Related papers: On the iterated estimation of dynamic discrete cho…
We consider approximate dynamic programming for the infinite-horizon stationary $\gamma$-discounted optimal control problem formalized by Markov Decision Processes. While in the exact case it is known that there always exists an optimal…
In policy learning, the goal is typically to optimize a primary performance metric, but other subsidiary metrics often also warrant attention. This paper presents two strategies for evaluating these subsidiary metrics under a policy that is…
The paper deals with asymptotic properties of the adaptive procedure proposed in the author paper, 2007, for estimating a unknown nonparametric regression. We prove that this procedure is asymptotically efficient for a quadratic risk, i.e.…
For the model of constrained multi-armed bandit, we show that by construction there exists an index-based deterministic asymptotically optimal algorithm. The optimality is achieved by the convergence of the probability of choosing an…
We study and compare three estimators of a discrete monotone distribution: (a) the (raw) empirical estimator; (b) the "method of rearrangements" estimator; and (c) the maximum likelihood estimator. We show that the maximum likelihood…
Linear thresholding models postulate that the conditional distribution of a response variable in terms of covariates differs on the two sides of a (typically unknown) hyperplane in the covariate space. A key goal in such models is to learn…
This paper proposes an agent-based optimistic policy iteration (OPI) scheme for learning stationary optimal stochastic policies in multi-agent Markov Decision Processes (MDPs), in which agents incur a Kullback-Leibler (KL) divergence cost…
We study some of the most commonly used mutual information estimators, based on histograms of fixed or adaptive bin size, $k$-nearest neighbors and kernels, and focus on optimal selection of their free parameters. We examine the consistency…
We study periodic review stochastic inventory control in the data-driven setting where the retailer makes ordering decisions based only on historical demand observations without any knowledge of the probability distribution of the demand.…
The maximum likelihood estimator (MLE) is pivotal in statistical inference, yet its application is often hindered by the absence of closed-form solutions for many models. This poses challenges in real-time computation scenarios,…
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…
This paper considers the theoretical, computational, and econometric properties of continuous time dynamic discrete choice games with stochastically sequential moves, introduced by Arcidiacono, Bayer, Blevins, and Ellickson (2016). We…
The goal of this paper is to investigate new and simple convergence analysis of dynamic programming for linear quadratic regulator problem of discrete-time linear time-invariant systems. In particular, bounds on errors are given in terms of…
We suggest an iterative approach to computing K-step maximum likelihood estimates (MLE) of the parametric components in semiparametric models based on their profile likelihoods. The higher order convergence rate of K-step MLE mainly depends…
The likelihood functions for discretely observed nonlinear continuous-time models based on stochastic differential equations are not available except for a few cases. Various parameter estimation techniques have been proposed, each with…
This work is concerned with the estimation of multidimensional regression and the asymptotic behaviour of the test involved in selecting models. The main problem with such models is that we need to know the covariance matrix of the noise to…
Optimum designs for parameter estimation in generalized regression models are standardly based on the Fisher information matrix (cf. Atkinson et al (2014) for a recent exposition). The corresponding optimality criteria are related to the…
Machine learning methods, particularly the double machine learning (DML) estimator (Chernozhukov et al., 2018), are increasingly popular for the estimation of the average treatment effect (ATE). However, datasets often exhibit unbalanced…
We propose a new simple and natural algorithm for learning the optimal Q-value function of a discounted-cost Markov Decision Process (MDP) when the transition kernels are unknown. Unlike the classical learning algorithms for MDPs, such as…
Maximum Likelihood Estimators (MLE) has many good properties. For example, the asymptotic variance of MLE solution attains equality of the asymptotic Cram{\'e}r-Rao lower bound (efficiency bound), which is the minimum possible variance for…