601 research outputs found
Inexact Online Proximal Mirror Descent for time-varying composite optimization
In this paper, we consider the online proximal mirror descent for solving the
time-varying composite optimization problems. For various applications, the
algorithm naturally involves the errors in the gradient and proximal operator.
We obtain sharp estimates on the dynamic regret of the algorithm when the
regular part of the cost is convex and smooth. If the Bregman distance is given
by the Euclidean distance, our result also improves the previous work in two
ways: (i) We establish a sharper regret bound compared to the previous work in
the sense that our estimate does not involve term appearing in that
work. (ii) We also obtain the result when the domain is the whole space
, whereas the previous work was obtained only for bounded
domains. We also provide numerical tests for problems involving the errors in
the gradient and proximal operator.Comment: 16 pages, 5 figure
Online Joint Topology Identification and Signal Estimation with Inexact Proximal Online Gradient Descent
Identifying the topology that underlies a set of time series is useful for
tasks such as prediction, denoising, and data completion. Vector autoregressive
(VAR) model based topologies capture dependencies among time series, and are
often inferred from observed spatio-temporal data. When the data are affected
by noise and/or missing samples, the tasks of topology identification and
signal recovery (reconstruction) have to be performed jointly. Additional
challenges arise when i) the underlying topology is time-varying, ii) data
become available sequentially, and iii) no delay is tolerated. To overcome
these challenges, this paper proposes two online algorithms to estimate the VAR
model-based topologies. The proposed algorithms have constant complexity per
iteration, which makes them interesting for big data scenarios. They also enjoy
complementary merits in terms of complexity and performance. A performance
guarantee is derived for one of the algorithms in the form of a dynamic regret
bound. Numerical tests are also presented, showcasing the ability of the
proposed algorithms to track the time-varying topologies with missing data in
an online fashion.Comment: 14 pages including supplementary material, 2 figures, submitted to
IEEE Transactions on Signal Processin
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