安全起始：极端风险下决策的优化算法配置
Safe Start: Configuring Optimization Algorithms for Decision-Making under Extreme Risks
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中文总结 AI 辅助
针对极端风险下的随机优化问题，提出基于安全起始的解决方案，结合方差缩减保障运行时间，在投资组合优化和神经网络鲁棒分类中验证了方法有效性。
中文摘要 AI 辅助
我们研究随机优化问题，其目标不仅是优化平均情况目标，还要降低罕见灾难性事件的发生概率。该问题由安全感知决策与AI训练驱动。我们首先指出，在存在仿真模型的情况下，即便以合理自适应方式尝试将方差缩减融入优化，使用常见的随机梯度下降（SGD）算法时，也会面临保障实际运行时间的根本挑战。这一挑战源于基于尾部的目标对决策变量的极端敏感性，无论选择何种步长，都会导致收敛的二分性失效。我们提出基于“安全起始”这一新概念的解决方案，该方案可实现高效的有限时间误差控制，并证明在安全起始与方差缩减结合下，采样复杂度呈有利缩放。我们在投资组合优化和神经网络鲁棒分类的示例中验证了所提方法。
英文摘要
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.
