Classical stochastic approximation methods rely on estimators of the first moment (mean) of a random regression function. We study methods that employ estimators of both the first and the second moments, which include modern deep-learning optimizers such as Adam and Muon as special cases. We derive second-moment stochastic approximation methods through the lens of optimal … Read more
Distributionally robust optimization hedges a decision against an ambiguity set of candidate distributions. In a cold-start setting the target distribution is unobserved and no sample from it is available, so only related source distributions provide evidence for constructing that set. We propose an inclusive-exclusive Wasserstein ball model that jointly learns a center and radius from … Read more
Large language models improve test-time accuracy by generating multiple rollouts and aggregating these answers. As generating additional rollouts consumes more tokens, test-time compute faces a fundamental cost accuracy trade-off, naturally raising the question: given a fixed token budget, how to allocate the budget to maximize accuracy? Existing approaches typically adapt the number of rollouts for … Read more
We study stochastic optimization with a completely unobserved target distribution and samples from related source distributions. Treating the sources and the target as independent draws from a common meta-distribution, we propose Wasserstein-metric meta-distribution support learning (MDSL). The model jointly learns the center and radius of a Wasserstein ball, with an exclusion parameter controlling the fraction … Read more
Exact mathematical programming formulations for estimating classification rules provide guarantees of empirical optimality, but their size grows rapidly with the number of predictive features and model complexity. This paper shows that interpretable classifiers can be estimated by directly maximizing empirical classification accuracy under complexity constraints, using truncation and warm-start strategies compatible with disjunctive normal form … Read more
We study the problem of learning revenue-maximizing bundle prices when customer valuations and market composition are unknown and the firm observes only customer choices. This problem is challenging because the number of bundle-price decisions grows exponentially with the number of items offered. We develop BLMP (Bundle Pricing via Learning the Market from Customer Preferences), a … Read more
Distributionally robust optimization (DRO) provides a principled framework for learning under distribution shift, but its practical use is hindered by the difficulty of evaluating worst-case risks for nonconvex loss functions. We study a penalized DRO formulation in which the adversary may choose any distribution but incurs a Wasserstein penalty for deviating from the empirical distribution. … Read more
Quantization-aware training (QAT) updates a full-precision shadow weight \(\mathbf{x}\) but deploys the quantized endpoint \(Q(\mathbf{x})\). Existing explanations for QAT largely view its success through the lens of shadow weights: QAT can move \(\mathbf{x}\) toward flatter basins, gain robustness from quantization-induced oscillations, or balance the shadow loss \(f(\mathbf{x})\) against the quantization error \(\|\mathbf{x}-Q(\mathbf{x})\|_2\). These perspectives do … Read more
Mixed integer nonlinear programs with binary coupling decisions naturally model selective coordination tasks where a fixed penalty is incurred whenever adjacent continuous variables differ. A prominent example is the classical Potts model, which is widely used in statistical inference. However, exact solvability remains theoretically challenging since the problem is NP hard on general graphs, and … Read more
Feature-based newsvendor models use observable covariates to tailor inventory decisions, aiming to balance holding and shortage costs under demand uncertainty. However, high-dimensional feature sets often hinder interpretability and inflate data collection and implementation costs. This paper studies variable selection for the feature-based newsvendor problem under a hard cardinality constraint on the number of selected features. … Read more