Research

Abstract: When treatments are assigned over time, updating assignment rules using past observations can improve welfare. However, finding an optimal way to update these rules requires accounting for how current assignments affect future observations and decisions, making the problem numerically intractable as the number of individuals grows. We consider a simpler optimization problem based on weak-signal asymptotics and show that its solution is asymptotically optimal. We then propose a new limiting problem robust to an unknown reward component shared across treatments.

We study dynamic pricing to maximize social welfare, defined as a weighted sum of public revenue and consumer surplus. We propose a policy based on information-directed sampling that starts with a prior over demand and adjusts prices based on observed purchase decisions. We establish a bound on the Bayesian regret that matches the known lower bound up to logarithmic factors

We consider the problem of estimating optimal transport maps, which are used in multivariate quantile analysis and nonlinear independent component analysis. These maps can be represented as gradients of convex functions, but approximating these functions on grids becomes computationally demanding in higher dimensions. We propose a projected gradient descent algorithm for estimating these potentials under shape restrictions without discretizing the space, and provide a convergence analysis.

We employ generic machine learning techniques to discover associations between features of the data generating process (e.g. its moments) and features of a given statistic’s sampling distribution (e.g. its quantiles). Formal asymptotic theory considerations underly the selection of suitable feature vectors. The current focus is on addressing the well-known failure of conventional bootstrap methods in parameter-at-the-boundary settings. We develop careful numerical benchmarks documenting the advantages of the proposed method.