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算法族，用于在约束域上进行采样，这些算法完全无需学习率调整。我们的方法借鉴了凸优化中的硬币赌注思想，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，我们还为若干现有约束采样算法（包括镜像朗之万动力学和镜像斯坦变分梯度下降）建立了统一框架。我们在多种数值实例上验证了算法的性能，包括单纯形目标分布采样、公平性约束采样以及后选择推理中的约束采样问题。结果表明，我们的算法在无需调整任何超参数的情况下，与现有约束采样方法相比具有竞争性表现。