Research map / Learning theory and algorithms / Kernels and regression theory
Statistical Properties of Robust Satisficing
Read the paperCheck your idea against 108,967 papers
AI-extracted summary. Written by AI from the paper's full text. Numbers and claims can be wrong or missing context, so check the paper before you cite or build on it.
Develops statistical theory for the Robust Satisficing model: two-sided non-asymptotic confidence intervals for the optimal loss, finite-sample generalization bounds, extensions under distribution shift, and a DRO correspondence showing RS is less sensitive to its hyperparameter.
Problem
Robust Satisficing (RS) models lack statistical guarantees; existing analyses focus on tractable optimization and experiments, and DRO's radius is hard to tune and can be overconservative.
Approach
RS constrains excess expected loss over a reference value tau by a multiple of Wasserstein distance to the empirical distribution, without a restricted ambiguity set; this structure yields two-sided confidence intervals for J* and generalization bounds via a Wasserstein concentration result, avoiding explicit minimax solving and strong duality assumptions required by DRO.
Key results
- Theory gives two-sided confidence interval -L·r_N + τ_ε/(1+ε) ≤ J* ≤ E_P*[h(x̂_N,ξ)] ≤ k_τ·r_N + τ_ε, with fragility bound k_τ ≤ L.
- Generalization bound E[R] ≤ ε·J* + O(L·N^{-min{1/m,1/2}}), extended to distribution shift by adding a linear multiple of the shift distance.
- In synthetic experiments RS beats ERM in small-sample regimes and under distribution shift; DRO's MSE spikes to 0.30 within a 15% range of its optimal radius while RS stays at 0.125.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use RS instead of ERM in small-sample regimes | linear regression with ℓ1 loss · Sampling distribution, small-sample regimes | MSE | Helped |
| increase tolerance rate ε among RS models | RS · Sampling distribution, small-sample regimes | MSE | Helped |
| use RS instead of ERM as sample size increases | linear regression with ℓ1 loss · Sampling distribution, larger sample sizes | MSE | No clear effect |
| increase tolerance rate ε for stronger robustness control | RS · Distribution shift, Degree less than 2 | MSE | Hurt |
| use RS instead of ERM | linear regression with ℓ1 loss · Distribution shift, Degree less than 2 | MSE | No clear effect |
| use RS instead of ERM | linear regression with ℓ1 loss · Distribution shift, Degree greater than 5 | MSE | Helped |
| vary RS tolerance rate ε within 15% relative error of its optimum rather than DRO radius r | RS compared with DRO · Distribution shift, hyperparameter sensitivity | MSE: 0.30 vs 0.125 | Helped |
| set DRO radius r below 0.24, with the reported optimum around 0.215 | DRO · Distribution shift | MSE: 0.24; 0.215 | Helped |
| set 1+ε below 1.4, with the reported optimum around 1.285 | RS · Distribution shift | MSE: 1.4; 1.285 | Helped |
Surprising findings
- The RS constraint's dual form under Lipschitz losses is equivalent to DRO with radius r(ε), but the mapping is concave, making RS less sensitive to its hyperparameter than DRO.
Limitations
- Confidence and remainder rates suffer the curse of dimensionality (exponent m in r_N).
- Results rely on Lipschitz continuity in ξ and light-tailed distributions; experiments are limited to synthetic linear regression.
- Proof of the fragility bound and remainder terms contain informal steps; generalization bound lacks lower bounds.
Experimental setup
Datasets: synthetic linear regression data (Gaussian features, linear labels with Gaussian noise)
Benchmarks: synthetic linear regression
Metrics: mean squared error on target distribution
Baselines: empirical risk minimization distributionally robust optimization
Builds on: Distributionally Robust Optimization Robust Satisficing Wasserstein concentration of empirical measures
Closest papers by meaning
- Distributionally Robust Performative Optimization (NeurIPS 2025 · similarity 0.89)
- Bayesian Nonparametrics Meets Data-Driven Distributionally Robust Optimization (NeurIPS 2024 · similarity 0.88)
- Distributionally Robust Optimization with Bias and Variance Reduction (ICLR 2024 · similarity 0.88)
- Outlier-Robust Distributionally Robust Optimization via Unbalanced Optimal Transport (NeurIPS 2024 · similarity 0.87)
- Wasserstein Distributionally Robust Optimization through the Lens of Structural Causal Models and Individual Fairness (NeurIPS 2024 · similarity 0.86)
- Large-Scale Non-convex Stochastic Constrained Distributionally Robust Optimization (AAAI 2024 · similarity 0.86)
Writing a paper in this area? scime draft is a free LaTeX editor with AI included, real-time co-authors and a check of your references and venue rules before you submit. It also imports OpenAI Prism projects.