Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Average-case Acceleration for Bilinear Games and Normal Matrices   Advances in generative modeling and adversarial learning have given rise to
renewed interest in smooth games. However, the absence of symmetry in the
matrix of second derivatives poses challenges that are not present in the
classical minimization framework. While a rich theory of average-case analysis
has been developed for minimization problems, little is known in the context of
smooth games. In this work we take a first step towards closing this gap by
developing average-case optimal first-order methods for a subset of smooth
games. We make the following three main contributions. First, we show that for
zero-sum bilinear games the average-case optimal method is the optimal method
for the minimization of the Hamiltonian. Second, we provide an explicit
expression for the optimal method corresponding to normal matrices, potentially
non-symmetric. Finally, we specialize it to matrices with eigenvalues located
in a disk and show a provable speed-up compared to worst-case optimal
algorithms. We illustrate our findings through benchmarks with a varying degree
of mismatch with our assumptions.

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The categories of this paper are: plasm-ph
25
The categories of this paper are: patt-sol
13
The categories of this paper are: quant-ph
18
The categories of this paper are: econ
15
The categories of this paper are: nucl-ex
31
The categories of this paper are: ao-sci
0
The categories of this paper are: hep-ph
17
The categories of this paper are: q-fin
14
The categories of this paper are: math-ph
20
The categories of this paper are: acc-phys
27
The categories of this paper are: comp-gas
5
The categories of this paper are: gr-qc
11
The categories of this paper are: hep-lat
32
The categories of this paper are: atom-ph
12
The categories of this paper are: nucl-th
30
The categories of this paper are: q-alg