How to Do Things with Words: A Bayesian Approach

Abstract

Communication changes the beliefs of the listener and of the speaker. The value of a communicative act stems from the valuable belief states which result from this act. To model this we build on the Interactive POMDP (IPOMDP) framework, which extends POMDPs to allow agents to model others in multi-agent settings, and we include communication that can take place between the agents to formulate Communicative IPOMDPs (CIPOMDPs). We treat communication as a type of action and therefore, decisions regarding communicative acts are based on decision-theoretic planning using the Bellman optimality principle and value iteration, just as they are for all other rational actions. As in any form of planning, the results of actions need to be precisely specified. We use the Bayes’ theorem to derive how agents update their beliefs in CIPOMDPs; updates are due to agents’ actions, observations, messages they send to other agents, and messages they receive from others. The Bayesian decision-theoretic approach frees us from the commonly made assumption of cooperative discourse – we consider agents which are free to be dishonest while communicating and are guided only by their selfish rationality. We use a simple Tiger game to illustrate the belief update, and to show that the ability to rationally communicate allows agents to improve efficiency of their interactions.