A novel multi-agent dynamic portfolio optimization learning system based on hierarchical deep reinforcement learning

Deep Reinforcement Learning (DRL) has been extensively used to address portfolio optimization problems. The DRL agents acquire knowledge and make decisions through unsupervised interactions with their environment without requiring explicit knowledge of the joint dynamics of portfolio assets. Among these DRL algorithms, the combination of actor-critic algorithms and deep function approximators is the most widely used DRL algorithm. Here, we find that training the DRL agent using the actor-critic algorithm and deep function approximators may lead to scenarios where the improvement in the DRL agent's risk-adjusted profitability is not significant. We propose that such situations primarily arise from the following two problems: sparsity in positive reward and the curse of dimensionality. These limitations prevent DRL agents from comprehensively learning asset price change patterns in the training environment. As a result, the DRL agents cannot explore the dynamic portfolio optimization policy to improve the risk-adjusted profitability in the training process. To address these problems, we propose a novel multi-agent Hierarchical Deep Reinforcement Learning (HDRL) algorithmic framework in this research. Under this framework, the agents work together as a learning system for portfolio optimization. Specifically, by designing an auxiliary agent that works together with the executive agent for optimal policy exploration, the learning system can focus on exploring the policy with higher risk-adjusted return in the action space with positive return and low variance. In this way, we can overcome the issue of the curse of dimensionality and improve the training efficiency in the positive reward sparse environment.