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+in+the+setup+of+non-smooth+Stochastic+Convex+Optimization.+We+show+that+the+generalization+error+of+GD%252C+with+common+choice+of+hyper-parameters%252C+can+be+%2524tilde+Theta(d%252Fm+%252B+1%252Fsqrt%7bm%7d)%2524%252C+where+%2524d%2524+is+the+dimension+and+%2524m%2524+is+the+sample+size.+This+matches+the+sample+complexity+of+emph%7bworst-case%7d+empirical+risk+minimizers.+That+means+that%252C+in+contrast+with+other+algorithms%252C+GD+has+no+advantage+over+naive+ERMs.+Our+bound+follows+from+a+new+generalization+bound+that+depends+on+both+the+dimension+as+well+as+the+learning+rate+and+number+of+iterations.+Our+bound+also+shows+that%252C+for+general+hyper-parameters%252C+when+the+dimension+is+strictly+larger+than+number+of+samples%252C+%2524T%253DOmega(1%252Fepsilon%5e4)%2524+iterations+are+necessary+to+avoid+overfitting.+This+resolves+an+open+problem+by+Schlisserman+et+al.23+and+Amir+er+Al.21%252C+and+improves+over+previous+lower+bounds+that+demonstrated+that+the+sample+size+must+be+at+least+square+root+of+the+dimension.&cdnurl=https%3a%2f%2fth.bing.com%2fth%2fid%2fR.6f498e2a97116c6f32575bb984ecc0fe%3frik%3dkvl63OxBQp7SsA%26pid%3dImgRaw%26r%3d0&exph=630&expw=1200&q=Stochastic+Gradient+Descent+Update+Rule+Time+Complexity&FORM=IRPRST&ck=E87E9D2F3DE18B0AF7F9247F1D5E57A2&selectedIndex=1&itb=0)
