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

arXiv: https://arxiv.org/abs/2605.12693 · HTML: https://mlsanity.com/paper/2605.12693/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 21 of its 37 references that are in the map.
- First posted on arXiv 12 May 2026.

## Builds on (most cited first, 21 of 21)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [OpenAI Gym](https://mlsanity.com/paper/1606.01540/) (2016)
- [Smart "Predict, then Optimize"](https://mlsanity.com/paper/1710.08005/) (2017)
- [Approximation Methods for Bilevel Programming](https://mlsanity.com/paper/1802.02246/) (2018)
- [Melding the Data-Decisions Pipeline: Decision-Focused Learning for Combinatorial Optimization](https://mlsanity.com/paper/1809.05504/) (2018)
- [Differentiation of Blackbox Combinatorial Solvers](https://mlsanity.com/paper/1912.02175/) (2019)
- [Bilevel Optimization: Convergence Analysis and Enhanced Design](https://mlsanity.com/paper/2010.07962/) (2020)
- [Online Learning under Delayed Feedback](https://mlsanity.com/paper/1306.0686/) (2013)
- [Decision-Focused Learning: Foundations, State of the Art, Benchmark and Future Opportunities](https://mlsanity.com/paper/2307.13565/) (2023)
- [Control-Oriented Model-Based Reinforcement Learning with Implicit Differentiation](https://mlsanity.com/paper/2106.03273/) (2021)
- [Online Learning with Optimism and Delay](https://mlsanity.com/paper/2106.06885/) (2021)
- [PyEPO: A PyTorch-based End-to-End Predict-then-Optimize Library for Linear and Integer Programming](https://mlsanity.com/paper/2206.14234/) (2022)
- [Online Bilevel Optimization: Regret Analysis of Online Alternating Gradient Methods](https://mlsanity.com/paper/2207.02829/) (2022)
- [Reducing the variance in online optimization by transporting past gradients](https://mlsanity.com/paper/1906.03532/) (2019)
- [Non-Convex Bilevel Optimization with Time-Varying Objective Functions](https://mlsanity.com/paper/2308.03811/) (2023)
- [Banker Online Mirror Descent: A Universal Approach for Delayed Online Bandit Learning](https://mlsanity.com/paper/2301.10500/) (2023)
- [Online Decision-Focused Learning](https://mlsanity.com/paper/2505.13564/) (2025)
- [Stochastic Regret Guarantees for Online Zeroth- and First-Order Bilevel Optimization](https://mlsanity.com/paper/2511.01126/) (2025)
- [A Reduction from Delayed to Immediate Feedback for Online Convex Optimization with Improved Guarantees](https://mlsanity.com/paper/2602.02634/) (2026)
- [Decentralized Online Convex Optimization with Unknown Feedback Delays](https://mlsanity.com/paper/2601.07901/) (2026)
- [Distributed Stochastic Gradient Descent with Staleness: A Stochastic Delay Differential Equation Based Framework](https://mlsanity.com/paper/2406.11159/) (2024)

## Abstract (arXiv)

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.