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AssumptionSettingICPCGuarantee
Extragradient(Iusem et al., 2017)pseudo-monotonicity 3stochastic0(e-4)2Tge-SP
OMD(Daskalakis et al., 2017)bilineardeterministicN/ATgasymptotic
AvgPastExtraSGD(Gidel et al., 2018)monotonicity stochastic0(€-2)TgE-DG
OMD(Mertikopoulos et al., 2018)coherencestochasticN/A2Tgasymptotic
IPP(Lin et al., 2018)MVI has solutionstochastic0(e-6)TgE-SP
Alternating Gradient(Gidel et al., 2019)bilinear form 4deterministicO(log(1/e)Tge-optim
SVRE(Chavdarova et al., 2019)strong-monotonicityfinite sumstochasticfinite sum0(log(1/e)(n+）Tgse-optim
Extragradient(Azizian et al., 2019)strong-monotonicitydeterministic0(log(1/e)2Tge-optim
OSG(this work)MVI has solutionstochastic0(e-4）Tge-SP
OAdagrad(this work)MVI has solutionstochastic0(c-r/a）Tge-SP
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1: Input: Zo = Xo = 0
2:fork=1,...,Ndo 3:Zk =IIx Xk-1-nmk-1∑1T（2k-1;5-1）)]
5: end for
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1:Input: zo= Xo=0,Ho=δI
2: fork=1,...,Ndo
3:Zk =Xk-1-nHk-1gk-1
4: 5:Xk =Xk-1-nH-11gk
6: end forUpdate go:k = [go:k-1 gk], Sk,i = |/go:k,il,i=1,...,d and set Hk = δI + diag(sk-1)
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\\widehat { \\mathbf { g } } _ { k } \\| _ { H _ { k } ^ { - 1 } } ^ { 2 } + \\displaystyle \\sum _ { k = 1 } ^ { N } \\Big ( \\mathbb { E } \\| \\widehat { \\mathbf { g } } _ { k } \\| _ { H _ { k - 1 } ^ { - 1 } } ^ { 2 } - \\mathbb { E } \\| \\widehat { \\mathbf { g } } _ { k } \\| _ { H _ { k } ^ { - 1 } } ^ { 2 } \\Big ) } \\\\ & { = \\displaystyle \\sum _ { k = 1 } ^ { N } \\mathbb { E } \\| \\widehat { \\mathbf { g } } _ { k } \\| _ { H _ { k } ^ { - 1 } } ^ { 2 } + \\displaystyle \\sum _ { k = 1 } ^ { N } \\mathbb { E } \\left. \\widehat { \\mathbf { g } } _ { k } , ( H _ { k - 1 } ^ { - 1 } - H _ { k } ^ { - 1 } ) \\widehat { \\mathbf { g } } _ { k } \\right. \\leq \\displaystyle \\sum _ { k = 1 } ^ { N } \\mathbb { E } \\| \\widehat { \\mathbf { g } } _ { k } \\| _ { H _ { k } ^ { - 1 } } ^ { 2 } + \\displaystyle \\sum _ { k = 1 } ^ { N } \\mathbb { E } \\left[ \\mathbb { r } ( H _ { k - 1 } ^ { - 1 } - H _ { k } ^ { - 1 } ) G ^ { 2 } \\right] } \\\\ & \\end{array}" + }, + { 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