# MILLION: A General Multi-Objective Framework with Controllable Risk for Portfolio Management

arXiv: https://arxiv.org/abs/2412.03038 · HTML: https://mlsanity.com/paper/2412.03038/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 50 references that are in the map.
- First posted on arXiv 4 Dec 2024.

## Builds on (most cited first, 9 of 9)

- [Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting](https://mlsanity.com/paper/2012.07436/) (2020)
- [Autoformer: Decomposition Transformers with Auto-Correlation for Long-Term Series Forecasting](https://mlsanity.com/paper/2106.13008/) (2021)
- [Multi-Task Learning Using Uncertainty to Weigh Losses for Scene Geometry and Semantics](https://mlsanity.com/paper/1705.07115/) (2017)
- [Temporal Relational Ranking for Stock Prediction](https://mlsanity.com/paper/1809.09441/) (2018)
- [FinRL: Deep Reinforcement Learning Framework to Automate Trading in Quantitative Finance](https://mlsanity.com/paper/2111.09395/) (2021)
- [Reinforcement-Learning based Portfolio Management with Augmented Asset Movement Prediction States](https://mlsanity.com/paper/2002.05780/) (2020)
- [AlphaStock: A Buying-Winners-and-Selling-Losers Investment Strategy using Interpretable Deep Reinforcement Attention Networks](https://mlsanity.com/paper/1908.02646/) (2019)
- [Deep Stock Trading: A Hierarchical Reinforcement Learning Framework for Portfolio Optimization and Order Execution](https://mlsanity.com/paper/2012.12620/) (2020)
- [DeepScalper: A Risk-Aware Reinforcement Learning Framework to Capture Fleeting Intraday Trading Opportunities](https://mlsanity.com/paper/2201.09058/) (2021)

## Built on by (most cited first, 6 of 6)

- [Efficient Large-Scale Traffic Forecasting with Transformers: A Spatial Data Management Perspective](https://mlsanity.com/paper/2412.09972/) (2024)
- [Unraveling Spatio-Temporal Foundation Models via the Pipeline Lens: A Comprehensive Review](https://mlsanity.com/paper/2506.01364/) (2025)
- [Multi-objective Portfolio Optimization Via Gradient Descent](https://mlsanity.com/paper/2507.16717/) (2025)
- [DATA-WA: Demand-based Adaptive Task Assignment with Dynamic Worker Availability Windows](https://mlsanity.com/paper/2503.21458/) (2025)
- [Large-scale portfolio optimization with variational neural annealing](https://mlsanity.com/paper/2507.07159/) (2025)
- [Virne: A Comprehensive Benchmark for RL-based Network Resource Allocation in NFV](https://mlsanity.com/paper/2507.19234/) (2025)

## Abstract (arXiv)

Portfolio management is an important yet challenging task in AI for FinTech, which aims to allocate investors' budgets among different assets to balance the risk and return of an investment. In this study, we propose a general Multi-objectIve framework with controLLable rIsk for pOrtfolio maNagement (MILLION), which consists of two main phases, i.e., return-related maximization and risk control. Specifically, in the return-related maximization phase, we introduce two auxiliary objectives, i.e., return rate prediction, and return rate ranking, combined with portfolio optimization to remit the overfitting problem and improve the generalization of the trained model to future markets. Subsequently, in the risk control phase, we propose two methods, i.e., portfolio interpolation and portfolio improvement, to achieve fine-grained risk control and fast risk adaption to a user-specified risk level. For the portfolio interpolation method, we theoretically prove that the risk can be perfectly controlled if the to-be-set risk level is in a proper interval. In addition, we also show that the return rate of the adjusted portfolio after portfolio interpolation is no less than that of the min-variance optimization, as long as the model in the reward maximization phase is effective. Furthermore, the portfolio improvement method can achieve greater return rates while keeping the same risk level compared to portfolio interpolation. Extensive experiments are conducted on three real-world datasets. The results demonstrate the effectiveness and efficiency of the proposed framework.