Statistical Learning with Conditional Value at Risk
This work addresses risk management in machine learning for applications requiring robust performance, though it is incremental by extending CVaR optimization to sample-based settings.
The authors tackled the problem of risk-averse statistical learning by proposing a framework that uses conditional value-at-risk (CVaR) instead of expected loss, and they developed stochastic gradient descent algorithms that achieve O(1/√n)-convergence for convex losses and provide generalization bounds for nonconvex losses.
We propose a risk-averse statistical learning framework wherein the performance of a learning algorithm is evaluated by the conditional value-at-risk (CVaR) of losses rather than the expected loss. We devise algorithms based on stochastic gradient descent for this framework. While existing studies of CVaR optimization require direct access to the underlying distribution, our algorithms make a weaker assumption that only i.i.d.\ samples are given. For convex and Lipschitz loss functions, we show that our algorithm has $O(1/\sqrt{n})$-convergence to the optimal CVaR, where $n$ is the number of samples. For nonconvex and smooth loss functions, we show a generalization bound on CVaR. By conducting numerical experiments on various machine learning tasks, we demonstrate that our algorithms effectively minimize CVaR compared with other baseline algorithms.