Citation	$g (x)$	$f (x)$	Constraint	Momentum	Algorithm	a.s.
Khaled et al. [25]	L-smooth	--	$ℝ^{d}$	×	SGD	×
Gower et al. [26]	--		--	--	--	--
Mertikopoulos et al. [27]	L-smooth,	--	X	×	SGD	√
Mertikopoulos et al. [27]	G-Lipschitz		--	--	--
Sebbouh et al. [21]	L-smooth	--	$ℝ^{d}$	×	SGD	√
Liu et al. [23]	--		--	--	--	--
Sebbouh et al. [21]	L-smooth	--	$ℝ^{d}$	√	SHB	√
Liu et al. [23]	--	--	--	--	--	--
Liu et al. [23]	L-smooth	--	$ℝ^{d}$	√	SNAG	√
Ward et al. [28]	L-smooth	--	$ℝ^{d}$	×	AdaGrad	×
Alacaoglu et al. [29]	--	ρ-weakly convex	X	×	AdaGrad	×
Davis et al. [30]	--	ρ-weakly convex	$ℝ^{d}$	×	PSGD	×
Cevher et al. [18]	L-smooth	Convex	$ℝ^{d}$	×	PSGD	×
Gorbunov et al. [17]	--	--	--	--	--	--
Ghadimi et al. [13]	L-smooth	Convex	X	×	SCOMID	×
Ours	L-smooth	Convex	$ℝ^{d}$	√	PSAG	√