Fast and Robust Simulation-Based Inference With Optimization Monte Carlo

arXiv stat.ML / 4/6/2026

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Key Points

The paper tackles Bayesian parameter inference for complex stochastic simulators where likelihoods are intractable, proposing a method that reduces the simulation burden.
It reformulates inference for differentiable simulators into deterministic optimization problems, using gradient-based search to reach high-posterior-density regions.
By avoiding simulations in low-probability areas, the approach substantially lowers runtime, especially in high-dimensional parameter spaces and cases with partially uninformative outputs.
A JAX-based implementation accelerates computation via vectorization, improving practical performance.
Experiments across challenging settings (high-dimensional, uninformative outputs, multiple observations, multimodal posteriors) show accuracy comparable to or better than state-of-the-art methods while cutting runtime significantly.

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.