This paper has an unusual and interesting goal, compared to those I more typically read: it wants to develop a “translation” between the messages produced by a model, and natural language used by a human. More specifically, the paper seeks to do this in the context of an two-player game, where one player needs to communicate information to the other. A few examples of this are: - Being shown a color, and needing to communicate to your partner so they can choose that color - Driving, in an environment where you can’t see the other car, but you have to send a coordinating message so that you don’t collide Recently, people have started training multi-agent that play games like these, where they send “message” vectors back and forth, in a way fully integrated with the rest of the backpropogation procedure. From just observing the agents’ actions, it’s not necessarily clear which communication strategy they’re using. That’s why this paper poses as an explicit problem: how can we map between the communication vectors produced by the agents and the words that would be produced by a human in a similar environment? Interestingly, the paper highlights two different ways you could think about structuring a translation objective. The first is “pragmatic interpretation,” under which you optimize what you communicate about something according to the operation that needs to be performed afterwards. To make that more clear, take a look at the attached picture. Imagine that player one is shown a shape, and needs to use a phrase from the bottom language (based on how many sides the shape has) to describe it to player two, who then needs to guess the size of the shape (big or small), and is rewarded for guessing correctly. Because “many” corresponds to both a large and a small shape, the strategy that optimizes the action that player two takes, conditional on getting player one’s message, is to lie and describe a hexagon as “few”, since that will lead to correct inference about the size of the shape, which is what’s most salient here. This example shows how, if you optimize a translation mapping by trying to optimize the reward that the post-translation agent can get, you might get a semantically incorrect translation. That might be good for the task at hand, but, because it leaves you with incorrect beliefs about the true underlying mapping, it will generalize poorly to different tasks. The alternate approach, championed by the paper, is to train a translation such that the utterances in both languages are similar insofar as, conditional on hearing them, and having some value for their own current state, the listening player arrives at similar beliefs about the current state of the player sending the message. This is mathematically framed as by defining a metric q, representing the quality of the translation between two z vectors, as: “taking an expectation over all possible contextual states of (player 1, player 2), what is the difference between the distribution of beliefs about the state of player 1 (the sending player) induced in player 2 by hearing each of the z vectors. Because taking the full expectation over this joint distribution is intractable, the approach is instead done by sampling. These equations require that you have reasonable models of human language, and understanding of human language, in the context of games. To do this, the authors used two types of datasets: 1. Linguistic descriptions of objects of things, like the xkcd color dataset. Here, the player’s hidden state is the color that they are trying to describe using some communication scheme. 2. Mechanical turk game runs playing the aforementioned driver game, where they have to communicate to the other driver. Here, the player’s “hidden state” represents a combination of its current location and intentions. From these datasets, they can train simple emulator models that learn “what terms is a human most likely to use for a given color” [p(z|x)], and “what colors will a human guess, conditional on those terms”. The paper closes by providing a proof as to how much reward-based value is lost by optimizing for the true semantic meaning, rather than the most pragmatically useful translation. They find that there is a bound on the gap, and that, in many empirical cases, the observed gap is quite small. Overall, this paper was limited in scope, but provided an interesting conceptual framework for thinking about how you might structure a translation, and the different implications that structure might have on your results.