Reasoning with counterfactuals is one of the hallmarks of human cognition, involved in various tasks such as explanation, credit assignment, blame, and responsibility. Counterfactual quantities that are not identifiable in the general non-parametric case may be identified under shape constraints on the functional mechanisms, such as monotonicity. One prominent example of such an approach is the celebrated result by Angrist and Imbens on identifying the Local Average Treatment Effect (LATE) in the instrumental variable setting. In this paper, we study the identification problem of more general settings under monotonicity constraints. We begin by proving the monotonicity reduction lemma, which simplifies counterfactual queries using monotonicity assumptions and facilitates the reduction of a larger class of these queries to interventional quantities. We then extend the existing identification results on Probabilities of Causation (PoCs) and LATE to a broader set of queries and graphs. Finally, we develop an algorithm, M-ID, for identifying arbitrary counterfactual queries from combinations of observational and experimental data, which takes as input a causal diagram with monotonicity constraints. We show that M-ID subsumes the previously known identification results in the literature. We demonstrate the applicability of our results using synthetic and real data.

Users' behavioral footprints online enable firms to discover behavior-based user segments (or, segments) and deliver segment specific messages to users. Following the discovery of segments, delivery of messages to users through preferred media channels like Facebook and Google can be challenging, as only a portion of users in a behavior segment find match in a medium, and only a fraction of those matched actually see the message (exposure). Even high quality discovery becomes futile when delivery fails. Many sophisticated algorithms exist for discovering behavioral segments; however, these ignore the delivery component. The problem is compounded because (i) the discovery is performed on the behavior data space in firms' data (e.g., user clicks), while the delivery is predicated on the static data space (e.g., geo, age) as defined by media; and (ii) firms work under budget constraint. We introduce a stochastic optimization based algorithm for delivery optimized discovery of behavioral user segments and offer new metrics to address the joint optimization. We leverage optimization under a budget constraint for delivery combined with a learning-based component for discovery. Extensive experiments on a public dataset from Google and a proprietary dataset show the effectiveness of our approach by simultaneously improving delivery metrics, reducing budget spend and achieving strong predictive performance in discovery.

Online browsing on firms' sites generates user behavior logs (or, logs). These logs are mainstays that drive several user modeling tasks. The logs that inform user modeling are the ones that are attributed to each user, termed Attributed Behaviors (AB). But, a lot more logs are anonymous, upwards of 85%. For example, many users do not sign in while browsing. These logs are not attributed to users, termed Unattributed Behaviors (UB), and are not recognized in user modeling. We examine whether and how UB can benefit user modeling. We focus on a common task, that of user segmentation, for which the prior art uses only AB. We demonstrate that information from UBs, although unattributed to any individual, when used along with ABs, enriches performance of machine learning model for user segmentation. We perform predictive segmentation, whereby predicted outcomes for each segment are evaluated against actual outcomes. Multiple evaluations on two datasets, one of which is public, relative to state of the art baseline, show strong performance of our model in predicting outcomes and in reducing user segmentation error.

This article investigates the dynamics of competition among organizations with unequal expertise. Multiagent reinforcement learning (MARL) has been used to simulate and understand the impact of various incentive schemes designed to offset such inequality. We design Touch-Mark, a game based on well-known multiagent particle environment, where two teams (weak and strong) with unequal but changing skill levels compete against each other. For training such a game, we propose a novel controller-assisted MARL algorithm C-MADDPG, which empowers each agent with an ensemble of policies along with a supervised controller that by selectively partitioning the sample space and triggers intelligent role division among the teammates. Using C-MADDPG as an underlying framework, we propose an incentive scheme for the weak team such that the final rewards of both teams become the same. We find that despite the incentive, the final reward of the weak team falls short of the strong team. On inspecting, we realize that an overall incentive scheme for the weak team does not incentivize the weaker agents within that team to learn and improve. To offset this, we now specially incentivize the weaker player to learn and, as a result, observe that the weak team beyond an initial phase performs at par with the stronger team. The final goal of this article has been to formulate a dynamic incentive scheme that continuously balances the reward of the two teams. This is achieved by devising an incentive scheme enriched with an RL agent, which takes minimum information from the environment.

We study the problem of determining the best atomic intervention in a Causal Bayesian Network (CBN) specified only by its causal graph. We model this as a stochastic multi-armed bandit (MAB) problem with side-information, where interventions on CBN correspond to arms of the bandit instance. First, we propose a simple regret minimization algorithm that takes as input a causal graph with observable and unobservable nodes and in $T$ exploration rounds achieves $\tilde{O}(\sqrt{m(\mathcal{C})/T})$ expected simple regret. Here $m(\mathcal{C})$ is a parameter dependent on the input CBN $\mathcal{C}$ and could be much smaller than the number of arms. We also show that this is almost optimal for CBNs whose causal graphs have an $n$-ary tree structure. Next, we propose a cumulative regret minimization algorithm that takes as input a causal graph with observable nodes and performs better than the optimal MAB algorithms that do not use causal side-information. We experimentally compare both our algorithms with the best known algorithms in the literature.

We study broadcasting of information in a system of moving agents equipped with omnidirectional as well as directional antenna. The agent communication protocol is inspired by the classical SIRS epidemics dynamics. We assume that the antennas of all agents have a fixed transmitting power, while signal reception only occurs when the receivers sense signals with power exceeding a certain threshold. Thus, information exchange is a local phenomenon which depends on the relative distance and antenna orientation between the transmitting and the receiving agent. We derive an expression for the mean broadcasting time and study the information dissemination robustness of the system using elements of classical epidemiology and physics. In particular, we show that the mean broadcasting time depends upon ¿ which quantifies the area the radiation pattern of the antenna sweeps as it moves. We report three important observations (a) directional antennas perform better than omnidirectional antennas, (b) directional antennas whose beam-width is narrower perform even better, and (c) the performance enhances a lot if directional antennas rotate. These behaviors can be understood in the light of the reported analytical findings.