Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Learning Valuation Functions   In this paper we study the approximate learnability of valuations commonly
used throughout economics and game theory for the quantitative encoding of
agent preferences. We provide upper and lower bounds regarding the learnability
of important subclasses of valuation functions that express
no-complementarities. Our main results concern their approximate learnability
in the distributional learning (PAC-style) setting. We provide nearly tight
lower and upper bounds of $\tilde{\Theta}(n^{1/2})$ on the approximation factor
for learning XOS and subadditive valuations, both widely studied superclasses
of submodular valuations. Interestingly, we show that the
$\tilde{\Omega}(n^{1/2})$ lower bound can be circumvented for XOS functions of
polynomial complexity; we provide an algorithm for learning the class of XOS
valuations with a representation of polynomial size achieving an $O(n^{\eps})$
approximation factor in time $O(n^{1/\eps})$ for any $\eps > 0$. This
highlights the importance of considering the complexity of the target function
for polynomial time learning. We also provide new learning results for
interesting subclasses of submodular functions.
  Our upper bounds for distributional learning leverage novel structural
results for all these valuation classes. We show that many of these results
provide new learnability results in the Goemans et al. model (SODA 2009) of
approximate learning everywhere via value queries.
  We also introduce a new model that is more realistic in economic settings, in
which the learner can set prices and observe purchase decisions at these prices
rather than observing the valuation function directly. In this model, most of
our upper bounds continue to hold despite the fact that the learner receives
less information (both for learning in the distributional setting and with
value queries), while our lower bounds naturally extend.

12
The categories of this paper are: nucl-th
17
The categories of this paper are: q-fin
31
The categories of this paper are: ao-sci
3
The categories of this paper are: physics
13
The categories of this paper are: quant-ph
7
The categories of this paper are: hep-th
24
The categories of this paper are: dg-ga
27
The categories of this paper are: comp-gas
33
The categories of this paper are: plasm-ph
37
The categories of this paper are: supr-con
18
The categories of this paper are: econ
23
The categories of this paper are: solv-int
29
The categories of this paper are: funct-an
20
The categories of this paper are: acc-phys
34
The categories of this paper are: chem-ph
15
The categories of this paper are: nucl-ex