Learning Bounds for Risk-sensitive Learning

The systematic minimization of the quantifiable uncertainty, or risk [22], is one of the core objectives in all disciplines involving decision-making, e.g., economics and finance. Within machine learning contexts, strategies for risk-aversion have been most actively studied under sequential decision-making and reinforcement learning frameworks [21, 8], giving birth to a number of algorithms based on Markov decision processes (MDPs) and multi-armed bandits. In those works, various risk-averse measures of loss have been used as a minimization objective, instead of the risk-neutral expected loss; popular risk measures include entropic risk [21, 6, 7], mean-variance [39, 13, 28], and a slightly more modern alternative known as conditional value-at-risk (CVaR [15, 10, 42]). Yet, with growing interest to the societal impacts of machine intelligence, the importance of risk-aversion under non-sequential scenarios has also been spotlighted recently. For instance, Williamson and Menon [45] give an axiomatic characterization of the fairness risk measures, and propose a convex fairness-aware objective based on CVaR.