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| 摘要: |
| 分布漂移下的学习系统可以表述为极小极大优化形式，如分布鲁棒优化、不变风险最小化和极小极大遗憾优化(minimax regret optimization, MRO). 尽管越来越受关注，但现有研究通常侧重于算法设计和计算策略，而对泛化性分析相对较少.
通过将条件风险价值(conditional value at risk, CVaR)的度量引入MRO，本文提出了一种新的学习框架，并从一致收敛分析的角度建立了其泛化误差界. 结果表明，基于CVaR的MRO可以取得超额风险的多项式衰减率，这将期望风险相关的泛化分析扩展到了风险规避情形. |
| 关键词: 极小极大遗憾优化 (MRO) 条件价值风险 (CVaR) 分布漂移 泛化误差 |
| DOI： |
| 分类号:O1-0; O29 |
| 基金项目:湖北省教育科学规划课题；湖北省自然科学基金 |
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| Generalization Analysis for CVaR-based Minimax Regret Optimization |
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Tao Yan-fang,Deng Hao
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| Abstract: |
| Learning systems under distribution shift can be formulated as minimax optimization schemes such as distribution robust optimization, invariant risk minimization, and minimax regret optimization (MRO). Despite attracting increasing attention, the existing studies often focus on algorithmic design and computing strategy. In contrast, there is far less work on characterizing their generalization behavior in theory. In this paper, we propose a new learning framework by injecting the measure of Conditional Value at Risk (CVaR) into MRO, and establish its generalization error bounds through the lens of uniform convergence analysis. These results reveal our CVaR-based MRO can achieve the polynomial decay rate on the excess risk, which extends the generalization analysis associated with the expected risk to the risk-averse case. |
| Key words: Minimax regret optimization (MRO) conditional value at risk (CVaR) distri- bution shift generalization error |
