Safe Start: Configuring Optimization Algorithms for Decision-Making under Extreme Risks

2026-08-10

AI Summary

This work addresses the challenge in safety-sensitive stochastic optimization where tail risk exhibits high sensitivity to decision variables, making it difficult for conventional methods to simultaneously optimize average performance and control extreme risks. The authors propose a novel framework that integrates a “safe-start” mechanism with variance reduction techniques. By employing simulation-guided safe initialization, the approach overcomes convergence failures in stochastic gradient descent caused by step-size selection, achieving provably improved sample complexity. Empirical evaluations on portfolio optimization and robust neural network classification demonstrate that the method substantially enhances decision safety under extreme risk scenarios while improving algorithmic efficiency.

Abstract

We consider stochastic optimization where the goal is not only to optimize an average-case objective, but also to mitigate the occurrence of rare catastrophic events. This problem is motivated by safety-aware decision-making and AI training. We first argue that, in the presence of a simulation model, natural attempts to integrate variance reduction into optimization, even executed in a reasonable adaptive fashion, encounter fundamental challenges in guaranteeing realistic runtime when using common stochastic gradient descent algorithms. This challenge arises from the extreme sensitivity of tail-based objectives with respect to the decision variables, which renders a dichotomic failure of convergence regardless of what step size we select. We offer remedies based on a new notion of safe start that allows for efficient finite-time error control, and show how the sampling complexity scales favorably under the combination of safe start and variance reduction. We illustrate our methodologies on examples in portfolio optimization and robust classification with neural networks.

Problem

• stochastic optimization
• catastrophic events
• safety-aware decision-making
• tail risk
• extreme risks

Innovation

• Safe Start
• stochastic optimization
• tail risk
• variance reduction
• convergence failure