Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Adapting to Function Difficulty and Growth Conditions in Private
  Optimization   We develop algorithms for private stochastic convex optimization that adapt
to the hardness of the specific function we wish to optimize. While previous
work provide worst-case bounds for arbitrary convex functions, it is often the
case that the function at hand belongs to a smaller class that enjoys faster
rates. Concretely, we show that for functions exhibiting $\kappa$-growth around
the optimum, i.e., $f(x) \ge f(x^*) + \lambda \kappa^{-1} \|x-x^*\|_2^\kappa$
for $\kappa > 1$, our algorithms improve upon the standard
${\sqrt{d}}/{n\varepsilon}$ privacy rate to the faster
$({\sqrt{d}}/{n\varepsilon})^{\tfrac{\kappa}{\kappa - 1}}$. Crucially, they
achieve these rates without knowledge of the growth constant $\kappa$ of the
function. Our algorithms build upon the inverse sensitivity mechanism, which
adapts to instance difficulty (Asi & Duchi, 2020), and recent localization
techniques in private optimization (Feldman et al., 2020). We complement our
algorithms with matching lower bounds for these function classes and
demonstrate that our adaptive algorithm is \emph{simultaneously} (minimax)
optimal over all $\kappa \ge 1+c$ whenever $c = \Theta(1)$.

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The categories of this paper are: alg-geom
11
The categories of this paper are: hep-lat
18
The categories of this paper are: econ
4
The categories of this paper are: cond-mat
36
The categories of this paper are: cmp-lg
26
The categories of this paper are: bayes-an
3
The categories of this paper are: physics
32
The categories of this paper are: atom-ph
12
The categories of this paper are: nucl-th
19
The categories of this paper are: eess
7
The categories of this paper are: hep-th
25
The categories of this paper are: patt-sol
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The categories of this paper are: q-alg
17
The categories of this paper are: q-fin
22
The categories of this paper are: chao-dyn
6
The categories of this paper are: astro-ph