%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 13 0 R 14 0 R 15 0 R ] /Type /Pages /Count 12 >> endobj 2 0 obj << /Subject (Neural Information Processing Systems http\072\057\057nips\056cc\057) /Publisher (Curran Associates\054 Inc\056) /Language (en\055US) /Created (2018) /EventType (Poster) /Description-Abstract (Error bound conditions \050EBC\051 are properties that characterize the growth of an objective function when a point is moved away from the optimal set\056 They have recently received increasing attention in the field of optimization for developing optimization algorithms with fast convergence\056 However\054 the studies of EBC in statistical learning are hitherto still limited\056 The main contributions of this paper are two\055fold\056 First\054 we develop fast and intermediate rates of empirical risk minimization \050ERM\051 under EBC for risk minimization with Lipschitz continuous\054 and smooth convex random functions\056 Second\054 we establish fast and intermediate rates of an efficient stochastic approximation \050SA\051 algorithm for risk minimization with Lipschitz continuous random functions\054 which requires only one pass of \044n\044 samples and adapts to EBC\056 For both approaches\054 the convergence rates span a full spectrum between \044\134widetilde O\0501\057\134sqrt\173n\175\051\044 and \044\134widetilde O\0501\057n\051\044 depending on the power constant in EBC\054 and could be even faster than \044O\0501\057n\051\044 in special cases for ERM\056 Moreover\054 these convergence rates are automatically adaptive without using any knowledge of EBC\056 Overall\054 this work not only strengthens the understanding of ERM for statistical learning but also brings new fast stochastic algorithms for solving a broad range of statistical learning problems\056) /Producer (PyPDF2) /Title (Fast Rates of ERM and Stochastic Approximation\072 Adaptive to Error Bound Conditions) /Date (2018) /ModDate (D\07220190218225719\05508\04700\047) /Published (2018) /Type (Conference Proceedings) /firstpage (4678) /Book (Advances in Neural Information Processing Systems 31) /Description (Paper accepted and presented at the Neural Information Processing Systems Conference \050http\072\057\057nips\056cc\057\051) /Editors (S\056 Bengio and H\056 Wallach and H\056 Larochelle and K\056 Grauman and N\056 Cesa\055Bianchi and R\056 Garnett) /Author (Mingrui Liu\054 Xiaoxuan Zhang\054 Lijun Zhang\054 Jing Rong\054 Tianbao Yang) /lastpage (4689) >> endobj 3 0 obj << /Type /Catalog /Pages 1 0 R >> endobj 4 0 obj << /Contents [ 16 0 R 17 0 R 18 0 R 19 0 R 20 0 R 21 0 R 22 0 R 23 0 R ] /Parent 1 0 R /Resources << /Font << /F14 24 0 R /F30 28 0 R /F26 33 0 R /F10 37 0 R /F11 41 0 R /F13 45 0 R /F43 49 0 R /F51 53 0 R /F27 58 0 R /F53 62 0 R /F23 66 0 R /F44 70 0 R /F1 74 0 R /F8 78 0 R >> >> /Rotate 360 /CropBox [ 0 0 612 792 ] /MediaBox [ 0 0 612 792 ] /Annots [ 82 0 R 83 0 R 84 0 R ] /Type /Page >> 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