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Tuning Sequential Monte Carlo Samplers via Greedy Incremental Divergence Minimization
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Proposes tuning SMC sampler Markov kernels by greedily minimizing the incremental KL divergence between path proposal and target, yielding a gradient-free step size adaptation for LMC and a coordinate-descent scheme for kinetic LMC.
Problem
Tuning unadjusted Markov kernels (e.g., LMC, KLMC) in SMC samplers, where standard MH acceptance-rate or ESJD tuning criteria do not apply, and end-to-end SGD-based tuning is expensive.
Approach
Greedily minimize, at each SMC step, the incremental forward-path KL objective (equivalently, expected negative log potential) over kernel parameters, using particle subsampling, sample average approximation, and a smoothness regularizer, solved by a gradient-free bracketing plus golden section search in log-space.
Key results
- Adaptive SMC-LMC matches or beats the best fixed step size on 20 of 22 benchmark problems in log Z estimate quality.
- On Sonar and Brownian, adaptive SMC-KLMC gives more accurate log Z estimates than the best-tuned end-to-end differentiable AIS, with Pines comparable.
- Step size tuning terminates after about 10 objective evaluations per SMC step for t>1, versus gradient-based end-to-end optimization using thousands of iterations.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Tune kernel parameters by greedy incremental KL minimization | SMC samplers · 20 of 22 benchmark problems | log Z estimate accuracy | Helped |
| Tune step sizes adaptively rather than use the best fixed step size | SMC-LMC and SMC-KLMC · Rats | log Z estimate accuracy | Hurt |
| Tune KLMC parameters with adaptive SMC instead of end-to-end tuning | SMC-KLMC · Sonar | log Z estimate accuracy | Helped |
| Tune KLMC parameters with adaptive SMC instead of end-to-end tuning | SMC-KLMC · Brownian | log Z estimate accuracy | Helped |
| Tune KLMC parameters with adaptive SMC instead of end-to-end tuning | SMC-KLMC · Pines | log Z estimate accuracy | No clear effect |
| Use unadjusted Langevin kernels rather than MH-adjusted MALA at high dimensionality | SMC samplers · d ≥ 128 | log Z estimate accuracy | Helped |
| Use the previous-step forward kernel as the backward kernel instead of the same-step forward kernel | SMC-LMC · Static-model SMC | normalizing constant estimate variance | Helped |
Surprising findings
- The adaptive method performed poorly on the Rats problem.
- For dimensions d >= 128, SMC-LMC step sizes tend to be larger than SMC-MALA step sizes, yielding more accurate estimates in high dimensions.
Limitations
- Greedy per-step optimization does not guarantee a solution to the joint objective.
- Sample average approximation and particle subsampling introduce bias in the tuned parameters; adaptive estimates are biased and require a separate vanilla SMC run for unbiased estimates.
- Performance was poor on the Rats problem.
Experimental setup
Datasets: Inference Gym problems (Funnel, Brownian, Sonar, Pines) PosteriorDB problems (e.g., Bones, Radon, Rats, Diamonds) Gaussian target N(3·1, I)
Benchmarks: Funnel Brownian Sonar Pines Bones Surgical HMM Loss Curves Pilots Diamonds Seeds Downloads
Metrics: log normalizing constant estimate accuracy variance of log Z estimates step size schedule
Baselines: SMC with fixed step sizes differentiable AIS with end-to-end SGD tuning SMC-MALA with acceptance rate control SMC-MALA with ESJD maximization
Builds on: annealed flow transport differentiable annealed importance sampling adaptive sequential monte carlo kinetic langevin monte carlo
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