Multi-period portfolio optimization is important for real portfolio management, as it accounts for transaction costs, path-dependent risks, and the intertemporal structure of trading decisions that single-period models cannot capture. Classical methods usually follow a two-stage framework: machine learning algorithms are employed to produce forecasts that closely fit the realized returns, and the predicted values are then used in a downstream portfolio optimization problem to determine the asset weights. This separation leads to a fundamental misalignment between predictions and decision outcomes, while also ignoring the impact of transaction costs. To bridge this gap, recent studies have proposed the idea of end-to-end learning, integrating the two stages into a single pipeline. This paper introduces IPMO (Integrated Prediction and Multi-period Portfolio Optimization), a model for multi-period mean-variance portfolio optimization with turnover penalties. The predictor generates multi-period return forecasts that parameterize a differentiable convex optimization layer, which in turn drives learning via portfolio performance. For scalability, we introduce a mirror-descent fixed-point (MDFP) differentiation scheme that avoids factorizing the Karush-Kuhn-Tucker (KKT) systems, which thus yields stable implicit gradients and nearly scale-insensitive runtime as the decision horizon grows. In experiments with real market data and two representative time-series prediction models, the IPMO method consistently outperforms the two-stage benchmarks in risk-adjusted performance net of transaction costs and achieves more coherent allocation paths. Our results show that integrating machine learning prediction with optimization in the multi-period setting improves financial outcomes and remains computationally tractable.

翻译：多期投资组合优化对于实际投资组合管理至关重要，因为它能够考虑交易成本、路径依赖风险以及单期模型无法捕捉的交易决策跨期结构。经典方法通常遵循两阶段框架：首先采用机器学习算法生成与实现收益紧密拟合的预测值，随后将这些预测值用于下游投资组合优化问题以确定资产权重。这种分离导致预测与决策结果之间存在根本性错位，同时忽略了交易成本的影响。为弥合这一差距，近期研究提出了端到端学习的思想，将两个阶段整合为单一流程。本文提出IPMO（集成预测与多期投资组合优化）模型，这是一种带有换手率惩罚的多期均值-方差投资组合优化模型。预测器生成多期收益预测，这些预测参数化一个可微凸优化层，进而通过投资组合表现驱动学习过程。为实现可扩展性，我们引入镜像下降不动点（MDFP）微分方案，避免对Karush-Kuhn-Tucker（KKT）系统进行因式分解，从而产生稳定的隐式梯度，且决策周期增长时运行时间几乎不受规模影响。在真实市场数据和两种代表性时间序列预测模型的实验中，IPMO方法在扣除交易成本的风险调整后表现上持续优于两阶段基准方法，并实现了更一致的资金配置路径。我们的结果表明，在多期设定中将机器学习预测与优化相结合能够改善财务结果，同时保持计算可行性。