IGT-OMD: Implicit Gradient Transport for Decision-Focused Learning under Delayed Feedback

Decision-focused learning trains predictive models end-to-end against downstream decision loss, but online settings suffer delayed feedback: outcomes may not arrive for many environment interactions. We identify staleness amplification, a failure mode unique to bilevel optimization under delay, in which gradient staleness couples with inner-solver sensitivity to inflate regret beyond single-level delay theory. We prove that any black-box delayed optimizer incurs an irreducible regret cost from inner-solver approximation error, and that gradient staleness contributes a quadratically growing transport error without bilevel-aware correction. Our algorithm, IGT-OMD, applies Implicit Gradient Transport to hypergradients within Online Mirror Descent, re-evaluating stale gradients at the current parameters using stored inner solutions. This method reduces transport error from a quadratic to a linear dependence on delay and achieves the first sublinear regret bound for delayed bilevel optimization with queue-length-adaptive step sizes. Controlled experiments provide a mechanistic fingerprint: transport benefit is exactly 0.0% (p=1.00) at unit delay and grows monotonically to 9.5% at fifty rounds (p<0.001), isolating the correction's effect. On Linear Quadratic Regulator, Warcraft shortest-path, and Sinkhorn optimal transport, IGT-OMD reduces decision loss by 17--55% relative to single-level baselines, with phase transitions matching the theory.