Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Random Hypervolume Scalarizations for Provable Multi-Objective Black Box
  Optimization   Single-objective black box optimization (also known as zeroth-order
optimization) is the process of minimizing a scalar objective $f(x)$, given
evaluations at adaptively chosen inputs $x$. In this paper, we consider
multi-objective optimization, where $f(x)$ outputs a vector of possibly
competing objectives and the goal is to converge to the Pareto frontier.
Quantitatively, we wish to maximize the standard hypervolume indicator metric,
which measures the dominated hypervolume of the entire set of chosen inputs. In
this paper, we introduce a novel scalarization function, which we term the
hypervolume scalarization, and show that drawing random scalarizations from an
appropriately chosen distribution can be used to efficiently approximate the
hypervolume indicator metric. We utilize this connection to show that Bayesian
optimization with our scalarization via common acquisition functions, such as
Thompson Sampling or Upper Confidence Bound, provably converges to the whole
Pareto frontier by deriving tight hypervolume regret bounds on the order of
$\widetilde{O}(\sqrt{T})$. Furthermore, we highlight the general utility of our
scalarization framework by showing that any provably convergent
single-objective optimization process can be effortlessly converted to a
multi-objective optimization process with provable convergence guarantees.

29
The categories of this paper are: funct-an
6
The categories of this paper are: astro-ph
0
The categories of this paper are: hep-ph
9
The categories of this paper are: nlin
15
The categories of this paper are: nucl-ex
20
The categories of this paper are: acc-phys
35
The categories of this paper are: mtrl-th
26
The categories of this paper are: bayes-an
4
The categories of this paper are: cond-mat
21
The categories of this paper are: adap-org
17
The categories of this paper are: q-fin
28
The categories of this paper are: alg-geom
19
The categories of this paper are: eess
7
The categories of this paper are: hep-th
12
The categories of this paper are: nucl-th
10
The categories of this paper are: q-bio