Simulation-Optimization of Systems of Optimizers: Exploiting the Inner Optimization's Geometry

Abstract

We study simulation-optimization of systems of optimizers (SOSO): agent-based simulations in which every agent solves a structured optimization - a linear program (LP), mixed-integer program, or dynamic program - at every decision epoch. Such systems arise in supply chains, electricity markets, and logistics, yet standard simulation optimization treats the simulation as a black box, discarding the inner optimization's geometry. We formalize SOSO and develop a framework that converts this geometry into computational advantage. We prove that the inner LP's optimal basis and dual variables propagate through the dynamics to yield an exact, unbiased, single-replication infinitesimal perturbation analysis (IPA) gradient of the outer objective, with measure-zero basis changes as the only obstructions. We derive a common-random-numbers covariance bound governed by a computable basis-disagreement count from the forward simulation. We further prove that IPA variance grows exponentially with feedback depth, formalizing the bullwhip effect, and introduce surrogate-as-decision with an error budget unifying LP-horizon and reinforcement-learning surrogates under one bound. We compose these into PRIME, a stochastic-approximation solver integrating the IPA gradient, adaptive step sizing, and multi-start spatial diversification. On six testbeds spanning the SOSO taxonomy, PRIME achieves the best or tied-best optimality gap at equal budget with near-zero oscillation and narrow seed-to-seed variance; IPA yields a ~2000x per-replication variance reduction over independent finite differences, and common random numbers cut paired-difference variance by over 10,000x in a 1,000-SKU, six-distribution-center supply chain. These results establish exploiting embedded-optimization geometry as a practically significant direction for simulation optimization.