Bayesian Theory of Mind: Modeling Joint Belief-Desire Attribution

Bayesian Theory of Mind: Modeling Joint Belief-Desire Attribution Chris L. Baker (clbaker@mit.edu) Rebecca R. Saxe (saxe@mit.edu) Joshua B. Tenenbaum (jbt@mit.edu) Department of Brain and Cognitive Sciences, MIT Cambridge, MA 02139 Abstract We present a computational framework for understanding The- ory of Mind (ToM): the human capacity for reasoning about agents’ mental states such as beliefs and desires. Our Bayesian model of ToM (or BToM) expresses the predictive model of belief- and desire-dependent action at the heart of ToM as a partially observable Markov decision process (POMDP), and reconstructs an agent’s joint belief state and reward func- tion using Bayesian inference, conditioned on observations of the agent’s behavior in some environmental context. We test BToM by showing participants sequences of agents moving in simple spatial scenarios and asking for joint inferences about the agents’ desires and beliefs about unobserved aspects of the environment. BToM performs substantially better than two simpler variants: one in which desires are inferred without ref- erence to an agent’s beliefs, and another in which beliefs are inferred without reference to the agent’s dynamic observations in the environment. Keywords: Theory of mind; Social cognition; Action un- derstanding; Bayesian inference; Partially Observable Markov Decision Processes Introduction Central to human social behavior is a theory of mind (ToM), the capacity to explain and predict people’s observable ac- tions in terms of unobservable mental states such as beliefs and desires. Consider the case of Harold, who leaves his dorm room one Sunday morning for the campus library. When he reaches to open the library’s front door he will find that it is locked – closed on Sunday. How can we explain his behav- ior? It seems plausible that he wants to get a book, that he believes the book he wants is at the library, and that he also believes (falsely, it turns out) that the library is open on Sun- day. Such mental state explanations for behavior go well be- yond the observable data, leading to an inference problem that is fundamentally ill-posed. Many different combinations of beliefs and desires could explain the same behavior, with inferences about the strengths of beliefs and desires trading off against each other, and relative probabilities modulated heavily by context. Perhaps Harold is almost positive that the library will be closed, but he needs a certain book so badly that he still is willing to go all the way across campus on the off chance it will be open. This explanation seems more prob- able if Harold shows up to find the library locked on Saturday at midnight, as opposed to noon on Tuesday. If he arrives after hours already holding a book with a due date of tomor- row, it is plausible that he knows the library is closed and is seeking not to get a new book, but merely to return a book checked out previously to the night drop box. Several authors have recently proposed models for how people infer others’ goals or preferences as a kind of Bayesian inverse planning or inverse decision theory (Baker, Saxe, & Tenenbaum, 2009; Feldman & Tremoulet, 2008; Lucas, Grif- fiths, Xu, & Fawcett, 2009; Bergen, Evans, & Tenenbaum, 2010; Yoshida, Dolan, & Friston, 2008; Ullman et al., 2010). These models adapt tools from control theory, econometrics and game theory to formalize the principle of rational ac- tion at the heart of children and adults’ concept of intentional agency (Gergely, N´adasdy, Csibra, & Bir´o, 1995; Dennett, 1987): all else being equal, agents are expected to choose ac- tions that achieve their desires as effectively and efficiently as possible, i.e., to maximize their expected utility. Goals or preferences are then inferred based on which objective or utility function the observed actions maximize most directly. ToM transcends knowledge of intentional agents’ goals and preferences by incorporating representational mental states such as subjective beliefs about the world (Perner, 1991). In particular, the ability to reason about false beliefs has been used to distinguish ToM from non-representational theories of intentional action (Wimmer & Perner, 1983; Onishi & Baillargeon, 2005). Our goal in this paper is to model hu- man ToM within a Bayesian framework. Inspired by mod- els of inverse planning, we cast Bayesian ToM (BToM) as a problem of inverse planning and inference, representing an agent’s planning and inference about the world as a partially observable Markov decision process (POMDP), and invert- ing this forward model using Bayesian inference. Critically, this model includes representations of both the agent’s de- sires (as a utility function), and the agent’s own subjective beliefs about the environment (as a probability distribution), which may be uncertain and may differ from reality. We test the predictions of this model quantitatively in an experiment where people must simultaneously judge beliefs and desires for agents moving in simple spatial environments under in- complete or imperfect knowledge. Important precursors to our work are several computational models (Goodman et al., 2006; Bello & Cassimatis, 2006; Goodman, Baker, & Tenenbaum, 2009) and informal theo- retical proposals by developmental psychologists (Wellman, 1990; Gopnik & Meltzoff, 1997; Gergely & Csibra, 2003). Goodman et al. (2006) model how belief and desire infer- ences interact in the classic “false belief” task used to assess ToM reasoning in children (Wimmer & Perner, 1983). This model instantiates the schema shown in Fig. 1(a) as a causal Bayesian network with several psychologically interpretable,