Geometry-Calibrated DRO: Combating Over-Pessimism with Free Energy Implications

• URL: http://arxiv.org/abs/2311.05054v1
• Date: Wed, 8 Nov 2023 23:33:39 GMT
• Title: Geometry-Calibrated DRO: Combating Over-Pessimism with Free Energy Implications
• Authors: Jiashuo Liu, Jiayun Wu, Tianyu Wang, Hao Zou, Bo Li, Peng Cui
• Abstract summary: Machine learning algorithms minimize average risk are susceptible to distributional shifts. distributionally robust optimization (DRO) addresses this issue by optimizing the worst-case risk within an uncertainty set. DRO suffers from over-pessimism, leading to low-confidence predictions, poor parameter estimations as well as poor generalization. In this work, we conduct a theoretical analysis of a probable root cause of over-pessimism: excessive focus on noisy samples.
• Score: 31.3535638804615
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: Machine learning algorithms minimizing average risk are susceptible to distributional shifts. Distributionally Robust Optimization (DRO) addresses this issue by optimizing the worst-case risk within an uncertainty set. However, DRO suffers from over-pessimism, leading to low-confidence predictions, poor parameter estimations as well as poor generalization. In this work, we conduct a theoretical analysis of a probable root cause of over-pessimism: excessive focus on noisy samples. To alleviate the impact of noise, we incorporate data geometry into calibration terms in DRO, resulting in our novel Geometry-Calibrated DRO (GCDRO) for regression. We establish the connection between our risk objective and the Helmholtz free energy in statistical physics, and this free-energy-based risk can extend to standard DRO methods. Leveraging gradient flow in Wasserstein space, we develop an approximate minimax optimization algorithm with a bounded error ratio and elucidate how our approach mitigates noisy sample effects. Comprehensive experiments confirm GCDRO's superiority over conventional DRO methods.

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