IGT-OMD: Implicit Gradient Transport for Decision-Focused Learning under Delayed Feedback
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arXiv
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866918498383429632 |
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| author | Amoh, Benjamin Parker, Geoffrey G. Marrero, Wesley |
| author_facet | Amoh, Benjamin Parker, Geoffrey G. Marrero, Wesley |
| contents | 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 \emph{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, \textbf{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 \emph{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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_12693 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | IGT-OMD: Implicit Gradient Transport for Decision-Focused Learning under Delayed Feedback Amoh, Benjamin Parker, Geoffrey G. Marrero, Wesley Machine Learning 68Q25, 90C25, 90C47 I.2.6; G.1.6 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 \emph{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, \textbf{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 \emph{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. |
| title | IGT-OMD: Implicit Gradient Transport for Decision-Focused Learning under Delayed Feedback |
| topic | Machine Learning 68Q25, 90C25, 90C47 I.2.6; G.1.6 |
| url | https://arxiv.org/abs/2605.12693 |