3 research outputs found
Efficient Online Convex Optimization with Adaptively Minimax Optimal Dynamic Regret
We introduce an online convex optimization algorithm using projected
sub-gradient descent with ideal adaptive learning rates, where each computation
is efficiently done in a sequential manner. For the first time in the
literature, this algorithm provides an adaptively minimax optimal dynamic
regret guarantee for a sequence of convex functions without any restrictions --
such as strong convexity, smoothness or even Lipschitz continuity -- against a
comparator decision sequence with bounded total successive changes. We show
optimality by generating the worst-case dynamic regret adaptive lower bound,
which constitutes of actual sub-gradient norms and matches with our guarantees.
We discuss the advantages of our algorithm as opposed to adaptive projection
with sub-gradient self outer products and also derive the extension for
independent learning in each decision coordinate separately. Additionally, we
demonstrate how to best preserve our guarantees when the bound on total
successive changes in the dynamic comparator sequence grows as time goes, in a
truly online manner.Comment: 10 pages, 1 figure, preprint, [v0] 201
Online Learning for Changing Environments using Coin Betting
A key challenge in online learning is that classical algorithms can be slow
to adapt to changing environments. Recent studies have proposed "meta"
algorithms that convert any online learning algorithm to one that is adaptive
to changing environments, where the adaptivity is analyzed in a quantity called
the strongly-adaptive regret. This paper describes a new meta algorithm that
has a strongly-adaptive regret bound that is a factor of
better than other algorithms with the same time complexity, where is the
time horizon. We also extend our algorithm to achieve a first-order (i.e.,
dependent on the observed losses) strongly-adaptive regret bound for the first
time, to our knowledge. At its heart is a new parameter-free algorithm for the
learning with expert advice (LEA) problem in which experts sometimes do not
output advice for consecutive time steps (i.e., \emph{sleeping} experts). This
algorithm is derived by a reduction from optimal algorithms for the so-called
coin betting problem. Empirical results show that our algorithm outperforms
state-of-the-art methods in both learning with expert advice and metric
learning scenarios.Comment: submitted to a journal. arXiv admin note: substantial text overlap
with arXiv:1610.0457