论文标题
随机近似与决策依赖性分布：渐近正态性和最佳性
Stochastic Approximation with Decision-Dependent Distributions: Asymptotic Normality and Optimality
论文作者
论文摘要
我们分析了一个随机近似算法，用于决策依赖性问题，其中算法沿迭代序列使用的数据分布。此类问题的主要示例出现在表演性预测及其多人游戏扩展中。我们表明，在温和的假设下，算法的平均迭代与溶液之间的偏差在渐近正常上，其协方差显然可以解除梯度噪声和分布变化的影响。此外，在Hájek和Le Cam的工作的基础上，我们表明该算法的渐近性能具有平均值，这在局部是最小的。
We analyze a stochastic approximation algorithm for decision-dependent problems, wherein the data distribution used by the algorithm evolves along the iterate sequence. The primary examples of such problems appear in performative prediction and its multiplayer extensions. We show that under mild assumptions, the deviation between the average iterate of the algorithm and the solution is asymptotically normal, with a covariance that clearly decouples the effects of the gradient noise and the distributional shift. Moreover, building on the work of Hájek and Le Cam, we show that the asymptotic performance of the algorithm with averaging is locally minimax optimal.
