Learning Bounds for Risk-sensitive Learning
This work addresses theoretical guarantees for risk-sensitive learning, which is important for applications requiring risk-averse or risk-seeking decisions, but it is incremental as it builds on existing OCE frameworks.
The paper tackles the generalization properties of risk-sensitive learning schemes using optimized certainty equivalents (OCE), providing two learning bounds: one based on Rademacher averages that improves existing results, and another using a variance-based characterization to suppress smoothness dependence, with exploratory experiments on neural networks.
In risk-sensitive learning, one aims to find a hypothesis that minimizes a risk-averse (or risk-seeking) measure of loss, instead of the standard expected loss. In this paper, we propose to study the generalization properties of risk-sensitive learning schemes whose optimand is described via optimized certainty equivalents (OCE): our general scheme can handle various known risks, e.g., the entropic risk, mean-variance, and conditional value-at-risk, as special cases. We provide two learning bounds on the performance of empirical OCE minimizer. The first result gives an OCE guarantee based on the Rademacher average of the hypothesis space, which generalizes and improves existing results on the expected loss and the conditional value-at-risk. The second result, based on a novel variance-based characterization of OCE, gives an expected loss guarantee with a suppressed dependence on the smoothness of the selected OCE. Finally, we demonstrate the practical implications of the proposed bounds via exploratory experiments on neural networks.