Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Constrained Optimization Approach to Bilevel Optimization with
  Multiple Inner Minima   Bilevel optimization has found extensive applications in modern machine
learning problems such as hyperparameter optimization, neural architecture
search, meta-learning, etc. While bilevel problems with a unique inner minimal
point (e.g., where the inner function is strongly convex) are well understood,
bilevel problems with multiple inner minimal points remains to be a challenging
and open problem. Existing algorithms designed for such a problem were
applicable to restricted situations and do not come with the full guarantee of
convergence. In this paper, we propose a new approach, which convert the
bilevel problem to an equivalent constrained optimization, and then the
primal-dual algorithm can be used to solve the problem. Such an approach enjoys
a few advantages including (a) addresses the multiple inner minima challenge;
(b) features fully first-order efficiency without involving second-order
Hessian and Jacobian computations, as opposed to most existing gradient-based
bilevel algorithms; (c) admits the convergence guarantee via constrained
nonconvex optimization. Our experiments further demonstrate the desired
performance of the proposed approach.

21
The categories of this paper are: adap-org
10
The categories of this paper are: q-bio
12
The categories of this paper are: nucl-th
32
The categories of this paper are: atom-ph
29
The categories of this paper are: funct-an
7
The categories of this paper are: hep-th
4
The categories of this paper are: cond-mat
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The categories of this paper are: solv-int
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The categories of this paper are: dg-ga
30
The categories of this paper are: q-alg
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The categories of this paper are: nucl-ex
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The categories of this paper are: acc-phys
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The categories of this paper are: nlin
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The categories of this paper are: q-fin
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The categories of this paper are: alg-geom
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The categories of this paper are: chao-dyn