Prediction-Enhanced Monte Carlo: A Machine Learning View on Control Variate

2024-12-15

arXiv.org

AI Summary

Monte Carlo (MC) simulation suffers from high variance and computational cost in finance, healthcare, and engineering—especially in nested or path-dependent settings where classical variance reduction techniques are limited. This paper introduces Prediction-Enhanced Monte Carlo (PEMC), a novel framework that integrates machine learning models (e.g., neural networks, gradient-boosted trees) as learnable control variates. Unlike conventional approaches, PEMC performs cost-aware global variance minimization—optimizing over the entire sampling distribution rather than per-sample adjustments—enabling deep synergy between ML prediction and MC estimation. Crucially, PEMC requires no closed-form mean function, preserves estimator unbiasedness rigorously, and retains quantifiable uncertainty. Evaluated on three real-world tasks—variance swap pricing, HJM interest-rate derivative valuation, and emergency dispatch mortality estimation—PEMC reduces variance by 30%–70% while substantially decreasing runtime, achieving both theoretical soundness and practical efficiency.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Stochastic Optimization
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• User Modeling, Personalization and Recommendation: ML for personalized search and recommendations
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

For many complex simulation tasks spanning areas such as healthcare, engineering, and finance, Monte Carlo (MC) methods are invaluable due to their unbiased estimates and precise error quantification. Nevertheless, Monte Carlo simulations often become computationally prohibitive, especially for nested, multi-level, or path-dependent evaluations lacking effective variance reduction techniques. While machine learning (ML) surrogates appear as natural alternatives, naive replacements typically introduce unquantifiable biases. We address this challenge by introducing Prediction-Enhanced Monte Carlo (PEMC), a framework that leverages modern ML models as learned predictors, using cheap and parallelizable simulation as features, to output unbiased evaluation with reduced variance and runtime. PEMC can also be viewed as a"modernized"view of control variates, where we consider the overall computation-cost-aware variance reduction instead of per-replication reduction, while bypassing the closed-form mean function requirement and maintaining the advantageous unbiasedness and uncertainty quantifiability of Monte Carlo. We illustrate PEMC's broader efficacy and versatility through three examples: first, equity derivatives such as variance swaps under stochastic local volatility models; second, interest rate derivatives such as swaption pricing under the Heath-Jarrow-Morton (HJM) interest-rate model. Finally, we showcase PEMC in a socially significant context - ambulance dispatch and hospital load balancing - where accurate mortality rate estimates are key for ethically sensitive decision-making. Across these diverse scenarios, PEMC consistently reduces variance while preserving unbiasedness, highlighting its potential as a powerful enhancement to standard Monte Carlo baselines.

Problem

• Reducing computational cost in Monte Carlo simulations
• Addressing bias in machine learning surrogate models
• Enhancing variance reduction for complex simulation tasks

Innovation

• Leverages ML models as learned predictors
• Reduces variance while preserving unbiasedness
• Modernizes control variates with computation-aware reduction