%PDF-1.3 1 0 obj << /Kids [ 4 0 R 5 0 R 6 0 R 7 0 R 8 0 R 9 0 R 10 0 R 11 0 R 12 0 R ] /Type /Pages /Count 9 >> endobj 2 0 obj << /Subject (Neural Information Processing Systems http\072\057\057nips\056cc\057) /Publisher (Curran Associates) /Language (en\055US) /Created (2013) /Description-Abstract (It is well known that the optimal convergence rate for stochastic optimization of smooth functions is \044\133O\0501\057\134sqrt\173T\175\051\135\044\054 which is same as stochastic optimization of Lipschitz continuous convex functions\056 This is in contrast to optimizing smooth functions using full gradients\054 which yields a convergence rate of \044\133O\0501\057T\1362\051\135\044\056 In this work\054 we consider a new setup for optimizing smooth functions\054 termed as \173\134bf Mixed Optimization\175\054 which allows to access both a stochastic oracle and a full gradient oracle\056 Our goal is to significantly improve the convergence rate of stochastic optimization of smooth functions by having an additional small number of accesses to the full gradient oracle\056 We show that\054 with an \044\133O\050\134ln T\051\135\044 calls to the full gradient oracle and an \044O\050T\051\044 calls to the stochastic oracle\054 the proposed mixed optimization algorithm is able to achieve an optimization error of \044\133O\0501\057T\051\135\044\056) /Producer (Python PDF Library \055 http\072\057\057pybrary\056net\057pyPdf\057) /Title (Mixed Optimization for Smooth Functions) /Date (2013) /EventType (Poster) /Type (Conference Proceedings) /firstpage (674) /Book (Advances in Neural Information Processing Systems 26) /Description (Paper accepted and presented at the Neural Information Processing Systems Conference \050http\072\057\057nips\056cc\057\051) /Editors (C\056J\056C\056 Burges and L\056 Bottou and M\056 Welling and Z\056 Ghahramani and K\056Q\056 Weinberger) /Author (Mehrdad Mahdavi\054 Lijun Zhang\054 Rong Jin) /lastpage (682) >> endobj 3 0 obj << /Type /Catalog /Pages 1 0 R >> endobj 4 0 obj << /Parent 1 0 R /Contents [ 13 0 R ] /Type /Page /Resources 14 0 R /MediaBox [ 0 0 612 792 ] >> endobj 5 0 obj << /Parent 1 0 R /Contents [ 69 0 R ] /Type /Page /Resources 70 0 R /MediaBox [ 0 0 612 792 ] >> endobj 6 0 obj << /Parent 1 0 R /Contents [ 88 0 R ] /Type /Page /Resources 89 0 R /MediaBox [ 0 0 612 792 ] >> endobj 7 0 obj << /Parent 1 0 R /Contents [ 99 0 R ] /Type /Page /Resources 100 0 R /MediaBox [ 0 0 612 792 ] >> endobj 8 0 obj << /Parent 1 0 R /Contents [ 113 0 R ] /Type /Page /Resources 114 0 R /MediaBox [ 0 0 612 792 ] >> endobj 9 0 obj << /Parent 1 0 R /Contents [ 115 0 R ] /Type /Page /Resources 116 0 R /MediaBox [ 0 0 612 792 ] >> endobj 10 0 obj << /Parent 1 0 R /Contents [ 117 0 R ] /Type /Page /Resources 118 0 R /MediaBox [ 0 0 612 792 ] >> endobj 11 0 obj << /Parent 1 0 R /Contents [ 119 0 R ] /Type /Page /Resources 120 0 R /MediaBox [ 0 0 612 792 ] >> endobj 12 0 obj << /Parent 1 0 R /Contents [ 121 0 R ] /Type /Page /Resources 122 0 R /MediaBox [ 0 0 612 792 ] >> endobj 13 0 obj << /Length 4108 /Filter /FlateDecode >> stream x[6~?hpkh.9\6imZ-毿IQ׻I[0"g3.~]EEdCw;u!Hw -Vt_HmeX؂1gfq!Ŭ\\nFj\4^z_mfevPetoaK?5.\| I~$U&)2ag~%mHmMen*o54G?fwVycM}88+gStMG?Qb]fR5fW7uTW7>]Jc5TKS,YeFhܫf_.5s'Lƌ t=RzRfWY;x+3YRygW۾?js4@X\ZVyb0/׃ZV.NV ǘE2cKGYFuOwj[DDxPǰ[R4E5(-ٗn+"4wp؊7]o~״j;zy~(Ҹ^G7R@U bxn 7t}m3qQޫpg)&+ ) V&q26xwœ4ft'ƃgYt+jT'PDO_sx]w2 WsLP uslBH펕1r[Fu3uhl&$G1>\{$Ŝvi$G{=Q kitUPFC# nӰ~~\H? koBS6R+("nHRhzcF< Op(yzЉwpybpdp(b_^"z>*iV5X)^C1NxDdm,;5:cfIF@'M,ɘdiUϞ$Z= 0PoAHЍ%IŒT:mk<QZݶՎJt fc#kZU2U?af䳓SB]OuangHx;S/{VK!Q Dͦzjgq%K({[3%Ѣ f9!}|"7˼ԄauNUK.l0ji,jvĨh>ۤd1*`("9K \@% Ml$x=)ٙ#P8923GN, :O,F:2:jr~4 ߨV۶[ ؚ0j42Z) Β?8e)4NN@{(Lc$_LXu%סVUÐL24z[թ,}K&\)ɣ^THހ#X;6*Γ>VN*e#LF(?V, G"=eQv)7*H9l4?uȺ[a-0(>|.9| >@$QꄢU$?DZq`mpL&r&Vqo~ iGY[%,W<CICaVC̵pkBg%[!7W;I.pN**#Zi9oHæQRzw(3JFbLvCTcS2 {-T ~u;>ݢoweb.8Um`N5 rI%5 bfϐ}іsاi.L Yg cz{`DXVȑ^!9ģy-Ԃ(G}HL*n)١s'SCY>1Ȍʋڅ]1dk☪+†=nmŭF^vԦ ƥS51'Xߌ점2\%@v14 (ބc>K [:0!d݊ӧ!(Ie0jC(e@\d(F]KQ9a F=t|Zqljqh~5Pqo:1My=z}my;g^عUvf5 ;.3>h;pBRx|jS?_." 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