Regret Equals Covariance: A Closed-Form Characterization for Stochastic Optimization

arXiv:2605.14019 · econ.EM, cs.LG, math.ST, stat.CO, stat.TH · Submitted 2026-05-13 · Read on arXiv

econ.EM, cs.LG, math.ST, stat.CO, stat.TH

Submitted: 2026-05-13

Updated: 2026-09-27

Terminology

• Regret — 209× in this paper · explained in 3 episodes
• Benchmark — 9× in this paper · explained in 2 episodes
• Combinatorial Optimization — 6× in this paper · explained in 2 episodes
• Commentary — 5× in this paper · explained in 2 episodes
• Distributionally Robust Optimization — 5× in this paper
• Sample Average Approximation — 5× in this paper
• Adam — 4× in this paper · explained in 2 episodes
• Optimal Transport — 4× in this paper · explained in 5 episodes
• Core — 3× in this paper · explained in 2 episodes
• Accuracy — 2× in this paper · explained in 1 episode
• Consistency — 2× in this paper · explained in 3 episodes
• Degeneracy — 2× in this paper · explained in 3 episodes
• Generalization — 2× in this paper · explained in 13 episodes
• Loss Function — 2× in this paper · explained in 2 episodes
• Sample Complexity — 2× in this paper · explained in 15 episodes
• Uncertainty Quantification — 2× in this paper · explained in 8 episodes
• Wasserstein Distance — 2× in this paper · explained in 4 episodes
• Benchmarking — 1× in this paper · explained in 3 episodes
• Center for Research in Security Prices — 1× in this paper
• Contextual Bandits — 1× in this paper · explained in 3 episodes
• Curse of Dimensionality — 1× in this paper · explained in 6 episodes
• Elias — 1× in this paper · explained in 2 episodes
• Feature Engineering — 1× in this paper · explained in 3 episodes
• Generalization Bounds — 1× in this paper · explained in 2 episodes
• Objective Function — 1× in this paper · explained in 2 episodes
• Robustness — 1× in this paper · explained in 5 episodes
• Trace — 1× in this paper · explained in 2 episodes

Sources

• Radial Oscillations and Dynamical Instability Analysis for Linear-Quadratic GUP-modified White Dwarfs
• DC3: A learning method for optimization with hard constraints
• End-to-End Constrained Optimization Learning: A Survey
• Learning to Optimize
• Ionic liquid-electrode interface: classification of ions, saturation of layers, and structure-determined potentials
• Distributionally Robust Optimization: A Review
• RegFormer: An Efficient Projection-Aware Transformer Network for Large-Scale Point Cloud Registration

Related papers

• SLIM: Stochastic Learning and Inference in Overidentified Models
• High-dimensional censored MIDAS logistic regression for corporate survival forecasting
• Cross-Fitting-Free Debiased Machine Learning with Multiway Dependence
• Can large language models assist choice modelling? Insights into prompting strategies and current models' capabilities
• Causal Inference in Possibly Nonlinear Factor Models
• Mining Causality: AI-Assisted Search for Instrumental Variables