Stochastic Optimization for Spectral Risk Measures

At first glance, this is a natural summary, inheriting both the statistical amenability of the sample mean (Shalev-Shwartz and Ben-David, 2014) and the wide arsenal of optimization algorithms designed specifically for finite sum objectives (Le Roux et al., 2012; Defazio et al., 2014; Johnson and Zhang, 2013; Reddi et al., 2016). However, as modern learning systems are deployed in critical domain applications such as energy planning (Guigues and Sagastizábal, 2013), materials engineering (Yeh, 2006), and financial regulation (He et al., 2022), safe and reliable performance in "worst-case" scenarios is paramount. This imperative can be modeled by alternate risk measures (statistical functionals of the loss distribution), particularly those that encapsulate the behavior of the distribution's upper tail.