Bayesian Causal Induction

Discovering causal relationships is a hard task, often hindered by the need for intervention, and often requiring large amounts of data to resolve statistical uncertainty. However, humans quickly arrive at useful causal relationships. One possible reason is that humans extrapolate from past experience to new, unseen situations: that is, they encode beliefs over causal invariances, allowing for sound generalization from the observations they obtain from directly acting in the world. Here we outline a Bayesian model of causal induction where beliefs over competing causal hypotheses are modeled using probability trees. Based on this model, we illustrate why, in the general case, we need interventions plus constraints on our causal hypotheses in order to extract causal information from our experience.Comment: 4 pages, 4 figures; 2011 NIPS Workshop on Philosophy and Machine Learnin

An Adversarial Interpretation of Information-Theoretic Bounded Rationality

Recently, there has been a growing interest in modeling planning with information constraints. Accordingly, an agent maximizes a regularized expected utility known as the free energy, where the regularizer is given by the information divergence from a prior to a posterior policy. While this approach can be justified in various ways, including from statistical mechanics and information theory, it is still unclear how it relates to decision-making against adversarial environments. This connection has previously been suggested in work relating the free energy to risk-sensitive control and to extensive form games. Here, we show that a single-agent free energy optimization is equivalent to a game between the agent and an imaginary adversary. The adversary can, by paying an exponential penalty, generate costs that diminish the decision maker's payoffs. It turns out that the optimal strategy of the adversary consists in choosing costs so as to render the decision maker indifferent among its choices, which is a definining property of a Nash equilibrium, thus tightening the connection between free energy optimization and game theory.Comment: 7 pages, 4 figures. Proceedings of AAAI-1