Related papers: Optimal Decision Rules when Payoffs are Partially …
Optimization under uncertainty deals with the problem of optimizing stochastic cost functions given some partial information on their inputs. These problems are extremely difficult to solve and yet pervade all areas of technological and…
Models of many real-life applications, such as queuing models of communication networks or computing systems, have a countably infinite state-space. Algorithmic and learning procedures that have been developed to produce optimal policies…
In many areas, practitioners seek to use observational data to learn a treatment assignment policy that satisfies application-specific constraints, such as budget, fairness, simplicity, or other functional form constraints. For example,…
We address an optimal stopping problem over the set of Bermudan-type strategies $\Theta$ (which we understand in a more general sense than the stopping strategies for Bermudan options in finance) and with non-linear operators (non-linear…
The problem of pricing Bermudan options using Monte Carlo and a nonparametric regression is considered. We derive optimal non-asymptotic bounds for a lower biased estimate based on the suboptimal stopping rule constructed using some…
The problems of optimally estimating a phase, a direction, and the orientation of a Cartesian frame (or trihedron) with general pure states are addressed. Special emphasis is put on estimation schemes that allow for inconclusive answers or…
This paper develops a model of \textit{identification design} and applies it to robust causal inference in microeconometrics. The decision maker observes the population distribution of signals generated by an information structure and ranks…
In this paper, we develop a unified approach to study partial identification of a finite-dimensional parameter defined by a general moment model with incomplete data. We establish a novel characterization of the identified set for the true…
Model selection criteria are one of the most important tools in statistics. Proofs showing a model selection criterion is asymptotically optimal are tailored to the type of model (linear regression, quantile regression, penalized…
Biased stochastic estimators, such as finite-differences for noisy gradient estimation, often contain parameters that need to be properly chosen to balance impacts from the bias and the variance. While the optimal order of these parameters…
We examine a stochastic formulation for data-driven optimization wherein the decision-maker is not privy to the true distribution, but has knowledge that it lies in some hypothesis set and possesses a historical data set, from which…
This paper presents a general asymptotic theory of sequential Bayesian estimation giving results for the strongest, almost sure convergence. We show that under certain smoothness conditions on the probability model, the greedy information…
We consider the development of adaptive, instance-dependent algorithms for interactive decision making (bandits, reinforcement learning, and beyond) that, rather than only performing well in the worst case, adapt to favorable properties of…
A challenging category of robotics problems arises when sensing incurs substantial costs. This paper examines settings in which a robot wishes to limit its observations of state, for instance, motivated by specific considerations of energy…
We consider the design of systems for sequential decentralized detection, a problem that entails several interdependent choices: the choice of a stopping rule (specifying the sample size), a global decision function (a choice between two…
Point identification of causal effects requires strong assumptions that are unreasonable in many practical settings. However, informative bounds on these effects can often be derived under plausible assumptions. Even when these bounds are…
We consider a simulation optimization problem for a context-dependent decision-making, which aims to determine the top-m designs for all contexts. Under a Bayesian framework, we formulate the optimal dynamic sampling decision as a…
Big data is ubiquitous in practices, and it has also led to heavy computation burden. To reduce the calculation cost and ensure the effectiveness of parameter estimators, an optimal subset sampling method is proposed to estimate the…
A new method of deriving comparative statics information using generalized compensated derivatives is presented which yields constraint-free semidefiniteness results for any differentiable, constrained optimization problem. More generally,…
We study the subtlety of optimal paternalism when a utilitarian planner has the power to design a discrete choice set for a heterogeneous population with bounded rationality. We first consider the planning problem in abstraction. We show…