面向证据组合优化的信念函数决策感知近似
Decision-Aware Approximation of Belief Functions for Evidential Combinatorial Optimization
- Univ. Artois（阿图瓦大学）
- UR 3926（UR 3926机构）
- Laboratoire de Génie Informatique et d’Automatique de l’Artois (LGI2A)（阿图瓦计算机与自动化实验室（LGI2A））
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
针对为带证据成本的线性组合优化提供输入的质量函数，提出决策感知近似方法，其决策时的决策翻转频率低于传统表示感知压缩。
AI中文摘要：
减少质量函数的焦元数量，经典方法是采用固有距离（如Jaccard或Jousselme距离），使近似结果作为证据体接近原始质量函数。本文研究的是质量函数为带有证据成本的线性组合优化问题提供输入的情况，此时需要保留的并非两个质量函数的接近度，而是它们所诱导决策的质量。本文提出一种决策感知近似方法，其目标是决策的遗憾：使用更简单的近似进行决策，再基于真实质量函数对该决策进行评估。在最小最短路径问题上，距离最优近似会翻转决策，而决策感知合并则能保留决策，这种情况在相当一部分随机实例中都会发生。本文证明了一个单点边界，可将遗憾定位于真实最优解处，将其转化为标量情况下的精确动态规划，并扩展为在线版本，该版本可在最终成本已知前对焦元进行剪枝。实验中，无论是线性准则还是非线性代理读出，决策感知压缩器翻转决策的频率都低于表示感知压缩。
英文摘要：
Reducing the number of focal elements of a mass function is classically driven by an intrinsic distance, such as Jaccard or Jousselme, that keeps the approximation close to the original as a body of evidence. We consider instead the case where the mass function feeds a linear combinatorial optimisation problem with evidential costs. What should then be preserved is not the closeness of the two mass functions, but the quality of the decision they induce. We introduce a decision-aware approximation that targets the regret of the decision: one decides with the cheaper approximation and is evaluated under the true mass function. On a minimal shortest path, the distance-optimal approximation flips the decision while a decision-aware merge preserves it, and this occurs on a non-negligible fraction of random instances. We prove a one-point bound that localises the regret at the true optimum, turn it into an exact dynamic program for the scalar case, and extend it to an online version that prunes focal elements before the final cost is known. In experiments the decision-aware compressor flips the decision less often than representation-aware compression, for both the linear criterion and a non-linear proxy read-out.
