Related papers: Deterministic Finite-Memory Bias Estimation

We prove a general existence result in stochastic optimal control in discrete time where controls take values in conditional metric spaces, and depend on the current state and the information of past decisions through the evolution of a…

When a parameter of interest is nondifferentiable in the probability, the existing theory of semiparametric efficient estimation is not applicable, as it does not have an influence function. Song (2014) recently developed a local asymptotic…

This paper investigates the optimization problem of an infinite stage discrete time Markov decision process (MDP) with a long-run average metric considering both mean and variance of rewards together. Such performance metric is important…

We consider the classical sequential binary hypothesis testing problem in which there are two hypotheses governed respectively by distributions $P_0$ and $P_1$ and we would like to decide which hypothesis is true using a sequential test. It…

In the target tracking and its engineering applications, recursive state estimation of the target is of fundamental importance. This paper presents a recursive performance bound for dynamic estimation and filtering problem, in the framework…

In the regression model with errors in variables, we observe $n$ i.i.d. copies of $(Y,Z)$ satisfying $Y=f_{\theta^0}(X)+\xi$ and $Z=X+\epsilon$ involving independent and unobserved random variables $X,\xi,\epsilon$ plus a regression…

Although Q-learning is one of the most successful algorithms for finding the best action-value function (and thus the optimal policy) in reinforcement learning, its implementation often suffers from large overestimation of Q-function values…

Variational methods for parameter estimation are an active research area, potentially offering computationally tractable heuristics with theoretical performance bounds. We build on recent work that applies such methods to network data, and…

Probabilistic automata are an extension of nondeterministic finite automata in which transitions are annotated with probabilities. Despite its simplicity, this model is very expressive and many of the associated algorithmic questions are…

We study stochastic approximation algorithms with Markovian noise and constant step-size $\alpha$. We develop a method based on infinitesimal generator comparisons to study the bias of the algorithm, which is the expected difference between…

We present an algorithm for the statistical learning setting with a bounded exp-concave loss in $d$ dimensions that obtains excess risk $O(d \log(1/\delta)/n)$ with probability at least $1 - \delta$. The core technique is to boost the…

This paper considers an empirical risk minimization problem under heavy-tailed settings, where data does not have finite variance, but only has $p$-th moment with $p \in (1,2)$. Instead of using estimation procedure based on truncated…

Consider the extreme value of a Bernoulli random walk on the one-dimensional integer lattice, with reflection at 0, over a finite discrete time interval. Only the asymmetric (biased) case is discussed. Asymptotic mean/variance results are…

An algorithm is presented that, taking a sequence of independent Bernoulli random variables with parameter $1/2$ as inputs and using only rational arithmetic, simulates a Bernoulli random variable with possibly irrational parameter $\tau$.…

We consider a class of systems with time-varying parameters, which are written as linear regressions with bounded disturbances. The task is to estimate such parameters under the condition that the regressor is finitely exciting (FE).…

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…

Sequential tests and their implied confidence sequences, which are valid at arbitrary stopping times, promise flexible statistical inference and on-the-fly decision making. However, strong guarantees are limited to parametric sequential…

In the random coefficients binary choice model, a binary variable equals 1 iff an index $X^\top\beta$ is positive.The vectors $X$ and $\beta$ are independent and belong to the sphere $\mathbb{S}^{d-1}$ in $\mathbb{R}^{d}$.We prove lower…

Doubly robust estimators have gained widespread popularity in various fields due to their ability to provide unbiased estimates under model misspecification. However, the asymptotic theory for doubly robust estimators with continuous-time…

We revisit the study of optimal regret rates in bandit combinatorial optimization---a fundamental framework for sequential decision making under uncertainty that abstracts numerous combinatorial prediction problems. We prove that the…