标题： 基于自适应网格的汤普森采样方法用于高效轨迹发现 显示英文标题

标题： Adaptive Grid-Based Thompson Sampling for Efficient Trajectory Discovery

摘要： 贝叶斯优化（BO）是一种用于估计计算昂贵的仿真模型参数的强大框架，特别是在似然不可处理且评估成本高昂的情况下。 在随机模型中，每次仿真都使用特定的参数集和隐式或显式的随机种子运行，其中每个参数集和随机种子的组合都会生成一个从底层随机过程中采样的个体实现，或轨迹。 现有的BO方法通常依赖于实现上的摘要统计量，如均值、中位数或分位数，当需要轨迹级别的信息时，可能会限制其效果。 我们提出了一种面向轨迹的贝叶斯优化方法，该方法使用输入参数和随机种子作为输入，构建高斯过程（GP）代理模型，从而能够在轨迹级别进行直接推断。 通过使用公共随机数（CRN）方法，我们在轨迹上定义了一个基于代理的似然，并引入了一种自适应的汤普森采样算法，该算法通过基于似然的过滤和基于梅特波利斯-哈金斯的密集化来优化固定大小的输入网格。 这种方法将计算集中在输入空间中统计上有希望的区域，同时平衡探索与利用。 我们将该方法应用于随机流行病模型，包括一个简单的分 compartment 模型和一个计算更复杂的基于代理的模型，证明了相对于仅基于参数的推断，该方法提高了采样效率并更快地识别出与数据一致的轨迹。 显示英文摘要

摘要： Bayesian optimization (BO) is a powerful framework for estimating parameters of computationally 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 Bayesian optimization method that incorporates a Gaussian process (GP) surrogate using both input parameters and random seeds as inputs, enabling direct inference at the trajectory level. Using a common random number (CRN) 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.