We introduce a suite of new particle-based algorithms for sampling on constrained domains which are entirely learning rate free. Our approach leverages coin betting ideas from convex optimisation, and the viewpoint of constrained sampling as a mirrored optimisation problem on the space of probability measures. Based on this viewpoint, we also introduce a unifying framework for several existing constrained sampling algorithms, including mirrored Langevin dynamics and mirrored Stein variational gradient descent. We demonstrate the performance of our algorithms on a range of numerical examples, including sampling from targets on the simplex, sampling with fairness constraints, and constrained sampling problems in post-selection inference. Our results indicate that our algorithms achieve competitive performance with existing constrained sampling methods, without the need to tune any hyperparameters.

翻译：我们提出了一套全新的基于粒子的采样算法，用于在约束域内进行采样，且这些算法完全无需学习率。该方法借鉴了凸优化中的“币赌”思想，并将约束采样视为概率测度空间上的镜像优化问题。基于这一视角，我们还为几种现有的约束采样算法（包括镜像朗之万动力学和镜像斯坦因变分梯度下降）构建了一个统一框架。我们通过一系列数值示例展示了算法的性能，包括在单纯形上对目标分布进行采样、具有公平性约束的采样，以及后选择推断中的约束采样问题。结果表明，我们的算法在无需调整任何超参数的情况下，能够达到与现有约束采样方法相媲美的性能。