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Online Variational Sequential Monte Carlo
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Proposes online variational SMC (OVSMC), a stochastic-approximation extension of VSMC that jointly learns SSM parameters and amortized particle proposals on streaming data, with convergence guarantees as the data length grows.
Problem
Parameter learning and proposal adaptation in state-space models are typically done offline by reprocessing batches; existing online methods need particle smoothing or local per-time-step proposals, which are costly or non-amortized.
Approach
Distribute the VSMC surrogate ELBO gradient over time via Robbins-Monro stochastic approximation, updating amortized Gaussian proposal parameters and model parameters on-the-fly with a small particle count for the proposal and a larger one for the model parameters, without particle smoothing or trajectory storage.
Key results
- On the 10-dimensional linear Gaussian SSM batch setting, OVSMC shows ELBO evolution comparable to or with less noise than VSMC across ADAM learning rates.
- On the comparison with online variational filtering, OVSMC reproduces the A and B learning with under one hour per run versus about 17 hours for OVF.
- On stochastic volatility, OVSMC was about three times faster than PaRIS-based RML in the reported case, with OVSMC converging faster for beta but fluctuating more for alpha and sigma.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use OVSMC instead of OVF for online parameter learning | Online parameter learning · Linear Gaussian SSM parameter-learning task | runtime: about 17 hours vs less than one hour | Helped |
| Use OVSMC instead of PaRIS-based RML | Stochastic volatility model · Stochastic volatility model | runtime: three times faster | Helped |
| Optimize an amortized proposal online with OVSMC | Linear Gaussian SSM particle filter · Linear Gaussian SSM | effective sample size | Helped |
| Use OVSMC instead of VSMC for repeated processing of a batch | Amortized Gaussian proposal learning · Linear Gaussian SSM batch setting | ELBO | Mixed |
| Use OVSMC instead of particle-based RML | Stochastic volatility parameter learning · Stochastic volatility model | parameter-learning convergence | Mixed |
Surprising findings
- The online method is competitive with or better than batch VSMC in batch-data settings, not only in streaming settings.
Limitations
- Theory requires strong mixing assumptions (compact state space, bounded densities) and biased gradient approximation without a true Lyapunov interpretation.
- Consistency of the parameter estimates for correctly specified SSMs is left open.
- Experiments are on small synthetic models run on a laptop; no real-world streaming data.
Experimental setup
Datasets: synthetic linear Gaussian SSM data synthetic stochastic volatility data synthetic moving-agent video (32x32 frames)
Benchmarks: synthetic linear Gaussian SSM stochastic volatility parameter estimation moving agent video generation
Metrics: parameter convergence ELBO effective sample size L2 norm of mean field gradient (theory) wall-clock time
Baselines: VSMC PaRIS-based recursive maximum likelihood online variational filtering
Builds on: variational sequential Monte Carlo importance weighted autoencoder PaRIS variational recurrent neural networks Adam
Closest papers by meaning
- Efficient Online Variational Estimation via Monte Carlo Sampling (ICML 2026 · similarity 0.91)
- Online Variational Filtering and Parameter Learning (NeurIPS 2021 · similarity 0.91)
- Free-Form Variational Inference for Gaussian Process State-Space Models (ICML 2023 · similarity 0.89)
- Efficient Learning of Deep State Space Models via Importance Smoothing (ICML 2026 · similarity 0.89)
- Bayesian Online Natural Gradient (BONG) (NeurIPS 2024 · similarity 0.89)
- Theoretical Guarantees for Variational Inference with Fixed-Variance Mixture of Gaussians (ICML 2024 · similarity 0.87)
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