93 research outputs found
Almost Optimal Sublinear Time Algorithm for Semidefinite Programming
We present an algorithm for approximating semidefinite programs with running
time that is sublinear in the number of entries in the semidefinite instance.
We also present lower bounds that show our algorithm to have a nearly optimal
running time
Faster Rates for the Frank-Wolfe Method over Strongly-Convex Sets
The Frank-Wolfe method (a.k.a. conditional gradient algorithm) for smooth
optimization has regained much interest in recent years in the context of large
scale optimization and machine learning. A key advantage of the method is that
it avoids projections - the computational bottleneck in many applications -
replacing it by a linear optimization step. Despite this advantage, the known
convergence rates of the FW method fall behind standard first order methods for
most settings of interest. It is an active line of research to derive faster
linear optimization-based algorithms for various settings of convex
optimization.
In this paper we consider the special case of optimization over strongly
convex sets, for which we prove that the vanila FW method converges at a rate
of . This gives a quadratic improvement in convergence rate
compared to the general case, in which convergence is of the order
, and known to be tight. We show that various balls induced by
norms, Schatten norms and group norms are strongly convex on one hand
and on the other hand, linear optimization over these sets is straightforward
and admits a closed-form solution. We further show how several previous
fast-rate results for the FW method follow easily from our analysis
Universal MMSE Filtering With Logarithmic Adaptive Regret
We consider the problem of online estimation of a real-valued signal
corrupted by oblivious zero-mean noise using linear estimators. The estimator
is required to iteratively predict the underlying signal based on the current
and several last noisy observations, and its performance is measured by the
mean-square-error. We describe and analyze an algorithm for this task which: 1.
Achieves logarithmic adaptive regret against the best linear filter in
hindsight. This bound is assyptotically tight, and resolves the question of
Moon and Weissman [1]. 2. Runs in linear time in terms of the number of filter
coefficients. Previous constructions required at least quadratic time.Comment: 14 page
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