A Unified Efficient Gradient-Based Heuristic For Box-Constrained Expectation-Related and Risk-Averse Stochastic Optimization Problems
TL;DR
The algorithm is parameterized so as to address various stochastic formulations spanning from Expectation-focused to Value-at-Risk (VaR) as well as Conditional-Value-at-Risk (CVaR) as well as Conditional-Value-at-Risk (CVaR)-focused formulations.
Abstract
This paper presents a new algorithm addressing the problem of stochastic optimization where the cost function depends on a vector of uncertain parameters with known statistics. The algorithm is parameterized so as to address various stochastic formulations spanning from Expectation-focused to Value-at-Risk (VaR) as well as Conditional-Value-at-Risk (CVaR)-focused formulations. The algorithm leverages a recently proposed gradient-based Search&Accelerate algorithm which is originally dedicated to deterministic optimization problems. The approach is based on a sequence of warm-started solutions of instances of the problem. These solutions together with a samples of other solutions belonging to the convex hull of the first ones constitute the set of admissible candidates. Among this discrete set of candidates, the optimal solution is selected with regards to a sample-based approximation of the targeted criterion. The relevance of the algorithm and its efficiency are discussed and shown using a tailored illustrative example.