A Note on Optimizing the Ratio of Monotone Supermodular Functions

超模秩：集合函数分解与优化

Supermodular Rank: Set Function Decomposition and Optimization

本文定义了格上函数的超模秩与子模秩，并提出一种利用子模分解将优化问题拆分为子模子问题的算法，从而在取决于子模秩的计算开销下，有效提升了单调集合函数最大化等问题的近似比保证。

基于老虎机反馈的在线子模+超模（BP）最大化

Online SuBmodular + SuPermodular (BP) Maximization with Bandit Feedback

本文研究在线组合目标的 BP 与弱子模最大化，提出分项反馈框架并结合 Nystrom sketching 降本，证明次线性遗憾且在推荐和子集选择中有效。

企业需要你找出差异：重访子模与超模比率优化问题

Corporate Needs You to Find the Difference: Revisiting Submodular and Supermodular Ratio Optimization Problems

研究子模/超模集合函数平均值的最优化问题，引入USSS与UDSS两种新表述，证明其与DSS、SFM等经典问题在强多项式时间归约下等价，并利用Fujishige-Wolfe算法和SuperGreedy++作为通用求解器，实验表明通用凸方法与流方法在多种问题上优于专用基线。

A Parameterized Family of Meta-Submodular Functions

Submodular function maximization has found a wealth of new applications in machine learning models during the past years. The related supermodular maximization models (submodular minimization) also offer an abundance of applications, but they appeared to be highly intractable even under simple cardinality constraints. Hence, while there are well-developed tools for maximizing a submodular function subject to a matroid constraint, there is much less work on the corresponding supermodular maximization problems. We give a broad parameterized family of monotone functions which includes submodular …

Optimizing Recurrent Neural Networks Architectures under Time Constraints

Recurrent neural network (RNN)'s architecture is a key factor influencing its performance. We propose algorithms to optimize hidden sizes under running time constraint. We convert the discrete optimization into a subset selection problem. By novel transformations, the objective function becomes submodular and constraint becomes supermodular. A greedy algorithm with bounds is suggested to solve the transformed problem. And we show how transformations influence the bounds. To speed up optimization, surrogate functions are proposed which balance exploration and exploitation. Experiments show that…

采用进化多目标算法优化单调机会约束子模函数

Optimizing Monotone Chance-Constrained Submodular Functions Using Evolutionary Multi-Objective Algorithms

该研究首次分析了基于帕累托优化的进化多目标算法求解机会约束子模函数的运行时间，证明GSEMO在特定条件下可达到与贪心算法相当的性能保证，并通过实验验证进化多目标算法在相关网络问题上性能显著优于现有贪心算法。