Learning Models with Uniform Performance via Distributionally Robust Optimization (1810.08750v6)

Abstract: A common goal in statistics and machine learning is to learn models that can perform well against distributional shifts, such as latent heterogeneous subpopulations, unknown covariate shifts, or unmodeled temporal effects. We develop and analyze a distributionally robust stochastic optimization (DRO) framework that learns a model providing good performance against perturbations to the data-generating distribution. We give a convex formulation for the problem, providing several convergence guarantees. We prove finite-sample minimax upper and lower bounds, showing that distributional robustness sometimes comes at a cost in convergence rates. We give limit theorems for the learned parameters, where we fully specify the limiting distribution so that confidence intervals can be computed. On real tasks including generalizing to unknown subpopulations, fine-grained recognition, and providing good tail performance, the distributionally robust approach often exhibits improved performance.

• The paper introduces a distributionally robust optimization framework that improves model performance under worst-case distributional shifts.
• It formulates the problem as a convex minimax optimization with proven convergence guarantees and finite-sample bounds.
• Empirical results highlight the framework's applicability to real-world tasks, ensuring fair and reliable performance across subpopulations.

Learning Models with Uniform Performance via Distributionally Robust Optimization

The paper "Learning Models with Uniform Performance via Distributionally Robust Optimization" by Duchi and Namkoong introduces a robust framework aimed at improving model performance amidst distributional variations and uncertainties. This is notably relevant in diverse subpopulations or under covariate shifts, where traditional statistical models often underperform.

Key Contributions and Methodology

The authors propose a distributionally robust optimization (DRO) framework that leverages a minimax approach to ensure model robustness against worst-case scenarios. The core of the methodology revolves around enhancing the generalization of models by focusing on perturbed data-generating distributions within specified divergence bounds. This strategy is articulated through a convex optimization problem, and the authors provide a series of convergence guarantees to reinforce the theoretical underpinnings.

1. Convex Formulation and Convergence: The paper presents a convex formulation for the DRO problem, which ensures computational feasibility in solving the optimization problem. Moreover, convergence guarantees are established, ensuring that the robust solutions are statistically sound.
2. Finite-Sample Bounds and Asymptotic Behavior: The authors elucidate finite-sample minimax upper and lower bounds, highlighting that robust optimization does impose a convergence rate cost. They incorporate limit theorems for the learned parameters, establishing the relevance of computing confidence intervals.
3. Theoretical and Practical Implications: The exploration of minimax formulations and the subsequent bounds introduces new theoretical insights into robust learning paradigms. From a practical standpoint, the approach caters to applications requiring consistent performance, like safety-critical systems.

Empirical Demonstrations

The authors support their theoretical framework by showcasing empirical applications in tasks that involve diverse subpopulations, unknown distributions, and fairness concerns. Particularly, the DRO approach is evaluated on tasks like fine-grained image recognition, where its robustness against demographic variations adds significant value.

Implications and Future Work

The implications of this work are multidimensional, impacting both the theoretical landscape of robust optimization and its practical applications in AI systems requiring uniform risk management. The DRO's performance on real-world datasets suggests a broader applicability, encouraging further exploration into alternate divergence measures and adaptive mechanisms for tailored robustness.

In future work, expanding the DRO framework to incorporate dynamic or non-static risk measures—potentially through adaptive divergence metrics—can advance system reliability. Additionally, exploring more computationally efficient algorithms for large-scale data and high-dimensional spaces remains an important frontier.

This paper represents a significant stride in bridging robustness with statistical learning, offering a robust alternative for models that must withstand the unpredictabilities inherent in real-world data environments.