Generalized Mean Absolute Directional Loss as a Solution to Overfitting and High Transaction Costs in Machine Learning Models Used in High-Frequency Algorithmic Investment Strategies

Paper: arXiv 2412.18405

Abstract

Regardless of the selected asset class and the level of model complexity (Transformer versus LSTM versus Perceptron/RNN), the GMADL loss function produces superior results than standard MSE-type loss functions and has better numerical properties in the context of optimization than MADL. Better results mean the possibility of achieving a higher risk-weighted return based on buy and sell signals built on forecasts generated by a given theoretical model estimated using the GMADL versus MSE or MADL function. In practice, GMADL solves the problem of selecting the most preferable feature in both classification and regression problems, improving the performance of each estimation. What is important is that, through additional parameterization, GMADL also solves the problem of optimizing investment systems on high-frequency data in such a way that they focus on strategy variants that contain fewer transactions so that transaction costs do not reduce the effectiveness of a given strategy to zero. Moreover, the implementation leverages state-of-the-art machine learning tools, including frameworks for hyperparameter tuning, architecture testing, and walk-forward optimization, ensuring robust and scalable solutions for real-world algorithmic trading.

Complexity vs Empirical Score

• Math Complexity: 7.5/10
• Empirical Rigor: 8.0/10
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper presents advanced mathematical derivations for a novel generalized loss function (GMADL) with multiple parameters and exponential smoothing, indicating high complexity. It also demonstrates strong empirical rigor through comprehensive backtesting on high-frequency data (Bitcoin, Crude Oil), hyperparameter tuning, walk-forward optimization, and risk-weighted return comparisons.

Research Flowchart

  flowchart TD
  A["Research Goal: Improve ML models for HFT<br>by reducing overfitting & transaction costs"] --> B["Data Input: High-Frequency Market Data"]
  B --> C{"Methodology: Compare Loss Functions"}
  C --> D["Model 1: Standard MSE Loss"]
  C --> E["Model 2: MADL Loss"]
  C --> F["Model 3: GMADL Loss"]
  
  subgraph Computational Process ["Model Estimation & Optimization"]
      direction LR
      G["Hyperparameter Tuning"] --> H["Walk-Forward Optimization"]
      H --> I["Signal Generation"]
  end
  
  D --> G
  E --> G
  F --> G
  
  G --> J["Key Findings/Outcomes"]
  
  J --> K["GMADL yields superior<br>risk-weighted returns"]
  J --> L["Optimizes for fewer transactions<br>reducing costs significantly"]
  J --> M["Solves feature selection<br>in both regression & classification"]

Cited References (103)

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2 of 103 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.