New bound tightens inverse optimization guarantees, matches bandit rates

Inverse optimization (IO) aims to recover the hidden objective behind a decision-maker's observed actions. A new paper by Fatemi, Maskan, Sra, and Esfahani (arXiv:2605.08866) provides the first tight generalization bounds for noiseless IO. Their main result is a high-probability O(d/T) bound on the induced action set error, where d is the number of unknown parameters and T the training dataset size. This rate is proven to be optimal over all consistent estimators considered, bringing IO guarantees in line with the best-arm identification results from multi-armed bandit literature. The authors also derive regret bounds that match the adversarial setting, revealing that the stochastic IO problem is effectively adversarial for these estimators.

Beyond the theoretical breakthrough, the team proposes a parameter-free algorithm that achieves lower per-iteration complexity than generic solvers. Crucially, the algorithm requires no tuning of hyperparameters while maintaining tight generalization guarantees. Experimental results validate the predicted O(d/T) convergence and confirm the tightness of the bounds. This work has immediate implications for applications like imitation learning, preference inference, and AI alignment, where reliably extracting objectives from demonstrations is critical. The results also open new connections between inverse optimization and bandit theory, suggesting future cross-pollination between the fields.