不同优化器让相同误差的模型做出不同决策，影响投资组合表现。
Same Error, Different Function: The Optimizer as an Implicit Prior in Financial Time Series
- 在模型误差相同时，优化器选择改变非线性响应与时间依赖结构。
- 相同预测精度下，投资组合换手率差异达3倍，但夏普比率相近。
- 适合关注模型决策影响的量化研究者，尤其金融时序建模场景。
将神经网络应用于金融时间序列时，处于模型欠定状态，不同模型预测器的样本外误差几乎无法区分。基于标普500股票的大规模波动率预测实验表明，即使测试损失相同，不同的模型训练管道会学习到质异的函数。尽管预测准确率不变，优化器的选择却显著改变非线性响应特征和时间依赖结构。这些差异带来实质性影响：以波动率排序的投资组合呈现近乎垂直的夏普-换手率前沿，在相近夏普比率下换手率差异接近3倍。我们得出结论，在欠定条件下，优化过程构成重要归纳偏置来源，因此模型评估应超越单一损失值，扩展至函数行为与决策层面的影响。
原文摘要 · Abstract (English)
Neural networks applied to financial time series operate in a regime of underspecification, where model predictors achieve indistinguishable out-of-sample error. Using large-scale volatility forecasting for S$\&$P 500 stocks, we show that different model-training-pipeline pairs with identical test loss learn qualitatively different functions. Across architectures, predictive accuracy remains unchanged, yet optimizer choice reshapes non-linear response profiles and temporal dependence differently. These divergences have material consequences for decisions: volatility-ranked portfolios trace a near-vertical Sharpe-turnover frontier, with nearly $3\times$ turnover dispersion at comparable Sharpe ratios. We conclude that in underspecified settings, optimization acts as a consequential source of inductive bias, thus model evaluation should extend beyond scalar loss to encompass functional and decision-level implications.
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