PAC generalization bounds on the risk, when expressed in terms of the expected loss, are often insufficient to capture imbalances between subgroups in the data. To overcome this limitation, we introduce a new family of risk measures, called constrained f-entropic risk measures, which enable finer control over distributional shifts and subgroup imbalances via f-divergences, and include the Conditional Value at Risk (CVaR), a well-known risk measure. We derive both classical and disintegrated PAC-Bayesian generalization bounds for this family of risks, providing the first disintegratedPAC-Bayesian guarantees beyond standard risks. Building on this theory, we design a self-bounding algorithm that minimizes our bounds directly, yielding models with guarantees at the subgroup level. Finally, we empirically demonstrate the usefulness of our approach.

翻译：当风险用期望损失表示时，关于风险的PAC泛化界通常不足以捕捉数据中不同子组之间的不平衡性。为克服这一局限，我们引入一类新的风险测度——称为约束f-熵风险测度——通过f-散度实现对分布偏移和子组不平衡的更精细控制，并涵盖了著名风险测度条件风险价值(CVaR)。我们推导了该类风险的经典和分解PAC-贝叶斯泛化界，首次提供了超越标准风险的分解PAC-贝叶斯保证。基于该理论，我们设计了一种自约束算法，可直接最小化我们的界限，从而得到具有子组级别保证的模型。最后，我们通过实验证明了该方法的有效性。