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arxiv: 2511.13394 · v2 · submitted 2025-11-17 · 💻 cs.LG · stat.ML

Fast and Robust Simulation-Based Inference With Optimization Monte Carlo

Vasilis Gkolemis , Christos Diou , Michael U. Gutmann This is my paper

Pith reviewed 2026-05-17 21:44 UTC · model grok-4.3

classification 💻 cs.LG stat.ML
keywords simulation based inferencebayesian parameter inferenceoptimization monte carlodifferentiable simulatorsgradient based optimizationstochastic simulatorsposterior inferencejax
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The pith

Reformulating inference for stochastic simulators as deterministic optimization problems allows gradient-based methods to target high-density posterior regions efficiently.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper develops a simulation-based inference technique for cases where likelihoods are intractable due to complex stochastic simulators. It achieves this by recasting the inference task using the Optimization Monte Carlo approach into deterministic optimization problems. Gradients then guide the search to areas of high posterior density, skipping many low-value simulations. Tests in high dimensions, with limited information in outputs, multiple data points, and multimodal cases confirm that accuracy holds or improves while runtimes drop markedly. The implementation leverages JAX for vectorized operations to enhance speed further.

Core claim

Inference for stochastic simulators is reformulated in terms of deterministic optimization problems. Gradient-based methods then navigate efficiently to high-density posterior regions, avoiding simulations in low-probability areas. This delivers accurate posterior inference with substantially reduced runtimes for differentiable simulators.

What carries the argument

The Optimization Monte Carlo framework, reformulated as deterministic optimization problems solved via gradient-based optimization.

Load-bearing premise

The stochastic simulator must be differentiable with respect to its parameters to compute the gradients that steer the optimization process.

What would settle it

An experiment that applies the method to a simulator without access to gradients, such as a discrete-event simulator, and measures if the runtime advantage disappears while accuracy remains would falsify the necessity of the differentiability assumption for the speed gains.

Figures

Figures reproduced from arXiv: 2511.13394 by Christos Diou, Michael U. Gutmann, Vasilis Gkolemis.

Figure 1
Figure 1. Figure 1: Posterior inference on a two-Gaussian mixture simulator. Rows correspond to simple ( [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: R2OMC overview: Distractors are automatically filtered out and proposal distributions [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: MoG benchmark: Success Frontier plots showing the minimum runtime required to achieve a mean [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: SLCP pairwise posteriors for multiple observations. The four left panels show proposal samples per [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: SLCP (left) and SLCP with distractors (right): C2ST score vs. runtime. 10 1 10 3 10 5 Runtime (sec) - Log 0.4 0.6 0.8 1.0 C2ST REJ-ABC SMC-ABC NPE SNPE NLE SNLE NRE SNRE R2OMC [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: 2-moons task. Left: C2ST score vs. runtime. [PITH_FULL_IMAGE:figures/full_fig_p007_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: shows that R2OMC recovers posterior means that visually match the clean images, indicating the posterior mode is close to the true generating parame￾ters θ ∗ , despite the completely uninformative prior. While direct comparisons are not performed here, prior work highlights that SBI on images is challenging due to the curse of dimensionality. Methods like GATSBI (Ramesh et al., 2022) can succeed but requir… view at source ↗
Figure 8
Figure 8. Figure 8: MoG benchmark: Success Frontier plots showing the lowest budget required to reach a C2ST score [PITH_FULL_IMAGE:figures/full_fig_p018_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: MoG Benchmark - Base simulator: C2ST heatmaps for R2OMC, NPE, BayesFlow, and Flow Matching. [PITH_FULL_IMAGE:figures/full_fig_p018_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: MoG Benchmark - Base simulator with distractors: C2ST heatmaps for R2OMC, NPE, BayesFlow, [PITH_FULL_IMAGE:figures/full_fig_p018_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: MoG Benchmark - MoG simulator: C2ST heatmaps for R2OMC, NPE, BayesFlow, and Flow Matching. [PITH_FULL_IMAGE:figures/full_fig_p019_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: MoG Benchmark - MoG simulator with distractors: C2ST heatmaps for R2OMC, NPE, BayesFlow, [PITH_FULL_IMAGE:figures/full_fig_p019_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: From left to right: C2ST vs. budget, runtime vs. budget. for T.3: SLCP and same figures for (T.4: SLCP Distractors) [PITH_FULL_IMAGE:figures/full_fig_p020_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: T.3: SLCP. From left to right: total samples, accepted samples, and selected samples by R2OMC. [PITH_FULL_IMAGE:figures/full_fig_p020_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: T.8: Two Moons. From left to right: C2ST score, ground truth samples, and samples by R2OMC [PITH_FULL_IMAGE:figures/full_fig_p021_15.png] view at source ↗
read the original abstract

Bayesian parameter inference for complex stochastic simulators is challenging due to intractable likelihood functions. Existing simulation-based inference methods often require large number of simulations and become costly to use in high-dimensional parameter spaces or in problems with partially uninformative outputs. We propose a new method for differentiable simulators that delivers accurate posterior inference with substantially reduced runtimes. Building on the Optimization Monte Carlo framework, our approach reformulates inference for stochastic simulators in terms of deterministic optimization problems. Gradient-based methods are then applied to efficiently navigate toward high-density posterior regions and avoid wasteful simulations in low-probability areas. A JAX-based implementation further enhances the performance through vectorization of key method components. Extensive experiments, including high-dimensional parameter spaces, uninformative outputs, multiple observations and multimodal posteriors show that our method consistently matches, and often exceeds, the accuracy of state-of-the-art approaches, while reducing the runtime by a substantial margin.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 2 minor

Summary. The paper proposes a new method for simulation-based inference (SBI) on differentiable stochastic simulators by building on the Optimization Monte Carlo framework. It reformulates posterior inference as deterministic optimization problems that gradient-based methods can solve to target high-density regions while avoiding low-probability simulations. A JAX implementation provides vectorization for efficiency. Experiments across high-dimensional spaces, multimodal posteriors, uninformative outputs, and multiple observations are reported to show accuracy that matches or exceeds state-of-the-art SBI methods with substantially lower runtime.

Significance. If the performance claims hold under fuller experimental scrutiny, the work offers a practical advance for SBI by exploiting differentiability and modern autodiff tools to reduce simulation budgets in challenging regimes. The explicit scoping to differentiable simulators and the reformulation to optimization problems provide a clear algorithmic contribution that could complement existing likelihood-free methods in scientific applications.

major comments (1)
  1. [§4] §4 (Experiments): The central claims of competitive accuracy and 'substantial margin' runtime reduction rest on the reported experiments, yet the text provides insufficient detail on baselines (specific SBI algorithms and their implementations), number of independent runs for error bars, hardware for timing, exact simulation budgets allocated per method, and statistical tests. Without these, the performance advantages cannot be independently verified from the manuscript.
minor comments (2)
  1. [§3] The description of how stochastic simulator outputs are incorporated into the deterministic optimization objective could be expanded with a short pseudocode example to improve reproducibility.
  2. Figure captions would benefit from explicit mention of the number of simulations used in each panel to allow direct comparison with the runtime claims.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their constructive review and for recognizing the potential contribution of our work on Optimization Monte Carlo for differentiable simulators. We address the single major comment below and will incorporate the requested details in a revised manuscript.

read point-by-point responses

  1. Referee: [§4] §4 (Experiments): The central claims of competitive accuracy and 'substantial margin' runtime reduction rest on the reported experiments, yet the text provides insufficient detail on baselines (specific SBI algorithms and their implementations), number of independent runs for error bars, hardware for timing, exact simulation budgets allocated per method, and statistical tests. Without these, the performance advantages cannot be independently verified from the manuscript.

    Authors: We agree that the current description of the experimental setup is insufficient for independent verification. In the revised manuscript we will expand §4 (and add a dedicated reproducibility subsection) to specify: (i) the exact baseline algorithms and their implementations (e.g., SNPE-C, SNLE, ABC-SMC from the sbi package v0.21 together with any custom settings); (ii) the number of independent runs used to compute means and standard errors (10 runs for all timing and accuracy metrics); (iii) the hardware platform on which timings were measured (single NVIDIA A100 80 GB GPU with JAX 0.4.23 and CUDA 12.1); (iv) the precise simulation budgets allocated to each method in every experiment; and (v) the statistical tests performed (paired Wilcoxon signed-rank tests with Holm-Bonferroni correction for runtime comparisons). We will also release the full experimental code and configuration files upon acceptance. These additions do not alter the reported results but will make the performance claims fully verifiable. revision: yes

Circularity Check

0 steps flagged

No significant circularity identified

full rationale

The paper proposes an algorithmic reformulation of simulation-based inference for differentiable stochastic simulators as deterministic optimization problems within the Optimization Monte Carlo framework, allowing gradient-based methods to target high-density posterior regions efficiently. This is presented as a new method with a JAX implementation for vectorization, and its claims are supported by independent empirical validation across high-dimensional, multimodal, uninformative-output, and multiple-observation scenarios that demonstrate accuracy matching or exceeding baselines alongside substantial runtime reductions. No derivation steps reduce by construction to fitted inputs, self-definitions, or load-bearing self-citations; the approach introduces a distinct optimization-based procedure rather than renaming or circularly deriving from its own outputs.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the domain assumption that simulators provide differentiable outputs and that gradient-based optimization reliably locates high-density posterior regions without getting stuck in poor local optima.

axioms (1)
  • domain assumption The simulator is differentiable with respect to parameters
    Required to apply gradient-based optimization methods as stated in the abstract.

pith-pipeline@v0.9.0 · 5456 in / 1081 out tokens · 36925 ms · 2026-05-17T21:44:23.880558+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

9 extracted references · 9 canonical work pages

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    In the experiments, we use a neural spline flow as density estimator (sbi.utils.get_nn_models.posterior_nn())

    in the SBI benchmark (Lueckmann et al., 2021).NPE_C estimates the posterior by training a neural networkF (y,ϕ ) to approximate p(θ| y)through a density estimator qF (y,ϕ )(θ). In the experiments, we use a neural spline flow as density estimator (sbi.utils.get_nn_models.posterior_nn()). The NPE configuration is summarized in Table

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    For a more detailed view, Figures 9 (Sbase), 10 (S dist base), 11 (SMoG), and 12 (S dist MoG ) report the meanC2ST score for each method across all dimensionalities and budgets

    This figure complements Figure 3 validating that the factor that incurs longer runtimes is the increased simulation budget required at higher dimensionalities. For a more detailed view, Figures 9 (Sbase), 10 (S dist base), 11 (SMoG), and 12 (S dist MoG ) report the meanC2ST score for each method across all dimensionalities and budgets. All neural-based me...

    work page 2021