Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Online Optimization and Learning in Uncertain Dynamical Environments
  with Performance Guarantees   We propose a new framework to solve online optimization and learning problems
in unknown and uncertain dynamical environments. This framework enables us to
simultaneously learn the uncertain dynamical environment while making online
decisions in a quantifiably robust manner. The main technical approach relies
on the theory of distributional robust optimization that leverages adaptive
probabilistic ambiguity sets. However, as defined, the ambiguity set usually
leads to online intractable problems, and the first part of our work is
directed to find reformulations in the form of online convex problems for two
sub-classes of objective functions. To solve the resulting problems in the
proposed framework, we further introduce an online version of the Nesterov
accelerated-gradient algorithm. We determine how the proposed solution system
achieves a probabilistic regret bound under certain conditions. Two
applications illustrate the applicability of the proposed framework.

30
The categories of this paper are: q-alg
5
The categories of this paper are: gr-qc
21
The categories of this paper are: adap-org
4
The categories of this paper are: cond-mat
33
The categories of this paper are: plasm-ph
15
The categories of this paper are: nucl-ex
11
The categories of this paper are: hep-lat
24
The categories of this paper are: dg-ga
13
The categories of this paper are: quant-ph
8
The categories of this paper are: hep-ex
20
The categories of this paper are: acc-phys
14
The categories of this paper are: math-ph
17
The categories of this paper are: q-fin
10
The categories of this paper are: q-bio
34
The categories of this paper are: chem-ph
37
The categories of this paper are: supr-con