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CATEGORIES:Data Science and Computational Statistics Seminar
SUMMARY:Smooth over-parametrized solvers for non-smooth st
ructured optimisation - Clarice Poon (University o
f Warwick)
DTSTART:20231106T140000Z
DTEND:20231106T150000Z
UID:TALK5363AT
URL:/talk/index/5363
DESCRIPTION:Non-smooth optimization is a core ingredient of ma
ny imaging or machine learning pipelines. Non-smoo
thness encodes structural constraints on the solut
ions\, such as sparsity\, group sparsity\, low-ran
k and sharp edges. It is also the basis for the de
finition of robust loss functions such as the squa
re-root lasso. Standard approaches to deal with n
on-smoothness leverage either proximal splitting o
r coordinate descent. The effectiveness of their u
sage typically depend on proper parameter tuning\,
preconditioning or some sort of support pruning.
In this work\, we advocate and study a different r
oute. By over-parameterization and marginalising o
n certain variables (Variable Projection)\, we sho
w how many popular non-smooth structured problems
can be written as smooth optimization problems. Th
e result is that one can then take advantage of qu
asi-Newton solvers such as L-BFGS and this\, in pr
actice\, can lead to substantial performance gains
. Another interesting aspect of our proposed solve
r is its efficiency when handling imaging problems
that arise from fine discretizations (unlike prox
imal methods such as ISTA whose convergence is kno
wn to have exponential dependency on dimension). O
n a theoretical level\, one can connect gradient d
escent on our over-parameterized formulation with
mirror descent with a varying Hessian metric. This
observation can then be used to derive dimension
free convergence bounds and explains the efficienc
y of our method in the fine-grids regime.
LOCATION:Room 104\, Arts Building (R16)
CONTACT:Xiaocheng Shang
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