Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Improved Dynamic Regret for Non-degenerate Functions   Recently, there has been a growing research interest in the analysis of
dynamic regret, which measures the performance of an online learner against a
sequence of local minimizers. By exploiting the strong convexity, previous
studies have shown that the dynamic regret can be upper bounded by the
path-length of the comparator sequence. In this paper, we illustrate that the
dynamic regret can be further improved by allowing the learner to query the
gradient of the function multiple times, and meanwhile the strong convexity can
be weakened to other non-degenerate conditions. Specifically, we introduce the
squared path-length, which could be much smaller than the path-length, as a new
regularity of the comparator sequence. When multiple gradients are accessible
to the learner, we first demonstrate that the dynamic regret of strongly convex
functions can be upper bounded by the minimum of the path-length and the
squared path-length. We then extend our theoretical guarantee to functions that
are semi-strongly convex or self-concordant. To the best of our knowledge, this
is the first time that semi-strong convexity and self-concordance are utilized
to tighten the dynamic regret.

14
The categories of this paper are: math-ph
20
The categories of this paper are: acc-phys
8
The categories of this paper are: hep-ex
0
The categories of this paper are: hep-ph
18
The categories of this paper are: econ
26
The categories of this paper are: bayes-an
2
The categories of this paper are: math
27
The categories of this paper are: comp-gas
31
The categories of this paper are: ao-sci
5
The categories of this paper are: gr-qc
36
The categories of this paper are: cmp-lg
9
The categories of this paper are: nlin
16
The categories of this paper are: stat
23
The categories of this paper are: solv-int
37
The categories of this paper are: supr-con
33
The categories of this paper are: plasm-ph