Related papers: Non-asymptotic confidence bounds for the optimal v…
We study nonasymptotic (finite-sample) confidence intervals for treatment effects in randomized experiments. In the existing literature, the effective sample sizes of nonasymptotic confidence intervals tend to be looser than the…
In this paper, we propose and analyze a trust-region model-based algorithm for solving unconstrained stochastic optimization problems. Our framework utilizes random models of an objective function $f(x)$, obtained from stochastic…
Stochastic optimization has found wide applications in minimizing objective functions in machine learning, which motivates a lot of theoretical studies to understand its practical success. Most of existing studies focus on the convergence…
In this paper, we study the portfolio optimization problem with general utility functions and when the return and volatility of underlying asset are slowly varying. An asymptotic optimal strategy is provided within a specific class of…
We consider the problem of estimating confidence intervals for the mean of a random variable, where the goal is to produce the smallest possible interval for a given number of samples. While minimax optimal algorithms are known for this…
Convex sample approximations of chance-constrained optimization problems are considered, in which chance constraints are replaced by sets of sampled constraints. We propose a randomized sample selection strategy that allows tight bounds to…
We study a statistical method to estimate the optimal value, and the optimality gap of a given solution for stochastic optimization as an assessment of the solution quality. Our approach is based on bootstrap aggregating, or bagging,…
Sharp asymptotic lower bounds of the expected quadratic variation of discretization error in stochastic integration are given. The theory relies on inequalities for the kurtosis and skewness of a general random variable which are themselves…
We consider selecting the top-$m$ alternatives from a finite number of alternatives via Monte Carlo simulation. Under a Bayesian framework, we formulate the sampling decision as a stochastic dynamic programming problem, and develop a…
In this paper, we compute finite sample bounds for data-driven approximations of the solution to stochastic reachability problems. Our approach uses a nonparametric technique known as kernel distribution embeddings, and provides…
We consider the problem of estimating the expected value of information (the knowledge gradient) for Bayesian learning problems where the belief model is nonlinear in the parameters. Our goal is to maximize some metric, while simultaneously…
We investigate a data-driven approach to constructing uncertainty sets for robust optimization problems, where the uncertain problem parameters are modeled as random variables whose joint probability distribution is not known. Relying only…
We consider maximization of stochastic monotone continuous submodular functions (CSF) with a diminishing return property. Existing algorithms only guarantee the performance \textit{in expectation}, and do not bound the probability of…
We propose a general method for constructing confidence intervals and statistical tests for single or low-dimensional components of a large parameter vector in a high-dimensional model. It can be easily adjusted for multiplicity taking…
We analyze a simple randomized subgradient method for approximating solutions to stochastic systems of convex functional constraints, the only input to the algorithm being the size of minibatches. By introducing a new notion of what is…
Using the techniques of [arXiv:0911.4271], upper bounds for a given confidence level are modified in an optimal fashion to incorporate the a priori information that the parameter being estimated is non-negative. A paradox with different…
One of the most commonly used methods for forming confidence intervals for statistical inference is the empirical bootstrap, which is especially expedient when the limiting distribution of the estimator is unknown. However, despite its…
In optimization problems, the quality of a candidate solution can be characterized by the optimality gap. For most stochastic optimization problems, this gap must be statistically estimated. We show that for risk-averse problems, standard…
An algorithm is proposed for solving stochastic and finite sum minimization problems. Based on a trust region methodology, the algorithm employs normalized steps, at least as long as the norms of the stochastic gradient estimates are within…
We propose a robust optimization approach for constructing confidence bands for stochastic processes using a finite number of simulated sample paths. Our approach can be used to quantify uncertainty in realizations of stochastic processes…