best-possible. Further, we outline extensions to other matroid oracle types, non-free dirty oracles and other matroid problems.

翻译：查询复杂模型以获取精确信息（例如交通模型、数据库系统、大型机器学习模型）通常需要大量计算，并导致较长的响应时间。因此，能够快速给出不精确结果的较弱模型可能具有优势，前提是可以通过少量对较强模型的查询来解决不精确性。在计算拟阵最大权重基这一基本问题中——它是许多组合优化问题的著名推广——算法可以访问一个纯净的预言机来查询拟阵信息。此外，我们为算法配备了一个快速但脏乱的预言机，用于模拟一个未知的、可能不同的拟阵。我们设计并分析了一些实用算法，这些算法仅使用少量纯净查询（相对于脏乱预言机的质量），同时保持对任意劣质脏乱拟阵的鲁棒性，其性能接近针对给定问题的经典算法。值得注意的是，我们证明了我们的算法在许多方面是最优的。此外，我们概述了向其他拟阵预言机类型、非免费脏乱预言机以及其他拟阵问题的扩展。