计算子模 utility 和 cost 交易的近似帕累托前沿
Approximate Pareto Frontiers for Submodular Utility and Cost Tradeoffs
AI总结：
本文提出了一种计算子模 utility 和 cost 交易近似帕累托前沿的框架，通过高效算法探索多种权衡方案，提升子模优化的实用性。
摘要：
在许多数据挖掘应用中，包括推荐系统、影响力最大化和团队组建，目标是选择一组元素（例如，项目、网络中的节点、执行任务的专家）以最大化单调子模 utility 函数的同时最小化成本函数。经典方法通过基数或背包约束，或通过将 utility 和 cost 合并成一个加权目标来建模这种权衡。然而，这些方法需要提前确定特定的权衡，并仅返回一个解决方案，对可行的 utility-cost 权衡空间提供有限的见解。在本文中，我们脱离单一解决方案范式，研究计算高质量解决方案代表集的问题，以暴露子模 utility 和 cost 之间的不同权衡。为此，我们引入了 (α₁,α₂) - 近似帕累托前沿，这些前沿可以证明地近似子模 utility 和 cost 之间的可实现权衡。具体来说，我们正式化了帕累托-⟨f,c⟩ 问题，并为不同组合的子模 utility f 和 cost 函数 c 开发了高效的算法。我们的结果提供了一个原则性且实用的框架，用于理解和利用子模优化中的 utility-cost 权衡。在来自不同应用领域的数据集上的实验表明，我们的算法在实践中能够高效地计算近似帕累托前沿。
英文摘要：
In many data-mining applications, including recommender systems, influence maximization, and team formation, the goal is to pick a subset of elements (e.g., items, nodes in a network, experts to perform a task) to maximize a monotone submodular utility function while simultaneously minimizing a cost function. Classical formulations model this tradeoff via cardinality or knapsack constraints, or by combining utility and cost into a single weighted objective. However, such approaches require committing to a specific tradeoff in advance and return only a single solution, offering limited insight into the space of viable utility-cost tradeoffs. In this paper, we depart from the single-solution paradigm and examine the problem of computing representative sets of high-quality solutions that expose different tradeoffs between submodular utility and cost. For this, we introduce $(α_1,α_2)$-approximate Pareto frontiers that provably approximate the achievable tradeoffs between submodular utility and cost. Specifically, we formalize the Pareto-$\langle f,c \rangle$ problem and develop efficient algorithms for multiple instantiations arising from different combinations of submodular utility $f$ and cost functions $c$. We also provide an adaptive search algorithm that computes only a small subset of points that collectively summarize the entire Pareto frontier. Our results offer a principled and practical framework for understanding and exploiting utility-cost tradeoffs in submodular optimization. Experiments on datasets from diverse application domains demonstrate that our algorithms efficiently compute approximate Pareto frontiers in practice.
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