# Combining Transformer based Deep Reinforcement Learning with Black-Litterman Model for Portfolio Optimization

arXiv: https://arxiv.org/abs/2402.16609 · HTML: https://mlsanity.com/paper/2402.16609/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Placed in Adversarial robustness and RL in finance, one of 15 directions in Deep reinforcement learning methods.
- Builds on 19 of its 90 references that are in the map.
- First posted on arXiv 23 Feb 2024.

## Placed in

- Deep reinforcement learning methods / [Adversarial robustness and RL in finance](https://mlsanity.com/deeprl/adversarial-robustness-and-rl-in-finance/)

## Builds on (most cited first, 19 of 19)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [Soft Actor-Critic: Off-Policy Maximum Entropy Deep Reinforcement Learning with a Stochastic Actor](https://mlsanity.com/paper/1801.01290/) (2018)
- [Continuous control with deep reinforcement learning](https://mlsanity.com/paper/1509.02971/) (2015)
- [Playing Atari with Deep Reinforcement Learning](https://mlsanity.com/paper/1312.5602/) (2013)
- [Addressing Function Approximation Error in Actor-Critic Methods](https://mlsanity.com/paper/1802.09477/) (2018)
- [Asynchronous Methods for Deep Reinforcement Learning](https://mlsanity.com/paper/1602.01783/) (2016)
- [Autoformer: Decomposition Transformers with Auto-Correlation for Long-Term Series Forecasting](https://mlsanity.com/paper/2106.13008/) (2021)
- [Are Transformers Effective for Time Series Forecasting?](https://mlsanity.com/paper/2205.13504/) (2022)
- [Dueling Network Architectures for Deep Reinforcement Learning](https://mlsanity.com/paper/1511.06581/) (2015)
- [Distributional Reinforcement Learning with Quantile Regression](https://mlsanity.com/paper/1710.10044/) (2017)
- [Adaptive Input Representations for Neural Language Modeling](https://mlsanity.com/paper/1809.10853/) (2018)
- [A Deep Reinforcement Learning Framework for the Financial Portfolio Management Problem](https://mlsanity.com/paper/1706.10059/) (2017)
- [Recent Advances in Reinforcement Learning in Finance](https://mlsanity.com/paper/2112.04553/) (2021)
- [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)
- [Breaking the Curse of Dimensionality in Multiagent State Space: A Unified Agent Permutation Framework](https://mlsanity.com/paper/2203.05285/) (2022)

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

- [LiveTradeBench: Seeking Real-World Alpha with Large Language Models](https://mlsanity.com/paper/2511.03628/) (2025)
- [DeltaHedge: A Multi-Agent Framework for Portfolio Options Optimization](https://mlsanity.com/paper/2509.12753/) (2025)
- [A novel multi-agent dynamic portfolio optimization learning system based on hierarchical deep reinforcement learning](https://mlsanity.com/paper/2501.06832/) (2025)
- [MTS: A Deep Reinforcement Learning Portfolio Management Framework with Time-Awareness and Short-Selling](https://mlsanity.com/paper/2503.04143/) (2025)
- [MIGT: Memory Instance Gated Transformer Framework for Financial Portfolio Management](https://mlsanity.com/paper/2502.07280/) (2025)
- [Addressing Market Regime Changes and Heavy-Tailed Returns in Portfolio Optimization via Bayesian VAR and Elliptical Black-Litterman](https://mlsanity.com/paper/2606.09104/) (2026)

## Abstract (arXiv)

As a model-free algorithm, deep reinforcement learning (DRL) agent learns and makes decisions by interacting with the environment in an unsupervised way. In recent years, DRL algorithms have been widely applied by scholars for portfolio optimization in consecutive trading periods, since the DRL agent can dynamically adapt to market changes and does not rely on the specification of the joint dynamics across the assets. However, typical DRL agents for portfolio optimization cannot learn a policy that is aware of the dynamic correlation between portfolio asset returns. Since the dynamic correlations among portfolio assets are crucial in optimizing the portfolio, the lack of such knowledge makes it difficult for the DRL agent to maximize the return per unit of risk, especially when the target market permits short selling (i.e., the US stock market). In this research, we propose a hybrid portfolio optimization model combining the DRL agent and the Black-Litterman (BL) model to enable the DRL agent to learn the dynamic correlation between the portfolio asset returns and implement an efficacious long/short strategy based on the correlation. Essentially, the DRL agent is trained to learn the policy to apply the BL model to determine the target portfolio weights. To test our DRL agent, we construct the portfolio based on all the Dow Jones Industrial Average constitute stocks. Empirical results of the experiments conducted on real-world United States stock market data demonstrate that our DRL agent significantly outperforms various comparison portfolio choice strategies and alternative DRL frameworks by at least 42% in terms of accumulated return. In terms of the return per unit of risk, our DRL agent significantly outperforms various comparative portfolio choice strategies and alternative strategies based on other machine learning frameworks.