claim,v1_anchor,anchor_present,v1_companion,companion_present,algorithm,label,present 1,label{alg:SDRO-NGD},1,label{alg:SDRO-WFR},1,,, 2,label{prop:gradient_oracle_error_control},1,log{\frac{L}{\sqrt{\lambda}\epsilon}},1,,, 3,label{thm:outer_loop},1,S = O(1/\epsilon_{\text{opt}}^2),1,,, 4,label{thm:ula},1,\epsilon_{\text{opt}}^4,1,,, 5,label{fig:robustness},1,"WFR and WGF, in particular, consistently achieve",1,,, 6,label{lem:sb-klform},1,"Schr\""odinger half bridge problem",1,,, ,,,,,1,alg:sampler,1 ,,,,,2,alg:GF-DRO,1 ,,,,,3,alg:SDRO-NGD,1 ,,,,,4,alg:SDRO-WFR,1 ,,,,,5,alg:SDRO-SVG,1 ,,,,,6,alg:SDRO_rgo,1