On the Fundamental Limitations of Dual Static CVaR Decompositions in Markov Decision Processes
When making decisions—from financial investments to routing autonomous vehicles—we care not only about average outcomes but also about risk. A widely used risk metric is the Conditional Value at Risk, or CVaR, defined for confidence level $\alpha\in(0,1)$ by: $$ CVaR_\alpha(X) =\inf_{\xi}{\xi + \tfrac{1}{1-\alpha},E[(X-\xi)_+]}. $$ In their recent paper, Godbout and Durand (2025) examine how to reliably compute this metric in Markov Decision Processes (MDPs). They reveal that the most common method—the dual decomposition—suffers from inherent limitations. ...