为数据驱动的前向-后向算法提供解的质量保证，无需假设数据分布。
Finite-sample guarantees for data-driven forward-backward operator methods
- 基于算法稳定性分析，给出解与真实解距离的概率上界。
- 迭代次数越多，稳定性界限越宽松；强假设下则与迭代无关。
- 在智能电网能量价格求解中验证理论，适用于不确定性建模场景。
我们建立了基于数据的前向-后向（FB）算子分裂方案所产生解的质量的有限样本保证。在随机情形下，常需寻找两个算子和的零点，其中一算子无法显式表达或计算代价高，须用有限数量的噪声查询样本近似。借助算法稳定性视角，我们推导出真零点与FB输出之间距离的概率界，未对底层数据分布做特定假设。结果表明，在较弱条件下确保FB收敛时，稳定性界随迭代次数线性增长；而在更强假设下，稳定性保证与迭代次数无关。随后将结果应用于流行的随机纳什均衡寻求FB算法，并在智能电网控制问题中验证理论边界，其中能源价格不确定性通过历史数据近似。
原文摘要 · Abstract (English)
We establish finite sample certificates on the quality of solutions produced by data-based forward-backward (FB) operator splitting schemes. As frequently happens in stochastic regimes, we consider the problem of finding a zero of the sum of two operators, where one is either unavailable in closed form or computationally expensive to evaluate, and shall therefore be approximated using a finite number of noisy oracle samples. Under the lens of algorithmic stability, we then derive probabilistic bounds on the distance between a true zero and the FB output without making specific assumptions about the underlying data distribution. We show that under weaker conditions ensuring the convergence of FB schemes, stability bounds grow proportionally to the number of iterations. Conversely, stronger assumptions yield stability guarantees that are independent of the iteration count. We then specialize our results to a popular FB stochastic Nash equilibrium seeking algorithm and validate our theoretical bounds on a control problem for smart grids, where the energy price uncertainty is approximated by means of historical data.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。