www-ai.cs.tu-dortmund.de/de/LEHRE/VORLESUNGEN/LOPT/SS16/papers/NemJ09.pdf
P:\TEX\SIOPT\19-4\70427\70427.dvi
at least 1 − δ. According to (3.30), to this end, one can use the randomized saddle point mirror SA algorithm (3.7), (3.8), (3.26) with stepsizes (3.12), (3.28) and with
(3.32) N = O(1) ln n + ln(1/δ)
ρ2 [...] setting Θ = 2 √
Ω and substituting (3.12), we obtain (3.17). Proof of Proposition 3.3. As in the proof of Proposition 3.2, when setting ΓN =∑N
t=1 γt and using the relations (3.9), (6.5), and (6.7), combined [...] holds:
(3.16) E [ exp { ‖Gx(u, v, ξ)‖2
∗,x /M2∗,x
}] ≤ exp{1}, E [ exp { ‖Gy(x, y, ξ)‖2
∗,y /M2 ∗,y
}] ≤ exp{1}.
Proposition 3.2. In the case of (3.16), with the stepsizes given by (3.12) and (3.6), one …
