Dynamic Inverse Optimization under Drift and Shocks: Theory, Regret Bounds, and Applications

Operational decisions often reflect priorities that evolve gradually and may shift abruptly after disruptions. We develop a dynamic inverse optimization framework for recovering time-varying preference parameters from observed allocation trajectories. The framework separates an offline temporally regularized trajectory formulation from an online mirror-descent estimator for streaming recovery, thereby linking inverse optimization with online convex optimization under nonstationarity. We establish sufficient conditions for local identifiability and existence, static regret of $O(\sqrt{T})$, dynamic regret of $O(\sqrt{T}(1+V_T))$ for the online estimator, and a residual-to-parameter stability bound governed by the conditioning of the projected inverse map. The analysis distinguishes uniqueness of the inverse explanation, conditioning of the recovery map, existence of a batch trajectory solution, and sequential performance under a moving comparator. Controlled experiments on two stylized allocation benchmarks examine noiseless recoverability, finite-horizon regret, gradual drift, observational noise, abrupt shocks, and temporal coupling. These experiments are interpreted as finite-sample diagnostics rather than proofs of asymptotic bounds. Across the tested settings, temporal coupling moderates the trade-off between static under-adaptation and excessive variation from independent period-by-period inversion. The resulting framework provides an interpretable foundation for online inverse optimization and nonstationary decision analytics under evolving priorities. It also clarifies when structural recovery and sequential adaptation require distinct guarantees.