Regularized Stein Variational Gradient Flow

Table 1 The results for SVGF and Regularized SVGF are strictly non-algorithmic, as the stated results require that the initial density supplied to the method must have finite KL divergence to \(\pi \)

Method	Source	Type	Iterations
SVGF	NA	Deterministic	unknown
LMC	[11, 45]	Randomized	\({\mathcal {O}}(\frac{1}{\epsilon }) \)
MALA	NA	Randomized	unknown
Proximal sampler	[9]	Randomized	\({\mathcal {O}} \left( \log ^\lambda (\frac{1}{\epsilon })\right) \)
Regularized SVGF	Theorem 6	Deterministic	\({\mathcal {O}} \left( \log \left( \frac{1}{\epsilon }\right) \right) \)

The results from [9, 11, 45] are for LMC, MALA and the proximal sampler are algorithmic, and are presented in a simplified manner to convey the dependency on the accuracy parameter \(\epsilon \). The result for the proximal sampler holds only in expectation. Currently, it is not clear how to obtain a high-probability result in KL-divergence; see [9] for details