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.

通过利用凸优化中的coin betting思想，将约束取样视为概率测度空间上的镜像优化问题，我们介绍了一套完全不依赖学习率的基于粒子的约束取样算法，并引入了现有约束取样算法的统一框架。数值实验表明，我们的算法在清单、公平约束、后选推理等任务中实现了非常有竞争力的性能，且无需调节任何超参数。

受限领域中的无学习率贝叶斯推理