Optimizing the CVaR via Sampling

Understand

Conditional Value at Risk (CVaR) is a prominent risk measure that is being used extensively in various domains.

• We develop a new formula for the gradient of the CVaR in the form of a conditional expectation.
• Based on this formula, we propose a novel sampling-based estimator for the CVaR gradient, in the spirit of the likelihood-ratio method.
• We analyze the bias of the estimator, and prove the convergence of a corresponding stochastic gradient descent algorithm to a local CVaR optimum.