Constrained Online Learning with Noisy Constraint Values
Quick summary
arXiv:2609.06921v1 Announce Type: cross Abstract: We study constrained online convex optimization with adversarial constraints when constraint values and gradients are observed through unbiased noise. Gaussian value noise of standard deviation $\sigma$ yields a worst-case lower bound of $\Omega(\min\{\sigma,1\}T/\log^7T)$ on the maximum of expected regret and expected hard violation, even with known gradients. This rules out any jointly $O(T^{1-\delta})$ guarantee for fixed $\delta>0$ and fixed positive noise level. We therefore study budget violation: the largest cumulative overspend over any
Key takeaways
- arXiv:2609.06921v1 Announce Type: cross Abstract: We study constrained online convex optimization with adversarial constraints when constraint values and gradients are observed through unbiased noise.
- Gaussian value noise of standard deviation $\sigma$ yields a worst-case lower bound of $\Omega(\min\{\sigma,1\}T/\log^7T)$ on the maximum of expected regret and expected hard violation, even with known gradients.
- This rules out any jointly $O(T^{1-\delta})$ guarantee for fixed $\delta>0$ and fixed positive noise level.
Why it matters
“Constrained Online Learning with Noisy Constraint Values” highlights the need for repeatable measurement rather than a single impressive demonstration. Independent validation across datasets and clearly stated limitations determine whether a result can guide product decisions.
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