使用输出敏感技术加速数据驱动算法设计的 ERM
Accelerating ERM for data-driven algorithm design using output-sensitive techniques
AI总结：
针对多参数组合算法的数据驱动设计，本文提出输出敏感的 ERM 加速框架，通过枚举实际损失分段、超平面诱导多面体和执行图表示状态，并在定价、聚类和序列比对中验证。
摘要：
数据驱动算法设计是一种很有前景的基于学习的方法，用于对具有可调参数的算法进行超越最坏情况的分析。一个重要的开放性问题是，为具有多个参数的组合算法族设计计算高效的数据驱动算法。当固定问题实例并改变参数时，“对偶”损失函数通常具有分段可分解结构，即除了在某些急剧转变的边界处之外，其表现良好。在本工作中，我们通过枚举一组问题实例的总对偶损失函数的分段，启动了对开发用于数据驱动算法设计的高效 ERM 学习算法的技术研究。我们方法的运行时间随实际出现的分段数量而扩展，而不是随分段数量的最坏情况上界而扩展。我们的方法包含两个新颖组成部分——一个使用计算几何工具枚举由一组超平面诱导的多面体的输出敏感算法，以及一个紧凑表示算法针对所有可能参数值可达到的所有状态的执行图。我们通过给出用于定价问题、基于链接的聚类以及基于动态规划的序列比对的算法来说明我们的技术。
英文摘要：
Data-driven algorithm design is a promising, learning-based approach for beyond worst-case analysis of algorithms with tunable parameters. An important open problem is the design of computationally efficient data-driven algorithms for combinatorial algorithm families with multiple parameters. As one fixes the problem instance and varies the parameters, the "dual" loss function typically has a piecewise-decomposable structure, i.e. is well-behaved except at certain sharp transition boundaries. In this work we initiate the study of techniques to develop efficient ERM learning algorithms for data-driven algorithm design by enumerating the pieces of the sum dual loss functions for a collection of problem instances. The running time of our approach scales with the actual number of pieces that appear as opposed to worst case upper bounds on the number of pieces. Our approach involves two novel ingredients -- an output-sensitive algorithm for enumerating polytopes induced by a set of hyperplanes using tools from computational geometry, and an execution graph which compactly represents all the states the algorithm could attain for all possible parameter values. We illustrate our techniques by giving algorithms for pricing problems, linkage-based clustering and dynamic-programming based sequence alignment.
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