Portfolio management is a multi-period multi-objective optimisation problem
subject to a wide range of constraints. However, in practice, portfolio
management is treated as a single-period problem partly due to the
computationally burdensome hyper-parameter search procedure needed to construct
a multi-period Pareto frontier. This study presents the \gls{ParDen-Sur}
modelling framework to efficiently perform the required hyper-parameter search.
\gls{ParDen-Sur} extends previous surrogate frameworks by including a reservoir
sampling-based look-ahead mechanism for offspring generation in \glspl{EA}
alongside the traditional acceptance sampling scheme. We evaluate this
framework against, and in conjunction with, several seminal \gls{MO} \glspl{EA}
on two datasets for both the single- and multi-period use cases. Our results
show that \gls{ParDen-Sur} can speed up the exploration for optimal
hyper-parameters by almost $2\times$ with a statistically significant
improvement of the Pareto frontiers, across multiple \glspl{EA}, for both
datasets and use cases.

本文提出了使用 ParDen-Sur 建模框架来解决组合管理作为一个多期多目标优化问题中的超参数搜索问题，并验证 ParDen-Sur 可以显著提高 Pareto 前沿的多个 EA 在单期和多期使用情况下的性能表现。

基于 Pareto 驱动代理的多周期组合回测模拟优化

Pareto Driven Surrogate (ParDen-Sur) Assisted Optimisation of Multi-period Portfolio Backtest Simulations

We investigate how the final parameters found by stochastic gradient descent
are influenced by over-parameterization. We generate families of models by
increasing the number of channels in a base network, and then perform a large
hyper-parameter search to study how the test error depends on learning rate,
batch size, and network width. We find that the optimal SGD hyper-parameters
are determined by a "normalized noise scale," which is a function of the batch
size, learning rate, and initialization conditions. In the absence of batch
normalization, the optimal normalized noise scale is directly proportional to
width. Wider networks, with their higher optimal noise scale, also achieve
higher test accuracy. These observations hold for MLPs, ConvNets, and ResNets,
and for two different parameterization schemes ("Standard" and "NTK"). We
observe a similar trend with batch normalization for ResNets. Surprisingly,
since the largest stable learning rate is bounded, the largest batch size
consistent with the optimal normalized noise scale decreases as the width
increases.

通过超参寻优与一系列不同的神经网络模型，我们探究了过度参数化情况下随机梯度下降最终调整到的参数状态，并发现优化算法的最优超参数取决于一项被规范化的噪声参数，其与网络宽度等因素有关，这对各种类型的神经网络均成立，对于 ResNets 这样的网络同样存在相似的趋势。