Risk-Adaptive Approaches to Stochastic Optimization: A Survey
This is an incremental survey that consolidates existing knowledge on risk-adaptive approaches for researchers and practitioners dealing with uncertainty in optimization problems.
The paper surveys the development and applications of risk measures in stochastic optimization over the past 25 years, highlighting their computational and theoretical advantages across fields like engineering and machine learning.
Uncertainty is prevalent in engineering design, data-driven problems, and decision making broadly. Due to inherent risk-averseness and ambiguity about assumptions, it is common to address uncertainty by formulating and solving conservative optimization models expressed using measures of risk and related concepts. We survey the rapid development of risk measures over the last quarter century. From their beginning in financial engineering, we recount the spread to nearly all areas of engineering and applied mathematics. Solidly rooted in convex analysis, risk measures furnish a general framework for handling uncertainty with significant computational and theoretical advantages. We describe the key facts, list several concrete algorithms, and provide an extensive list of references for further reading. The survey recalls connections with utility theory and distributionally robust optimization, points to emerging applications areas such as fair machine learning, and defines measures of reliability.