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

ArXiv ID: 2509.14080 “View on arXiv”

Authors: JINHO CHA

Abstract

The growing prevalence of drift and shocks in modern decision environments exposes a gap between classical optimization theory and real-world practice. Standard models assume fixed objectives, yet organizations from hospitals to power grids routinely adapt to shifting priorities, noisy data, and abrupt disruptions. To address this gap, this study develops a dynamic inverse optimization framework that recovers hidden, time-varying preferences from observed allocation trajectories. The framework unifies identifiability analysis with regret guarantees conditions are established for existence and uniqueness of recovered parameters, and sharp static and dynamic regret bounds are derived to characterize responsiveness to gradual drift and sudden shocks. Methodologically, a drift-aware estimator grounded in convex analysis and online learning theory is introduced, with finite-sample guarantees on recovery accuracy. Computational experiments in healthcare, energy, logistics, and finance reveal heterogeneous recovery patterns, ranging from rapid resilience to persistent vulnerability. Overall, dynamic inverse optimization emerges as both a theoretical contribution and a broadly applicable diagnostic tool for benchmarking resilience, uncovering hidden behavioral shifts, and guiding policy interventions in complex stochastic systems.

Keywords: inverse optimization, regret analysis, online learning, dynamic programming, convex analysis, General

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 4.0/10
• Quadrant: Lab Rats
• Why: The paper is highly theoretical, featuring advanced mathematics like bilevel optimization, identifiability analysis, and dynamic regret bounds from convex analysis and online learning. While it includes computational experiments across several domains, the methods are conceptual and algorithm-focused, lacking specific backtesting datasets, code, or implementation details that would indicate high empirical readiness.

  flowchart TD
    A["Research Goal:<br>Model Dynamic Inverse<br>Optimization under Drift & Shocks"] --> B["Input: Observed Allocation Trajectories<br>Healthcare, Energy, Logistics, Finance"]
    B --> C["Methodology: Drift-Aware Estimator<br>Convex Analysis & Online Learning"]
    C --> D["Computational Process:<br>Recover Time-Varying Preferences<br>Regret Bounds & Identifiability"]
    D --> E["Outcome 1: Theoretical Contributions<br>Existence, Uniqueness, Sharp Regret Bounds"]
    D --> F["Outcome 2: Applications<br>Benchmarking Resilience & Policy Interventions"]