%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 (For smooth and strongly convex optimization\054 the optimal iteration complexity of the gradient\055based algorithm is \044O\050\134sqrt\173\134kappa\175\134log 1\057\134epsilon\051\044\054 where \044\134kappa\044 is the conditional number\056 In the case that the optimization problem is ill\055conditioned\054 we need to evaluate a larger number of full gradients\054 which could be computationally expensive\056 In this paper\054 we propose to reduce the number of full gradient required by allowing the algorithm to access the stochastic gradients of the objective function\056 To this end\054 we present a novel algorithm named Epoch Mixed Gradient Descent \050EMGD\051 that is able to utilize two kinds of gradients\056 A distinctive step in EMGD is the mixed gradient descent\054 where we use an combination of the gradient and the stochastic gradient to update the intermediate solutions\056 By performing a fixed number of mixed gradient descents\054 we are able to improve the sub\055optimality of the solution by a constant factor\054 and thus achieve a linear convergence rate\056 Theoretical analysis shows that EMGD is able to find an \044\134epsilon\044\055optimal solution by computing \044O\050\134log 1\057\134epsilon\051\044 full gradients and \044O\050\134kappa\1362\134log 1\057\134epsilon\051\044 stochastic gradients\056) /Producer (Python PDF Library \055 http\072\057\057pybrary\056net\057pyPdf\057) /Title (Linear Convergence with Condition Number Independent Access of Full Gradients) /Date (2013) /EventType (Poster) /Type (Conference Proceedings) /firstpage (980) /Book (Advances in Neural Information Processing Systems 26) /Description (Paper accepted and presented at 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