Recursive Bayesian models of language production and comprehension
capture a variety of intricate phenomena concerning context dependence 
and pragmatic enrichment 
\citep{Jaeger:2007,
Franke09DISS,
Frank:Goodman:2012,
Bergen:Goodman:Levy:2012,
Vogel-etal:2013,
Smith:Goodman:Frank:2013}.
In these models, speakers and listeners reason about each other
recursively in order to achieve ever more optimal communication
systems. These approaches offer precise, algorithmic perspectives on
philosophical and linguistic theories of communication
\citep{Lewis69,Grice75,Horn84}, and they make robust predictions about
experimental data
\citep{Stiller:Goodman:Frank:2011,Rohde-etal:2012,Degen-etal:2013}.

Despite the success of these models, they raise concerns about
inferential power, in that they assume that the agents are
invariably optimal reasoners with unbounded computational resources.
These concerns can be mitigated by stipulations about depth of
iteration \citep{CamererHo:2004,Franke09DISS,Jaeger:2007,Jaeger:2011}, but the
models remain computationally demanding and powerful.

We seek to capitalize on the insights of these approaches while
addressing these concerns. We define a discriminative model of
pragmatic reasoning that requires no explicit representation of the
context. Rather, it relies only on features of the environment and
language. In addition, the recursive aspects of the model are limited
to training: we employ a \emph{self-training} regime in which,
starting with basic models of the speaker and the hearer, we use the
speaker to generate supervised training data for the listener, and
vice versa. Once this phase is complete, the model makes decisions
without any recursion. The models are both more efficient and more
fallible than the above generative ones. 

Our model also offers a way to reconcile previous explanations of the
interpretation or production of pragmatically complex utterances:
slowly via complex recursive inferences made as each sentence is
processed, \citep{Geurts09,Huang:Snedeker:2009} or quickly via
inferences that are pre-compiled and cached based on previous
interactions
\citep{Levinson00,Grodner-etal:2010,Smith:Goodman:Frank:2013}. Instead,
our discriminatively-trained model instantiates a third possibility,
extending \citealt{Jurafsky04}: learning to directly map surface
linguistic cues to speaker intent. Like the interpretive models, a
learned model explains how context-sensitive inferences could be drawn
at communication time; like the cached models, it explains why
processing could be fast and direct.

Our central question is whether our model's behavior matches human
performance across a wide range of situations. To address this, we use
collaborative reference games
\citep{Rosenberg:Cohen:1964,Clark:Wilkes-Gibbs:1986,DeVault-etal:2005}
in which a speaker refers to an object in a shared visual scene and
the listener uses the speaker's message to try to guess the intended
referent. By manipulating the properties of the scene and the
speaker's available messages, we can ensure that pragmatic reasoning,
of various levels of complexity, is required for reliable success. We
report several experiments that seek to identify the bounds on human
performance in these reference games, and we compare human performance
to our model, showing that its inferences closely align with human
performance.