Eigenvalue-Decomposition Cost Denoising as an Alternative to Predict-then-Optimize for Shortest-Path Problems

The paper proposes using eigenvalue decomposition (or PCA) to denoise noisy cost observations for shortest‑path problems, instead of the traditional predict‑then‑optimize approach. By projecting new cost vectors onto the top‑k eigenvectors of the training covariance matrix before running Dijkstra’s algorithm, the method can recover the true underlying costs. Experiments on a 5×5 grid benchmark show that choosing k equal to the true latent feature dimension (k=5) yields the best performance, outperforming the SPO+ method especially under high model misspecification.

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