Learning and using language via recursive pragmatic reasoning about other agents
Language users are remarkably good at making inferences about speakers' intentions in context, and children learning their native language also display substantial skill in acquiring the meanings of unknown words. These two cases are deeply related: Language users invent new terms in conversation, and language learners learn the literal meanings of words based on their pragmatic inferences about how those words are used. While pragmatic inference and word learning have both been independently characterized in probabilistic terms, no current work unifies these two. We describe a model in which language learners assume that they jointly approximate a shared, external lexicon and reason recursively about the goals of others in using this lexicon. This model captures phenomena in word learning and pragmatic inference; it additionally leads to insights about the emergence of communicative systems in conversation and the mechanisms by which pragmatic inferences become incorporated into word meanings.
This paper puts forward a model of learning 
      vocabulary, in the context of a hypothetical 'naming game'. A row of 
      objects visible ton two players, the 'speaker' and the 'listener'. There 
      are repeated rounds; in each round an object is indicated to the speaker, 
      who must then say a word that will cause the listener to point to that 
      object. This game can be (and has been) set up to be played 
      between people, but this paper considers simulated play between learning 
      algorithms. Both players start with prior beliefs about a lexicon; 
      they mutually refine these beliefs during repeated play. The paper 
      starts with a nice discussion of different ways in which to model this 
      vocabulary learning problem. In my view this is the best part of the 
      paper. The authors point out that there can be deep recursions if both 
      players attempt to optimise their communication strategy in a game 
      theoretic manner, and they make an interesting point that this deep 
      recursion does not seem to allow vocabulary learning. To prevent such 
      recursion, the authors introduce what seems a nice idea that both players 
      believe that there is some correct conventional lexicon, of which they 
      themselves have incomplete knowledge. This allows apparently simpler 
      shallow reasoning about what the lexicon may be. There are then 
      case studies of two learning problems: uninformative prior beliefs, but 
      objects with different frequencies and words with different costs; and the 
      case of specificity implicature, where the problem is to learn that 'some' 
      is pragmatically used to mean some, though it can also mean all. I 
      feel that this is potentially a rather nice line of research, but I also 
      feel that this paper has some problems in its current form. First, 
      there are rather few simulations; the results of a few individual 
      simulations only are given, and there is no systematic empirical analysis 
      under a range of conditions. How do these algorithms fare with slightly 
      larger problems? I take the point that different amounts of 
      experimentation with simulations are expected in different fields -- but 
      the authors should realise that if they propose an algorithm, they should 
      give sufficient simulations to give some empirical idea of how it behaves, 
      and what its behaviour is on problems of different sizes. Traces of 
      individual runs are not enough. Second, I was a little unclear as 
      to what the prior distributions over lexicons are. In the case of Horn 
      implicature, each word is assumed to match a single object, so the prior 
      can be represented as a multinomial distribution over the objects. In the 
      case of specificity implicature, the word some can mean some or all, which 
      seems to be represented as a probability distribution across objects: what 
      is the prior distribution in this case? Thanks to the authors for 
      clarifying this point. Third, a rather simpler model would be for 
      a learner to maintain a current assumed lexicon; if there are 
      communication failures, then the learner may change it. The learner (and 
      speaker?) may then repeatedly change their own lexicons, until they reach 
      a state where the lexicons match, communication succeeds, and no further 
      changes are necessary. This idea might turn out to need a Bayesian 
      formulation -- but there could be simpler possibilities requiring less 
      computation? As a suggestion, what about two-word phrases? Can you 
      produce a model of learning nouns when there are adjectives also? You 
      could have arrays of objects with two features, and you have one word 
      describing one feature, and the other word describing the other feature. 
      You could only say 'red' if there is only one red object, but you could 
      say 'red car' if there is a red car, a green car, and a red lorry. Your 
      present examples are rather small...