We define a Causal Decision Problem as a Decision Problem where the available actions, the family of uncertain events and the set of outcomes are related through the variables of a Causal Graphical Model @math . A solution criteria based on Pearl's Do-Calculus and the Expected Utility criteria for rational preferences is proposed. The implementation of this criteria leads to an on-line decision making procedure that has been shown to have similar performance to classic Reinforcement Learning algorithms while allowing for a causal model of an environment to be learned. Thus, we aim to provide the theoretical guarantees of the usefulness and optimality of a decision making procedure based on causal information.
Motivated by applications in computational advertising and systems biology, we consider the problem of identifying the best out of several possible soft interventions at a source node V in an acyclic causal directed graph, to maximize the expected value of a target node Y (located downstream of V). Our setting imposes a fixed total budget for sampling under various interventions, along with cost constraints on different types of interventions. We pose this as a best arm identification bandit problem with K arms where each arm is a soft intervention at V, and leverage the information leakage among the arms to provide the first gap dependent error and simple regret bounds for this problem. Our results are a significant improvement over the traditional best arm identification results. We empirically show that our algorithms outperform the state of the art in the Flow Cytometry data-set, and also apply our algorithm for model interpretation of the Inception-v3 deep net that classifies images. We study the problem of using causal models to improve the rate at which good interventions can be learned online in a stochastic environment. Our formalism combines multi-arm bandits and causal inference to model a novel type of bandit feedback that is not exploited by existing approaches. We propose a new algorithm that exploits the causal feedback and prove a bound on its simple regret that is strictly better (in all quantities) than algorithms that do not use the additional causal information.