Meta-Learning the Optimal Mixture of Strategies for Online Portfolio Selection
Jiayu Shen, Jia Liu, Zhiping Chen
TL;DR
The paper tackles online portfolio selection under non-stationary markets by decomposing long-horizon decisions into short-term tasks and learning a fast-adapting mixture of candidate policies. It integrates model-agnostic meta-learning (MAML) with a mixture-policy framework: candidate policies are identified via clustering, and a neural network outputs mixture weights to combine these policies into the final portfolio, enabling rapid adaptation to new tasks. The approach, evaluated as LMPS-SMO for single-market and LMPS-CMO for cross-market scenarios, shows superior performance in cumulative wealth and risk metrics and demonstrates strong transferability across markets with reduced training data requirements. This framework is particularly suited for high-frequency trading, offering data-efficient adaptation and robust generalization across market regimes. Key formulas include the final portfolio $\boldsymbol{b}_t=\sum_{j=1}^M \omega_t^j \boldsymbol{b}_t^j$ with $\boldsymbol{\omega}_t \in \Delta_M^+$ and cumulative wealth $S_T=S_0\prod_{t=1}^T \mu_{t-1}\boldsymbol{b}_t^\top \boldsymbol{x}_t$, illustrating the core mechanics of mixture policies under non-stationary dynamics.
Abstract
This paper presents an innovative online portfolio selection model, situated within a meta-learning framework, that leverages a mixture policies strategy. The core idea is to simulate a fund that employs multiple fund managers, each skilled in handling different market environments, and dynamically allocate our funding to these fund managers for investment. To address the non-stationary nature of financial markets, we divide the long-term process into multiple short-term processes to adapt to changing environments. We use a clustering method to identify a set of historically high-performing policies, characterized by low similarity, as candidate policies. Additionally, we employ a meta-learning method to search for initial parameters that can quickly adapt to upcoming target investment tasks, effectively providing a set of well-suited initial strategies. Subsequently, we update the initial parameters using the target tasks and determine the optimal mixture weights for these candidate policies. Empirical tests show that our algorithm excels in terms of training time and data requirements, making it particularly suitable for high-frequency algorithmic trading. To validate the effectiveness of our method, we conduct numerical tests on cross-training datasets, demonstrating its excellent transferability and robustness.