Staying on Track: Efficient Trajectory Discovery with Adaptive Batch Sampling

TL;DR

This paper introduces a trajectory-oriented Bayesian optimization method that uses Gaussian processes with input parameters and random seeds, improving efficiency in stochastic models by focusing on promising regions.

Contribution

It proposes a novel surrogate-based likelihood and adaptive sampling algorithm that directly infers trajectories, enhancing efficiency over traditional summary statistic methods.

Findings

Improved sampling efficiency in stochastic epidemic models.

Faster identification of data-consistent trajectories.

Effective balancing of exploration and exploitation.

Abstract

Bayesian optimization (BO) is a powerful framework for estimating parameters of expensive simulation models, particularly in settings where the likelihood is intractable and evaluations are costly. In stochastic models every simulation is run with a specific parameter set and an implicit or explicit random seed, where each parameter set and random seed combination generates an individual realization, or trajectory, sampled from an underlying random process. Existing BO approaches typically rely on summary statistics over the realizations, such as means, medians, or quantiles, potentially limiting their effectiveness when trajectory-level information is desired. We propose a trajectory-oriented BO method that incorporates a Gaussian process surrogate using both input parameters and random seeds as inputs, enabling direct inference at the trajectory level. Using a common random number approach, we define a surrogate-based likelihood over trajectories and introduce an adaptive Thompson Sampling algorithm that refines a fixed-size input grid through likelihood-based filtering and Metropolis-Hastings-based densification. This approach concentrates computation on statistically promising regions of the input space while balancing exploration and exploitation. We apply the method to stochastic epidemic models, a simple compartmental and a more computationally demanding agent-based model, demonstrating improved sampling efficiency and faster identification of data-consistent trajectories relative to parameter-only inference.