Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Accelerated Stochastic Greedy Coordinate Descent by Soft Thresholding
  Projection onto Simplex   In this paper we study the well-known greedy coordinate descent (GCD)
algorithm to solve $\ell_1$-regularized problems and improve GCD by the two
popular strategies: Nesterov's acceleration and stochastic optimization.
Firstly, we propose a new rule for greedy selection based on an $\ell_1$-norm
square approximation which is nontrivial to solve but convex, then an efficient
algorithm called "SOft ThreshOlding PrOjection (SOTOPO)" is proposed to exactly
solve the $\ell_1$-regularized $\ell_1$-norm square approximation problem,
which is induced by the new rule. Based on the new rule and the SOTOPO
algorithm, the Nesterov's acceleration and stochastic optimization strategies
are then successfully applied to the GCD algorithm. The resulted algorithm
called accelerated stochastic greedy coordinate descent (ASGCD) has the optimal
convergence rate $O(\sqrt{1/\epsilon})$, meanwhile, it reduces the iteration
complexity of greedy selection up to a factor of sample size. Both
theoretically and empirically, we show that ASGCD has better performance for
high-dimensional and dense problems with sparse solution.

9
The categories of this paper are: nlin
11
The categories of this paper are: hep-lat
20
The categories of this paper are: acc-phys
23
The categories of this paper are: solv-int
30
The categories of this paper are: q-alg
17
The categories of this paper are: q-fin
33
The categories of this paper are: plasm-ph
12
The categories of this paper are: nucl-th
36
The categories of this paper are: cmp-lg
7
The categories of this paper are: hep-th
32
The categories of this paper are: atom-ph
22
The categories of this paper are: chao-dyn
31
The categories of this paper are: ao-sci
16
The categories of this paper are: stat
6
The categories of this paper are: astro-ph
10
The categories of this paper are: q-bio