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Stream stochastic gradient descent (SGD) is a simple and efficient method forsolving online optimization problems in operations research (OR), where data isgenerated by parameter-dependent Markov chains. Unlike traditional approacheswhich require increasing batch sizes during iterations, stream SGD uses asingle sample per iteration, significantly improving sample efficiency. Thispaper establishes a systematic framework for analyzing stream SGD, leveragingthe Poisson equation solution to address gradient bias and statisticaldependence. We prove optimal O(1/T) convergence rates and the state-of-the-artO(log T) regret, while also introducing an online inference method foruncertainty quantification and supporting it by a novel functional centrallimit theorem. We propose a novel Wasserstein-type divergence to describe theframework's conditions, which makes the assumptions in question directlyverified via coupling techniques tailored to underlying OR models. We considerapplications in queueing systems and inventory management, demonstrating thepracticality and broad relevance, as well as providing new insights into theeffectiveness of stream SGD in OR fields.

Convergence and Inference of Stream SGD, with Applications to Queueing Systems and Inventory Control