Proximal Residual Value Functions for Consistent Planning and Real-Time Execution

Abstract:We study two-timescale decision systems in which a planning layer periodically supplies a continuation-value function to a real-time optimizer that allocates arriving resources, with inventory placement as our motivating application. We propose an end-to-end reinforcement learning (RL) method for learning this function using \emph{proximal residual value functions}, which combine a strictly convex potential of post-decision inventory with a learned convex residual. This general form yields a well-posed optimization layer that supports end-to-end differentiation while preserving an explicit convex objective for real-time execution. We characterize the necessary and sufficient conditions under which a smooth value function yields decisions that are consistent across the planning and execution timescales. In an offline simulation using historical inventory arrival and demand patterns from a large e-commerce retailer, learned proximal residual value functions reduce total routing and transfer cost relative to a historical-production-system proxy by 5.0%.

Machine Learning (cs.LG)

arXiv:2609.23242 [cs.LG]

(or arXiv:2609.23242v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2609.23242 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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