The performance of Hamiltonian Monte Carlo crucially depends on its parameters, in particular the integration timestep and the number of integration steps. We present an adaptive general-purpose framework to automatically tune these parameters based on a loss function which promotes the fast exploration of phase-space. For this, we make use of a fully-differentiable set-up and use backpropagation for optimization. An attention-like loss is defined which allows for the gradient driven learning of the distribution of integration steps. We also highlight the importance of jittering for a smooth loss-surface. Our approach is demonstrated for the one-dimensional harmonic oscillator and alanine dipeptide, a small protein common as a test-case for simulation methods. We find a good correspondence between our loss and the autocorrelation times, resulting in well-tuned parameters for Hamiltonian Monte Carlo.

翻译：哈密顿蒙特卡洛方法的性能关键取决于其参数，特别是积分时间步长和积分步数。本文提出一种自适应通用框架，基于促进相空间快速探索的损失函数自动调谐这些参数。为此，我们利用完全可微的设置并通过反向传播进行优化。我们定义了一种类注意力损失函数，使得积分步数分布的梯度驱动学习成为可能。同时我们强调了抖动对平滑损失曲面的重要性。该方法在一维谐振子和丙氨酸二肽（一种常用于模拟方法测试的小型蛋白质）上进行了验证。实验表明，我们的损失函数与自相关时间具有良好对应关系，从而为哈密顿蒙特卡洛方法获取调优参数。