David Simchi-Levi

Haichen Hu, David Simchi-Levi

We study the problem of evaluating the excess risk of large-scale empirical risk minimization under the square loss. Leveraging the idea of wild refitting and resampling, we assume only black-box access to the training algorithm and develop an efficient procedure for estimating the excess risk. Our evaluation algorithm is both computationally and data efficient. In particular, it requires access to only a single dataset and does not rely on any additional validation data. Computationally, it only requires refitting the model on several much smaller datasets obtained through sequential resampling, in contrast to previous wild refitting methods that require full-scale retraining and might therefore be unsuitable for large-scale trained predictors. Our algorithm has an interleaved sequential resampling-and-refitting structure. We first construct pseudo-responses through a randomized residual symmetrization procedure. At each round, we thus resample two sub-datasets from the resulting covariate pseudo-response pairs. Finally, we retrain the model separately on these two small artificial datasets. We establish high probability excess risk guarantees under both fixed design and random design settings, showing that with a suitably chosen noise scale, our interleaved resampling and refitting algorithm yields an upper bound on the prediction error. Our theoretical analysis draws on tools from empirical process theory, harmonic analysis, Toeplitz operator theory, and sharp tensor concentration inequalities.

Ruicheng Ao, Jiashuo Jiang, David Simchi-Levi

We study the dynamic pricing problem with knapsack, addressing the challenge of balancing exploration and exploitation under resource constraints. We introduce three algorithms tailored to different informational settings: a Boundary Attracted Re-solve Method for full information, an online learning algorithm for scenarios with no prior information, and an estimate-then-select re-solve algorithm that leverages machine-learned informed prices with known upper bound of estimation errors. The Boundary Attracted Re-solve Method achieves logarithmic regret without requiring the non-degeneracy condition, while the online learning algorithm attains an optimal $O(\sqrt{T})$ regret. Our estimate-then-select approach bridges the gap between these settings, providing improved regret bounds when reliable offline data is available. Numerical experiments validate the effectiveness and robustness of our algorithms across various scenarios. This work advances the understanding of online resource allocation and dynamic pricing, offering practical solutions adaptable to different informational structures.

Haichen Hu, David Simchi-Levi

We study the problem of excess risk evaluation for empirical risk minimization (ERM) under general convex loss functions. Our contribution is an efficient refitting procedure that computes the excess risk and provides high-probability upper bounds under the fixed-design setting. Assuming only black-box access to the training algorithm and a single dataset, we begin by generating two sets of artificially modified pseudo-outcomes termed wild response, created by stochastically perturbing the gradient vectors with carefully chosen scaling. Using these two pseudo-labeled datasets, we then refit the black-box procedure twice to obtain two corresponding wild predictors. Finally, leveraging the original predictor, the two wild predictors, and the constructed wild responses, we derive an efficient excess risk upper bound. A key feature of our analysis is that it requires no prior knowledge of the complexity of the underlying function class. As a result, the method is essentially model-free and holds significant promise for theoretically evaluating modern opaque machine learning system--such as deep nerral networks and generative model--where traditional capacity-based learning theory becomes infeasible due to the extreme complexity of the hypothesis class.