Improving Bayesian Optimization for Portfolio Management with an Adaptive Scheduling

Paper: arXiv 2504.13529

Abstract

Existing black-box portfolio management systems are prevalent in the financial industry due to commercial and safety constraints, though their performance can fluctuate dramatically with changing market regimes. Evaluating these non-transparent systems is computationally expensive, as fixed budgets limit the number of possible observations. Therefore, achieving stable and sample-efficient optimization for these systems has become a critical challenge. This work presents a novel Bayesian optimization framework (TPE-AS) that improves search stability and efficiency for black-box portfolio models under these limited observation budgets. Standard Bayesian optimization, which solely maximizes expected return, can yield erratic search trajectories and misalign the surrogate model with the true objective, thereby wasting the limited evaluation budget. To mitigate these issues, we propose a weighted Lagrangian estimator that leverages an adaptive schedule and importance sampling. This estimator dynamically balances exploration and exploitation by incorporating both the maximization of model performance and the minimization of the variance of model observations. It guides the search from broad, performance-seeking exploration towards stable and desirable regions as the optimization progresses. Extensive experiments and ablation studies, which establish our proposed method as the primary approach and other configurations as baselines, demonstrate its effectiveness across four backtest settings with three distinct black-box portfolio management models.

Complexity vs Empirical Score

• Math Complexity: 7.5/10
• Empirical Rigor: 6.0/10 (capped from 8.0: transaction costs not modelled; see penalty flags)
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper involves advanced Bayesian optimization concepts like Lagrangian estimators, TPE, and importance sampling, requiring solid mathematical foundations. It also demonstrates empirical rigor through extensive experiments and ablation studies across multiple backtest settings with real-world portfolio models.

Research Flowchart

  flowchart TD
  A["Research Goal: Stable & Sample-Efficient<br>Black-Box Portfolio Optimization"] --> B{"Key Methodology:<br>TPE-AS Framework"}
  B --> C["Adaptive Scheduling<br>Dynamically balances<br>Exploration vs. Exploitation"]
  C --> D["Weighted Lagrangian Estimator<br>Minimizes Performance Variance<br>+ Maximizes Return"]
  D --> E["Computational Process:<br>Bayesian Optimization with<br>Limited Evaluation Budgets"]
  E --> F["Data Inputs:<br>3 Black-Box Models<br>4 Backtest Settings"]
  F --> G["Outcomes:<br>Superior Stability &<br>Sample Efficiency"]

Cited References (69)

1. Practical bayesian optimization of machine learning algorithms (2012)
2. High dimensional Bayesian optimization with elastic Gaussian process (2017)
3. Multiobjective tree-structured Parzen estimator (2022)
4. Lagrange multiplier approach to variational problems and applications (2008)
5. A demystification of the Black-Litterman model: Managing quantitative and traditional portfolio construction (2007)
6. Particle Swarm Optimization (PSO) for the constrained portfolio optimization problem (2011)
7. Explaining deep neural networks and beyond: A review of methods and applications (2021)
8. Efficient processing of deep neural networks: A tutorial and survey (2017)

1 of 69 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.