Sampling Luck Masquerades as Allocation Gain: Auditing Test-Time Budget Allocation for Neural Combinatorial Optimization

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arXiv:2608.13087v1 Announce Type: cross Abstract: Neural combinatorial optimization (NCO) solvers report the best of many sampled solutions per instance, and the sample count is, by convention, identical for every instance. Whether a non-uniform allocation of a fixed total budget would buy anything has not been measured. We measure it, and we audit the measurement itself. First, on in-distribution workloads the allocation headroom is not detectable. Across three pretrained solvers (POMO, AM, SymNCO) on uniform TSP-100, an oracle allocation computed and evaluated on the same stored samples reports a 2.2-2.6% gain with intervals excluding zero; measured out of sample the same gain is indistinguishable from zero (0.457, 0.015, -0.512 percent). Following the customary in-sample procedure, all three solvers would have supported a published 2%-level gain that does not exist. We calibrate this bias against an instance-wise null in which the true gain is zero by construction; over the ranges we test it does not shrink with more samples or more instances. Second, the same correction that removes the phantom gains preserves a real one. Under distribution shift (a workload mixing uniform and clustered instances), a pre-registered confirmatory experiment finds that allocation guided by held-out sample statistics improves best-of-k by 11.5% (AM, primary endpoint; 95% CI [7.4, 19.7]) and 12.0% (SymNCO, replication) at equal evaluation budget, with the signal-acquisition cost not charged; a pre-registered negative control (POMO, an order of magnitude more robust to shift) shows -0.3% …

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