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）通常需要密集计算并导致较长的响应时间。因此，若能通过少量对更强模型的查询来修正不准确性，则能够快速提供不精确结果的较弱模型将具有优势。在计算拟阵的最大权基这一基础问题中（该问题是许多组合优化问题的著名推广），算法可通过精确预言机查询拟阵信息。我们进一步为算法配备了一个快速但不精确的预言机，用于模拟一个未知且可能不同的拟阵。我们设计并分析了实用算法，这些算法仅需相对于不精确预言机质量而言少量的精确查询，同时在面对任意低质量的不精确拟阵时保持鲁棒性，其性能逼近针对该问题的经典算法。值得注意的是，我们证明了所提算法在多方面均达到最优可能。此外，我们概述了该框架向其他类型拟阵预言机、非免费不精确预言机以及其他拟阵问题的扩展。