Combining Retrospective Approximation with Importance Sampling for Optimising Conditional Value at Risk

TL;DR

This paper presents a novel method combining retrospective approximation and importance sampling to efficiently optimize Conditional Value at Risk, addressing challenges in variance reduction and measure tailoring.

Contribution

It introduces a univariate importance sampling transformation integrated with retrospective approximation for risk-averse optimization, improving efficiency and variance reduction.

Findings

Achieves uniform variance reduction across optimization iterations

Reduces sample requirements for CVaR estimation

Demonstrates computational efficiency in risk-averse optimization

Abstract

This paper investigates the use of retrospective approximation solution paradigm in solving risk-averse optimization problems effectively via importance sampling (IS). While IS serves as a prominent means for tackling the large sample requirements in estimating tail risk measures such as Conditional Value at Risk (CVaR), its use in optimization problems driven by CVaR is complicated by the need to tailor the IS change of measure differently to different optimization iterates and the circularity which arises as a consequence. The proposed algorithm overcomes these challenges by employing a univariate IS transformation offering uniform variance reduction in a retrospective approximation procedure well-suited for tuning the IS parameter choice. The resulting simulation based approximation scheme enjoys both the computational efficiency bestowed by retrospective approximation and logarithmically efficient variance reduction offered by importance sampling