提出新优化方法，能在更广场景下快速稳定收敛。
Adaptive Gradient-Based Methods for a Broader Class of Optimization Problems under Performative Prediction
- 用有限差分估计分布变化，放宽对数据和损失的假设
- 支持高维优化，实验显示收敛更快更稳定
- 适合实际部署中数据分布会变的场景
我们研究优化中的表现性预测问题，即模型部署会影响未来的数据分布。现有基于梯度的方法通常依赖特定的数据分布或损失函数，限制了实际应用。为此，我们提出一种在更弱假设下具有收敛保证的梯度优化方法。该方法通过有限差分显式估计诱导的分布偏移，支持更高维度的优化，适用于更广泛的损失函数和数据分布。我们还提出了一个实用变体，减少采样需求。数值实验表明，所提算法比现有方法收敛更快且更一致。
原文摘要 · Abstract (English)
We study optimization under performative prediction, where deploying a model affects the future data distribution. For this setting, several gradient-based approaches have been proposed. However, they typically assume specific data distributions or loss functions, which limit their practical applicability. To overcome these limitations, we propose a gradient-based optimization method with convergence guarantees under substantially weaker assumptions. Our method explicitly estimates the induced distribution shift through finite differences. It enables higher-dimensional optimization across broader classes of loss functions and data distributions. We also propose a practical variant that reduces the number of samples required. Numerical experiments demonstrate that our proposed algorithms converge faster and more consistently than existing ones.
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