Human social behavior is structured by relationships. We form teams, groups, tribes, and alliances at all scales of human life. These structures guide multi-agent cooperation and competition, but when we observe others these underlying relationships are typically unobservable and hence must be inferred. Humans make these inferences intuitively and flexibly, often making rapid generalizations about the latent relationships that underlie behavior from just sparse and noisy observations. Rapid and accurate inferences are important for determining who to cooperate with, who to compete with, and how to cooperate in order to compete. Towards the goal of building machine-learning algorithms with human-like social intelligence, we develop a generative model of multi-agent action understanding based on a novel representation for these latent relationships called Composable Team Hierarchies (CTH). This representation is grounded in the formalism of stochastic games and multi-agent reinforcement learning. We use CTH as a target for Bayesian inference yielding a new algorithm for understanding behavior in groups that can both infer hidden relationships as well as predict future actions for multiple agents interacting together. Our algorithm rapidly recovers an underlying causal model of how agents relate in spatial stochastic games from just a few observations. The patterns of inference made by this algorithm closely correspond with human judgments and the algorithm makes the same rapid generalizations that people do.
@cite_30: This paper introduces a model of ‘theory of mind’, namely, how we represent the intentions and goals of others to optimise our mutual interactions. We draw on ideas from optimum control and game theory to provide a ‘game theory of mind’. First, we consider the representations of goals in terms of value functions that are prescribed by utility or rewards. Critically, the joint value functions and ensuing behaviour are optimised recursively, under the assumption that I represent your value function, your representation of mine, your representation of my representation of yours, and so on ad infinitum. However, if we assume that the degree of recursion is bounded, then players need to estimate the opponent's degree of recursion (i.e., sophistication) to respond optimally. This induces a problem of inferring the opponent's sophistication, given behavioural exchanges. We show it is possible to deduce whether players make inferences about each other and quantify their sophistication on the basis of choices in sequential games. This rests on comparing generative models of choices with, and without, inference. Model comparison is demonstrated using simulated and real data from a ‘stag-hunt’. Finally, we note that exactly the same sophisticated behaviour can be achieved by optimising the utility function itself (through prosocial utility), producing unsophisticated but apparently altruistic agents. This may be relevant ethologically in hierarchal game theory and coevolution.
@cite_35: Plan recognition is the problem of inferring the goals and plans of an agent from partial observations of her behavior. Recently, it has been shown that the problem can be formulated and solved using planners, reducing plan recognition to plan generation. In this work, we extend this model-based approach to plan recognition to the POMDP setting, where actions are stochastic and states are partially observable. The task is to infer a probability distribution over the possible goals of an agent whose behavior results from a POMDP model. The POMDP model is shared between agent and observer except for the true goal of the agent that is hidden to the observer. The observations are action sequences O that may contain gaps as some or even most of the actions done by the agent may not be observed. We show that the posterior goal distribution P(G|O) can be computed from the value function VG(b) over beliefs b generated by the POMDP planner for each possible goal G. Some extensions of the basic framework are discussed, and a number of experiments are reported.
@cite_37: Humans are adept at inferring the mental states underlying other agents’ actions, such as goals, beliefs, desires, emotions and other thoughts. We propose a computational framework based on Bayesian inverse planning for modeling human action understanding. The framework represents an intuitive theory of intentional agents’ behavior based on the principle of rationality: the expectation that agents will plan approximately rationally to achieve their goals, given their beliefs about the world. The mental states that caused an agent’s behavior are inferred by inverting this model of rational planning using Bayesian inference, integrating the likelihood of the observed actions with the prior over mental states. This approach formalizes in precise probabilistic terms the essence of previous qualitative approaches to action understanding based on an ‘‘intentional stance” [Dennett, D. C. (1987). The intentional stance. Cambridge, MA: MIT Press] or a ‘‘teleological stance” [Gergely, G., Nadasdy, Z., Csibra, G., & Biro, S. (1995). Taking the intentional stance at 12 months of age. Cognition, 56, 165–193]. In three psychophysical experiments using animated stimuli of agents moving in simple mazes, we assess how well different inverse planning models based on different goal priors can predict human goal inferences. The results provide quantitative evidence for an approximately rational inference mechanism in human goal inference within our simplified stimulus paradigm, and for the flexible nature of goal representations that human observers can adopt. We discuss the implications of our experimental results for human action understanding in real-world contexts, and suggest how our framework might be extended to capture other kinds of mental state inferences, such as inferences about beliefs, or inferring whether an entity is an intentional agent.
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@cite_1: An important use of machine learning is to learn what people value. What posts or photos should a user be shown? Which jobs or activities would a person find rewarding? In each case, observations of people's past choices can inform our inferences about their likes and preferences. If we assume that choices are approximately optimal according to some utility function, we can treat preference inference as Bayesian inverse planning. That is, given a prior on utility functions and some observed choices, we invert an optimal decision-making process to infer a posterior distribution on utility functions. However, people often deviate from approximate optimality. They have false beliefs, their planning is sub-optimal, and their choices may be temporally inconsistent due to hyperbolic discounting and other biases. We demonstrate how to incorporate these deviations into algorithms for preference inference by constructing generative models of planning for agents who are subject to false beliefs and time inconsistency. We explore the inferences these models make about preferences, beliefs, and biases. We present a behavioral experiment in which human subjects perform preference inference given the same observations of choices as our model. Results show that human subjects (like our model) explain choices in terms of systematic deviations from optimal behavior and suggest that they take such deviations into account when inferring preferences.
@cite_27: Objective—To evaluate the pharmacokinetics of a novel commercial formulation of ivermectin after administration to goats. Animals—6 healthy adult goats. Procedure—Ivermectin (200 μg kg) was initially administered IV to each goat, and plasma samples were obtained for 36 days. After a washout period of 3 weeks, each goat received a novel commercial formulation of ivermectin (200 μg kg) by SC injection. Plasma samples were then obtained for 42 days. Drug concentrations were quantified by use of high-performance liquid chromatography with fluorescence detection. Results—Pharmacokinetics of ivermectin after IV administration were best described by a 2-compartment open model; values for main compartmental variables included volume of distribution at a steady state (9.94 L kg), clearance (1.54 L kg d), and area under the plasma concentration-time curve (AUC; 143 [ng•d] mL). Values for the noncompartmental variables included mean residence time (7.37 days), AUC (153 [ng•d] mL), and clearance (1.43 L kg d). After ...
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@cite_15: A Bayesian theory of mind model is shown to infer and quantify the mental state and judgements of humans in decision-making scenarios. The model is a key step towards enabling machines to ‘intuit’ human thoughts and desires.
@cite_34: Most human behaviors consist of multiple parts, steps, or sub-tasks. These structures guide our action planning and execution, but when we observe others, the latent structure of their actions is typically unobservable, and must be inferred in order to learn new skills by demonstration, or to assist others in completing their tasks. For example, an assistant who has learned the subgoal structure of a colleague's task can more rapidly recognize and support their actions as they unfold. Here we model how humans infer subgoals from observations of complex action sequences using a nonparametric Bayesian model, which assumes that observed actions are generated by approximately rational planning over unknown subgoal sequences. We test this model with a behavioral experiment in which humans observed different series of goal-directed actions, and inferred both the number and composition of the subgoal sequences associated with each goal. The Bayesian model predicts human subgoal inferences with high accuracy, and significantly better than several alternative models and straightforward heuristics. Motivated by this result, we simulate how learning and inference of subgoals can improve performance in an artificial user assistance task. The Bayesian model learns the correct subgoals from fewer observations, and better assists users by more rapidly and accurately inferring the goal of their actions than alternative approaches.
@cite_13: Everyday social interactions are heavily influenced by our snap judgments about others' goals. Even young infants can infer the goals of intentional agents from observing how they interact with objects and other agents in their environment: e.g., that one agent is 'helping' or 'hindering' another's attempt to get up a hill or open a box. We propose a model for how people can infer these social goals from actions, based on inverse planning in multiagent Markov decision problems (MDPs). The model infers the goal most likely to be driving an agent's behavior by assuming the agent acts approximately rationally given environmental constraints and its model of other agents present. We also present behavioral evidence in support of this model over a simpler, perceptual cue-based alternative.
Inferring the latent mental states of agents (e.g., beliefs, desires, and intentions) from behavior features prominently in machine learning and cognitive science (see for a recent and comprehensive review from the machine learning point of view and for a developmental perspective). Previous computational treatments similar in spirit to the approach here have focused on making inferences about other individuals acting in a single agent setting @cite_27 @cite_37 @cite_35 @cite_1 @cite_34 @cite_15 @cite_23 . When these tools are applied to multi-agent and game theoretic contexts they have focused on dyadic interactions @cite_30 @cite_13 @cite_7 @cite_28 . Dyadic interactions are significantly simpler from a representational perspective since an observer must merely determine whether each agent is cooperating or competing.