Efficient Stochastic Optimisation via Sequential Monte Carlo

2026-01-29

AI Summary

This work addresses the challenge of optimizing objectives with intractable gradients—such as maximum marginal likelihood estimation and generative model fine-tuning—by introducing, for the first time, a sequential Monte Carlo (SMC) sampler into a gradient-free optimization framework. The proposed approach replaces the conventional inner-loop sampling procedure to efficiently approximate stochastic gradients, substantially reducing computational overhead while preserving optimization performance. A theoretical convergence analysis is provided to support the method’s validity. Empirical evaluations across multiple energy-based models on reward tuning tasks demonstrate that the proposed algorithm achieves significant acceleration without compromising, and in some cases even improving, optimization quality.

Technology Category

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

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

The problem of optimising functions with intractable gradients frequently arise in machine learning and statistics, ranging from maximum marginal likelihood estimation procedures to fine-tuning of generative models. Stochastic approximation methods for this class of problems typically require inner sampling loops to obtain (biased) stochastic gradient estimates, which rapidly becomes computationally expensive. In this work, we develop sequential Monte Carlo (SMC) samplers for optimisation of functions with intractable gradients. Our approach replaces expensive inner sampling methods with efficient SMC approximations, which can result in significant computational gains. We establish convergence results for the basic recursions defined by our methodology which SMC samplers approximate. We demonstrate the effectiveness of our approach on the reward-tuning of energy-based models within various settings.

Problem

• intractable gradients
• stochastic optimisation
• function optimisation
• machine learning
• statistical inference

Innovation

• Sequential Monte Carlo
• Stochastic Optimization
• Intractable Gradients
• SMC Samplers
• Energy-Based Models