%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 ] /Type /Pages /Count 10 >> 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 (2017) /EventType (Poster) /Description-Abstract (Recently\054 there has been a growing research interest in the analysis of dynamic regret\054 which measures the performance of an online learner against a sequence of local minimizers\056 By exploiting the strong convexity\054 previous studies have shown that the dynamic regret can be upper bounded by the path\055length of the comparator sequence\056 In this paper\054 we illustrate that the dynamic regret can be further improved by allowing the learner to query the gradient of the function multiple times\054 and meanwhile the strong convexity can be weakened to other non\055degenerate conditions\056 Specifically\054 we introduce the squared path\055length\054 which could be much smaller than the path\055length\054 as a new regularity of the comparator sequence\056 When multiple gradients are accessible to the learner\054 we first demonstrate that the dynamic regret of strongly convex functions can be upper bounded by the minimum of the path\055length and the squared path\055length\056 We then extend our theoretical guarantee to functions that are semi\055strongly convex or self\055concordant\056 To the best of our knowledge\054 this is the first time that semi\055strong convexity and self\055concordance are utilized to tighten the dynamic regret\056) /Producer (PyPDF2) /Title (Improved Dynamic Regret for Non\055degenerate Functions) /Date (2017) /ModDate (D\07220180213015331\05508\04700\047) /Published (2017) /Type (Conference Proceedings) /firstpage (732) /Book (Advances in Neural Information Processing Systems 30) /Description (Paper accepted and presented at the Neural Information Processing Systems Conference 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