EvoMIDFL: Agentic Self-Evolving Decision-Focused Learning For Mixed-Integer Programming

Decision-focused learning (DFL) embeds optimization problems into learning architectures and trains using downstream decision loss rather intermediate prediction errors alone. In mixed-integer DFL (MIDFL), however, the discontinuous prediction-to-decision map obstructs informative gradient propagation. Existing approaches typically rely on a fixed approximate backward mechanism with hand-tuned configurations, limiting the adaptation across problems, scales and leaving potentially useful gradient combinations unexplored. Recent advances in agentic evolution offer a promising way to search and refine mechanisms through successive evolution. To this end, we propose EvoMIDFL (Evolutionary Mixed-Integer Decision-Focused Learning), an agentic self-evolving MIDFL framework that adaptively discovers, configures, and composes surrogate backward-gradient policies across diverse settings. EvoMIDFL employs a validation-guided actor–critic workflow supported by a three-layer memory architecture: the Gradient Actor proposes gradient estimators, combinations, and configurations; the Critic Agent diagnoses failures and filters unsafe candidates; and the Memory Agent stores formulation-level experience, mechanism-level evidence, and transferable skills to guide subsequent evolution. Retrieved policies are further refined on the target task to mitigate negative transfer. Extensive experiments show that EvoMIDFL not only improves downstream decision quality over fixed MIDFL backward methods, but also discovers reusable policies across scales and scenarios.