Model Alignment and Personalization Trade-off in Federated Learning for Cross-Institutional Financial Time Series Forecasting

Model Alignment and Personalization Trade-off in Federated Learning for Cross-Institutional Financial Time Series Forecasting

1. Problem Background
In financial time series forecasting scenarios (e.g., stock price prediction, credit risk trend prediction), multiple financial institutions (e.g., banks, securities firms) may possess similar time series data with different distributions. Due to data privacy and regulatory compliance requirements, institutions cannot directly share raw data, limiting the effectiveness of traditional centralized modeling. Federated Learning (FL) allows institutions to train models locally, exchanging only model parameters rather than raw data. However, it faces two main challenges:

  • Model Alignment: Different institutions have varying data distributions (e.g., customer demographics, market environments). Directly aggregating model parameters may lead to degraded performance of the global model on local data.
  • Personalization Trade-off: Excessive personalization (using independent models per institution) fails to leverage cross-institutional information, while enforcing global consistency may neglect local characteristics.

2. Core Concepts

  • Basic Federated Learning Process:

    1. The central server initializes a global model.
    2. Each institution downloads the global model and trains it with local data to obtain local model updates.
    3. Institutions upload model updates (e.g., gradients, parameters) to the server.
    4. The server aggregates the updates (e.g., using the FedAvg algorithm) to generate a new global model.
    5. Repeat steps 2-4 until convergence.

  • Special Characteristics of Time Series Data:
    Financial time series data exhibit non-stationarity, serial dependence, heteroskedasticity, and other features. Data from different institutions may come from distinct markets (e.g., A-shares vs. Hong Kong stocks), leading to distribution shifts (e.g., volatility differences, cyclical misalignment).

3. Difficulties in Model Alignment

  • Statistical Heterogeneity: Data distributions vary across institutions \(P_i(X,Y) \neq P_j(X,Y)\), for example:
    • Feature shift: Income distributions differ among customers in different regions.
    • Label shift: Economic cycles cause varying default rate trends over time.
  • System Heterogeneity: Differences in data volume, collection frequency, and storage formats across institutions.

4. Solution: Personalized Federated Learning (Personalized FL)
The goal of Personalized FL is to enable institutions to leverage global information while preserving local characteristics. Main methods include:

Step 1: Local Fine-tuning

  • Training Process:
    1. First, train a global model \(M_g\) using federated learning.
    2. Each institution downloads \(M_g\) and continues training (fine-tuning) with local data to obtain a personalized model \(M_i\).
  • Key Issue: The number of fine-tuning steps requires balancing—too few steps lead to insufficient personalization, while too many may cause overfitting to local data.

Step 2: Model Mixture

  • Each institution's model is represented as a weighted combination of the global model and a local model:

\[ M_i = \alpha M_g + (1-\alpha) M_{local,i} \]

  • The weight \(\alpha\) can be adjusted via a local validation set: increase \(\alpha\) if local data distribution is similar to the global distribution.

Step 3: Meta-Learning-Based Personalization

  • Core Idea: Train a meta-model that can quickly adapt to new institutions.
  • Steps:
    1. Treat each institution as a different "task" during federated training.
    2. Meta-learning algorithms (e.g., MAML) learn a set of initialization parameters that allow the model to adapt to new institutions with minimal local training.
    3. During inference, each institution fine-tunes the meta-model with a small amount of local data to obtain a personalized model.

Step 4: Clustered Federated Learning

  • Idea: Group institutions with similar data distributions and train a cluster-specific model per group.
  • Steps:
    1. The server clusters institutions based on model parameter or data distribution similarity (e.g., using gradient similarity metrics).
    2. Institutions within the same cluster collaboratively train a sub-global model.
    3. Each institution further personalizes based on the sub-global model.

5. Specific Adjustments for Financial Time Series Forecasting

  • Handling Temporal Dependencies:
    • Local models can use sequence models like LSTM or Transformer. During federated aggregation, attention must be paid to how recurrent neural network parameters are aggregated (e.g., aggregating only fully connected layer parameters).
  • Handling Concept Drift:
    • Introduce time-decay weights, giving higher weight to recent data during local training.
  • Evaluating Personalization Effectiveness:
    • Use local test sets to compute personalized model performance, comparing prediction errors (e.g., MAPE, RMSE) against the global model and locally independent models.

6. Practical Deployment Considerations

  • Communication Efficiency: Time series models have large parameter counts, necessitating communication data compression (e.g., gradient quantization).
  • Security Enhancement: Add differential privacy noise or use homomorphic encryption to prevent parameter leakage of local information.
  • Dynamic Adjustment: Financial markets change rapidly, requiring regular re-evaluation of personalization weights or re-clustering.

7. Example: Cross-Bank Stock Volatility Forecasting

  • Scenario: Three banks possess daily trading data for stocks in different industries.
  • Steps:
    1. Use FedAvg to train a global LSTM model for forecasting 7-day ahead volatility.
    2. Bank A (primarily tech stocks) finds the global model has large prediction errors for cyclical stocks and employs local fine-tuning (10 additional training epochs).
    3. Bank B (primarily financial stocks) and Bank C (financial stocks) have similar data distributions. The server clusters them and trains a cluster-specific model.
    4. Bank B fine-tunes based on the cluster model to obtain the final personalized model.

Summary: Federated learning for cross-institutional time series forecasting requires balancing model alignment and personalization. Methods like fine-tuning, meta-learning, and clustering can address both data privacy and prediction performance, but aggregation strategies must be dynamically adjusted according to the temporal characteristics of financial data.