Constrained Online Learning with Noisy Constraint Values
We study constrained online convex optimization with adversarial constraints and conditionally unbiased, finite-variance observations of constraint values and gradients. Under common feasibility, our \LEDGER\ algorithm attains $O(\sqrt T)$ expected regret and $O(\sqrt{T\log(eT)})$ expected budget violation, the largest cumulative overspend over any window. It uses a reflected exponential potential, clipped signed observations, and predictable adaptive regularization, with one feedback triple and one projection per round. Neither a Slater condition, independence between feedback channels, nor an absolute constraint-value bound is needed. A Gaussian testing lower bound proves that the budge...
| Authors | Vaneet Aggarwal |
|---|---|
| Primary category | cs.LG |
| Published | 7 September 2026 |
| Last updated at source | 13 September 2026 |
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