Efficient Stochastic Optimisation via Sequential Monte Carlo

2026-06-12 · Source: stat.ML updates on arXiv.org · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Mathematics & Computational Sciences · Depth: Expert, extended

Summary

This work introduces Stochastic Optimisation via Sequential Monte Carlo (SOSMC), a novel framework for optimizing functions with intractable gradients, a common challenge in machine learning and statistics. It replaces computationally expensive inner sampling loops, typically using Markov chain Monte Carlo (MCMC) methods, with efficient Sequential Monte Carlo (SMC) approximations. The approach establishes convergence results for its underlying recursions and demonstrates significant computational gains. SOSMC's effectiveness is empirically validated through extensive experiments, particularly on the reward-tuning of energy-based models (EBMs) across various settings, including Langevin processes, 2D synthetic datasets, and MNIST image data, showing faster convergence and improved performance compared to methods like ImpDiff and SOUL.

Key takeaway

For AI Scientists and Machine Learning Engineers dealing with optimization problems involving intractable gradients, you should consider adopting the SOSMC framework. Its use of Sequential Monte Carlo approximations offers substantial computational efficiency over traditional MCMC-based methods, leading to faster convergence and more stable tuning dynamics, especially for tasks like reward-tuning energy-based models. This approach allows you to achieve higher objective values in fewer iterations, reducing the need for costly fresh evaluations.

Key insights

SOSMC efficiently optimizes intractable gradient functions by replacing costly MCMC sampling with faster Sequential Monte Carlo approximations.

Principles

• SMC approximations can replace MCMC for gradient estimation.
• Reusing samples from previous iterations improves efficiency.
• Adaptive step-size based on ESS can maintain stability.

Method

SOSMC uses a first-order optimizer with gradient estimates derived from weighted particles generated by one iteration of an SMC sampler. It sequentially samples from evolving distributions, reusing particles.

In practice

• Reward-tune energy-based models (EBMs) efficiently.
• Optimize maximum marginal likelihood estimation (MMLE).
• Apply to Langevin processes with non-differentiable rewards.

Topics

• Stochastic Optimization
• Sequential Monte Carlo
• Intractable Gradients
• Energy-Based Models
• Reward Tuning
• Langevin Dynamics

Best for: Research Scientist, AI Scientist, Machine Learning Engineer

Related on AIssential

• Tempered Sequential Monte Carlo for Trajectory and Policy Optimization with Differentiable Dynamics — TSMC optimizes trajectories and policies by framing controller design as inference, using tempered sampling and gradient-based rejuvenation.
• SMCEvolve: Principled Scientific Discovery via Sequential Monte Carlo Evolution — SMCEvolve grounds LLM-driven program evolution in a rigorous probabilistic framework with convergence guarantees.
• stochastic gradient descent #maths #statistics #datascience #machinelearning #dataanlysis — Faster iteration with noisy gradients often outperforms slow, precise convergence in machine learning.
• Fast Computation of Superquantile-Constrained Optimization Through Implicit Scenario Reduction — Superquantile-constrained optimization can be significantly accelerated using a specialized second-order computational framework.
• Efficient Learning of Deep State Space Models via Importance Smoothing — Parallel variational Monte Carlo (PVMC) robustly and efficiently trains Deep State Space Models for both discriminative and generative tasks.
• Robust Stochastic Gradient Posterior Sampling with Lattice Based Discretisation — SGLRW improves SG-MCMC robustness by localizing stochastic noise to off-diagonal covariance elements via lattice-based updates.

Open in AIssential →

Editorial summary, takeaway, and curation by AIssential. Original article published by stat.ML updates on arXiv.org.