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 \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.

Multi-Agent Decision-Focused Learning via Value-Aware Sequential Communication

Multi-agent coordination under partial observability requires agents to share complementary private information. While recent methods optimize messages for intermediate objectives (e.g., reconstruction accuracy or mutual information), rather than decision quality, we introduce \textbf{SeqComm-DFL}, unifying the sequential communication with decision-focused learning for task performance. Our approach features \emph{value-aware message generation with sequential Stackelberg conditioning}: messages maximize receiver decision quality and are generated in priority order, with agents conditioning on their predecessors. The \emph{guidance potential} determined by their prosocial ordering. We extend Optimal Model Design to communication-augmented world models with QMIX factorization, enabling efficient end-to-end training via implicit differentiation. We prove information-theoretic bounds showing that communication value scales with coordination gaps and establish $\mathcal{O}(1/\sqrt{T})$ convergence for the bilevel optimization, where $T$ denotes the number of training iterations. On collaborative healthcare and StarCraft Multi-Agent Challenge (SMAC) benchmarks, SeqComm-DFL achieves four to six times higher cumulative rewards and over 13\% win rate improvements, enabling coordination strategies inaccessible under information asymmetry.