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Data acquisition efficiency is a central challenge in deploying reinforcement learning in business and healthcare operations, where interactions are costly, slow, and often involve humans in the loop. This paper develops a unified large…

We study the recovery of functions in various norms, including $L_p$ with $1\le p\le\infty$, based on function evaluations. We obtain worst case error bounds for general classes of functions in terms of the best $L_2$-approximation from a…

Inverse Reinforcement Learning (IRL) techniques deal with the problem of deducing a reward function that explains the behavior of an expert agent who is assumed to act optimally in an underlying unknown task. In several problems of…

The exponential growth of volume, variety and velocity of data is raising the need for investigations of automated or semi-automated ways to extract useful patterns from the data. It requires deep expert knowledge and extensive…

This paper studies the statistical theory of batch data reinforcement learning with function approximation. Consider the off-policy evaluation problem, which is to estimate the cumulative value of a new target policy from logged history…

This paper examines issues of data completion and location uncertainty, popular in many practical PDE-based inverse problems, in the context of option calibration via recovery of local volatility surfaces. While real data is usually more…

Policy learning can be used to extract individualized treatment regimes from observational data in healthcare, civics, e-commerce, and beyond. One big hurdle to policy learning is a commonplace lack of overlap in the data for different…

In this paper we present an algorithm to fit data via exponentials when the error is measured using the max-norm. We prove the necesssary results to show that the algorithm will converge to the best approximation no matter the dataset.

Inconsistent values are commonly encountered in real-world applications, which can negatively impact data analysis and decision-making. While existing research primarily focuses on identifying the smallest removal set to resolve…

Predicting which action (treatment) will lead to a better outcome is a central task in decision support systems. To build a prediction model in real situations, learning from biased observational data is a critical issue due to the lack of…

Algorithm designers typically assume that the input data is correct, and then proceed to find "optimal" or "sub-optimal" solutions using this input data. However this assumption of correct data does not always hold in practice, especially…

Imaging problems such as the one in nanoCT require the solution of an inverse problem, where it is often taken for granted that the forward operator, i.e., the underlying physical model, is properly known. In the present work we address the…

Mathematical optimization is widely used in various research fields. With a carefully-designed objective function, mathematical optimization can be quite helpful in solving many problems. However, objective functions are usually…

Absolute value linear programming problems is quite a new area of optimization problems, involving linear functions and absolute values in the description of the model. In this paper, we consider interval uncertainty of the input…

Neural networks have achieved remarkable success in many cognitive tasks. However, when they are trained sequentially on multiple tasks without access to old data, their performance on early tasks tend to drop significantly. This problem is…

We consider the problem of deriving from experimental data an approximation of an unknown function, whose derivatives also approximate the unknown function derivatives. Solving this problem is useful, for instance, in the context of…

In this paper we consider two recovery problems based on information given with an error. First is the problem of optimal recovery of the class $W^T_q = \{(t_1h_1,t_2h_2,\ldots)\in \ell_q\,:\,\|h\|_q\leqslant 1\}$, where $1\le q < \infty$…

Data in the real world frequently involve binary status: truth or falsehood, positiveness or negativeness, similarity or dissimilarity, spam or non-spam, and to name a few, with applications into the regression, classification problems and…

The goal of inverse reinforcement learning (IRL) is to infer a reward function that explains the behavior of an agent performing a task. The assumption that most approaches make is that the demonstrated behavior is near-optimal. In many…

Many real-world applications require machine-learning models to be able to deal with non-stationary data distributions and thus learn autonomously over an extended period of time, often in an online setting. One of the main challenges in…