# Integrated Prediction and Multi-period Portfolio Optimization

arXiv: https://arxiv.org/abs/2512.11273 · HTML: https://mlsanity.com/paper/2512.11273/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 53 references that are in the map.
- First posted on arXiv 12 Dec 2025.

## Builds on (most cited first, 13 of 13)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [OptNet: Differentiable Optimization as a Layer in Neural Networks](https://mlsanity.com/paper/1703.00443/) (2017)
- [Differentiable Convex Optimization Layers](https://mlsanity.com/paper/1910.12430/) (2019)
- [Smart "Predict, then Optimize"](https://mlsanity.com/paper/1710.08005/) (2017)
- [Efficient and Modular Implicit Differentiation](https://mlsanity.com/paper/2105.15183/) (2021)
- [Multi-Period Trading via Convex Optimization](https://mlsanity.com/paper/1705.00109/) (2017)
- [Estimate-Then-Optimize versus Integrated-Estimation-Optimization versus Sample Average Approximation: A Stochastic Dominance Perspective](https://mlsanity.com/paper/2304.06833/) (2023)
- [Distributionally Robust End-to-End Portfolio Construction](https://mlsanity.com/paper/2206.05134/) (2022)
- [Differentiation Through Black-Box Quadratic Programming Solvers](https://mlsanity.com/paper/2410.06324/) (2024)
- [BPQP: A Differentiable Convex Optimization Framework for Efficient End-to-End Learning](https://mlsanity.com/paper/2411.19285/) (2024)
- [Dissecting the Impact of Model Misspecification in Data-driven Optimization](https://mlsanity.com/paper/2503.00626/) (2025)
- [A Scalable Algorithm For Sparse Portfolio Selection](https://mlsanity.com/paper/1811.00138/) (2018)
- [End-to-End Large Portfolio Optimization for Variance Minimization with Neural Networks through Covariance Cleaning](https://mlsanity.com/paper/2507.01918/) (2025)

## Abstract (arXiv)

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.