While many works have studied statistical data fusion, they typically assume that the various datasets are given in advance. However, in practice, estimation requires difficult data collection decisions like determining the available data sources, their costs, and how many samples to collect from each source. Moreover, this process is often sequential because the data collected at a given time can improve collection decisions in the future. In our setup, given access to multiple data sources and budget constraints, the agent must sequentially decide which data source to query to efficiently estimate a target parameter. We formalize this task using Online Moment Selection, a semiparametric framework that applies to any parameter identified by a set of moment conditions. Interestingly, the optimal budget allocation depends on the (unknown) true parameters. We present two online data collection policies, Explore-then-Commit and Explore-then-Greedy, that use the parameter estimates at a given time to optimally allocate the remaining budget in the future steps. We prove that both policies achieve zero regret (assessed by asymptotic MSE) relative to an oracle policy. We empirically validate our methods on both synthetic and real-world causal effect estimation tasks, demonstrating that the online data collection policies outperform their fixed counterparts.

Supply chain management (SCM) has been recognized as an important discipline with applications to many industries, where the two-echelon stochastic inventory model, involving one downstream retailer and one upstream supplier, plays a fundamental role for developing firms' SCM strategies. In this work, we aim at designing online learning algorithms for this problem with an unknown demand distribution, which brings distinct features as compared to classic online optimization problems. Specifically, we consider the two-echelon supply chain model introduced in [Cachon and Zipkin, 1999] under two different settings: the centralized setting, where a planner decides both agents' strategy simultaneously, and the decentralized setting, where two agents decide their strategy independently and selfishly. We design algorithms that achieve favorable guarantees for both regret and convergence to the optimal inventory decision in both settings, and additionally for individual regret in the decentralized setting. Our algorithms are based on Online Gradient Descent and Online Newton Step, together with several new ingredients specifically designed for our problem. We also implement our algorithms and show their empirical effectiveness.

Non-deterministic measurements are common in real-world scenarios: the performance of a stochastic optimization algorithm or the total reward of a reinforcement learning agent in a chaotic environment are just two examples in which unpredictable outcomes are common. These measures can be modeled as random variables and compared among each other via their expected values or more sophisticated tools such as null hypothesis statistical tests. In this paper, we propose an alternative framework to visually compare two samples according to their estimated cumulative distribution functions. First, we introduce a dominance measure for two random variables that quantifies the proportion in which the cumulative distribution function of one of the random variables stochastically dominates the other one. Then, we present a graphical method that decomposes in quantiles i) the proposed dominance measure and ii) the probability that one of the random variables takes lower values than the other. With illustrative purposes, we re-evaluate the experimentation of an already published work with the proposed methodology and we show that additional conclusions (missed by the rest of the methods) can be inferred. Additionally, the software package RVCompare was created as a convenient way of applying and experimenting with the proposed framework.

We have earlier shown that the standard mappings from action languages B and C to logic programs under answer set semantics can be captured by sets of properties on transition systems. In this paper, we consider action language BC and show that a standard mapping from BC action descriptions to logic programs can be similarly captured when the action rules in the descriptions do not have consistency conditions.

The causal inference literature has provided a clear formal definition of confounding expressed in terms of counterfactual independence. The literature has not, however, come to any consensus on a formal definition of a confounder, as it has given priority to the concept of confounding over that of a confounder. We consider a number of candidate definitions arising from various more informal statements made in the literature. We consider the properties satisfied by each candidate definition, principally focusing on (i) whether under the candidate definition control for all "confounders" suffices to control for "confounding" and (ii) whether each confounder in some context helps eliminate or reduce confounding bias. Several of the candidate definitions do not have these two properties. Only one candidate definition of those considered satisfies both properties. We propose that a "confounder" be defined as a pre-exposure covariate C for which there exists a set of other covariates X such that effect of the exposure on the outcome is unconfounded conditional on (X,C) but such that for no proper subset of (X,C) is the effect of the exposure on the outcome unconfounded given the subset. We also provide a conditional analogue of the above definition; and we propose a variable that helps reduce bias but not eliminate bias be referred to as a "surrogate confounder." These definitions are closely related to those given by Robins and Morgenstern [Comput. Math. Appl. 14 (1987) 869-916]. The implications that hold among the various candidate definitions are discussed.

We introduce a framework so that communities can exchange reputation information about agents in environments where agents are migrating between communities. We view the acquisition of the reputation information as a purchase and focus on the design of a payment function to facilitate the payment for information in a way that motivates communities to truthfully report reputation information for agents. We prove that in our proposed framework, honesty is the optimal policy and demonstrate the value of using a payment-function approach for the exchange of reputation information about agents between communities in multiagent environments. Using our payment function, each community is strengthened: it is able to reason more effectively about which agents to accept and can enjoy agents that are motivated to contribute strongly to the benefit of the community.