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We consider the off-policy estimation problem of estimating the expected reward of a target policy using samples collected by a different behavior policy. Importance sampling (IS) has been a key technique to derive (nearly) unbiased…

Machine Learning · Computer Science 2018-10-31 Qiang Liu , Lihong Li , Ziyang Tang , Dengyong Zhou

Evaluating a policy by deploying it in the real world can be risky and costly. Off-policy policy evaluation (OPE) algorithms use historical data collected from running a previous policy to evaluate a new policy, which provides a means for…

Artificial Intelligence · Computer Science 2017-12-07 Zhaohan Daniel Guo , Philip S. Thomas , Emma Brunskill

Motivated by the many real-world applications of reinforcement learning (RL) that require safe-policy iterations, we consider the problem of off-policy evaluation (OPE) -- the problem of evaluating a new policy using the historical data…

Machine Learning · Computer Science 2020-04-02 Tengyang Xie , Yifei Ma , Yu-Xiang Wang

A central challenge to applying many off-policy reinforcement learning algorithms to real world problems is the variance introduced by importance sampling. In off-policy learning, the agent learns about a different policy than the one being…

Machine Learning · Computer Science 2022-06-20 Eric Graves , Sina Ghiassian

Importance sampling (IS) is a widely used simulation method for estimating rare event probabilities. In IS, the relative variance of an estimator is the most common measure of estimator accuracy, and the focus of existing literature is on…

Statistics Theory · Mathematics 2026-01-05 Julie Choi , Peter Glynn

In many domains, the exploration process of reinforcement learning will be too costly as it requires trying out suboptimal policies, resulting in a need for off-policy evaluation, in which a target policy is evaluated based on data…

Machine Learning · Computer Science 2024-05-07 David M. Bossens , Philip S. Thomas

Importance sampling (IS) represents a fundamental technique for a large surge of off-policy reinforcement learning approaches. Policy gradient (PG) methods, in particular, significantly benefit from IS, enabling the effective reuse of…

Machine Learning · Computer Science 2024-05-10 Matteo Papini , Giorgio Manganini , Alberto Maria Metelli , Marcello Restelli

Importance sampling (IS) is an important technique to reduce the estimation variance in Monte Carlo simulations. In many practical problems, however, the use of IS method may result in unbounded variance, and thus fail to provide reliable…

Computation · Statistics 2019-02-26 Tengchao Yu , Linjun Lu , Jinglai Li

We consider the problem of off-policy evaluation in Markov decision processes. Off-policy evaluation is the task of evaluating the expected return of one policy with data generated by a different, behavior policy. Importance sampling is a…

Machine Learning · Computer Science 2019-05-13 Josiah P. Hanna , Scott Niekum , Peter Stone

Importance sampling is a popular variance reduction method for Monte Carlo estimation, where a notorious question is how to design good proposal distributions. While in most cases optimal (zero-variance) estimators are theoretically…

Statistics Theory · Mathematics 2021-02-22 Carsten Hartmann , Lorenz Richter

Off-policy learning exhibits greater instability when compared to on-policy learning in reinforcement learning (RL). The difference in probability distribution between the target policy ($\pi$) and the behavior policy (b) is a major cause…

Importance sampling (IS) is a common reweighting strategy for off-policy prediction in reinforcement learning. While it is consistent and unbiased, it can result in high variance updates to the weights for the value function. In this work,…

Machine Learning · Computer Science 2019-11-15 Matthew Schlegel , Wesley Chung , Daniel Graves , Jian Qian , Martha White

Importance sampling (IS) is a technique that enables statistical estimation of output performance at multiple input distributions from a single nominal input distribution. IS is commonly used in Monte Carlo simulation for variance reduction…

Methodology · Statistics 2025-05-07 Yijuan Liang , Guangxin Jiang , Michael C. Fu

Off-policy estimation for long-horizon problems is important in many real-life applications such as healthcare and robotics, where high-fidelity simulators may not be available and on-policy evaluation is expensive or impossible. Recently,…

Machine Learning · Computer Science 2020-03-26 Ali Mousavi , Lihong Li , Qiang Liu , Denny Zhou

Infinite horizon off-policy policy evaluation is a highly challenging task due to the excessively large variance of typical importance sampling (IS) estimators. Recently, Liu et al. (2018a) proposed an approach that significantly reduces…

Machine Learning · Computer Science 2019-10-17 Ziyang Tang , Yihao Feng , Lihong Li , Dengyong Zhou , Qiang Liu

This paper investigates asymptotically optimal importance sampling (IS) schemes for pricing European call options under the Heston stochastic volatility model. We focus on two distinct rare-event regimes where standard Monte Carlo methods…

Mathematical Finance · Quantitative Finance 2025-11-26 Yun-Feng Tu , Chuan-Hsiang Han

Many sequential decision making problems are high-stakes and require off-policy evaluation (OPE) of a new policy using historical data collected using some other policy. One of the most common OPE techniques that provides unbiased estimates…

Machine Learning · Computer Science 2021-12-06 Christina J. Yuan , Yash Chandak , Stephen Giguere , Philip S. Thomas , Scott Niekum

Importance sampling-based estimators for off-policy evaluation (OPE) are valued for their simplicity, unbiasedness, and reliance on relatively few assumptions. However, the variance of these estimators is often high, especially when…

Machine Learning · Computer Science 2021-09-15 Simon P. Shen , Yecheng Jason Ma , Omer Gottesman , Finale Doshi-Velez

We consider the problem of off-policy evaluation for reinforcement learning, where the goal is to estimate the expected reward of a target policy $\pi$ using offline data collected by running a logging policy $\mu$. Standard…

Machine Learning · Computer Science 2020-07-09 Ming Yin , Yu-Xiang Wang

Importance Sampling (IS) is a widely used variance reduction technique for enhancing the efficiency of Monte Carlo methods, particularly in rare-event simulation and related applications. Despite its effectiveness, the performance of IS is…

Optimization and Control · Mathematics 2026-02-11 Liviu Aolaritei , Bart P. G. Van Parys , Henry Lam , Michael I. Jordan
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