Timezone: »

 
A Stochastic Prox-Linear Method for CVaR Minimization
Si Yi Meng · Vasileios Charisopoulos · Robert Gower

@
in OPT 2022: Optimization for Machine Learning »
Event URL: https://openreview.net/forum?id=5wZDv71acVp »

We develop an instance of the stochastic prox-linear method for minimizing the Conditional Value-at-Risk (CVaR) objective. CVaR is a risk measure focused on minimizing worst-case performance, defined as the average of the top quantile of the losses. In machine learning, such a risk measure is useful to train more robust models. Although the stochastic subgradient method (SGM) is a natural choice for minimizing CVaR objective, we show that the prox-linear algorithm can be used to better exploit the structure of the objective, while still providing a convenient closed form update. We then specialize a general convergence theorem for the prox-linear method to our setting, and show that it allows for a wider selection of step sizes compared to SGM. We support this theoretical finding experimentally, by showing that the performance of stochastic prox-linear is more robust to the choice of step size compared to SGM.

Author Information

Si Yi Meng (Cornell University)
Vasileios Charisopoulos (Cornell University)
Robert Gower (Flatiron Institute)

More from the Same Authors