Year: 2026
Type: preprint
Abstract: A shortest-path decision is often made from edge costs that are only observed through noisy samples, such as the average of $m$ simulation replications. When the mean cost vectors of different instances lie near a $k$-dimensional subspace, projecting the averaged sample onto that subspace should remove noise. We make this precise. The mean squared error of any projection estimator splits exactly into a variance term and a bias term. The best projector is the positive eigenspace of $Σ_c - D/m$, where $Σ_c$ is the covariance of the true costs and $D$ is the noise covariance. For a rank-$k$ signal, the projection has the error of a sample mean with a factor $d/(μk)$ more replications, where $d$ is the number of edges and $μ$ is an incoherence constant. For a signal that is only approximately low-rank, every rank-$k$ projection has an error floor, and the plain average wins beyond an explicit replication count. A margin bound shows that the chance of choosing a suboptimal path falls at the same improved rate. A projector learned from $n$ noisy instances loses at most an $O(d/n)$ term.
Source: arXiv (Cornell University)
Authors: Aldridge-Krawciw, Henry, Aldridge, Irene
Language: English
Subfield: Signal Processing
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7213326967