Original: DOPE: A B ENCHMARK FOR D EEP O FF -P OLICY E VALUATION
Revised: B ENCHMARKS FOR D EEP O FF -P OLICY E VALUATION

Original: Anonymous authors
Revised: Anonymous authors

Original: Paper under double-blind review
Revised: Paper under double-blind review

Original: A BSTRACT
Revised: A BSTRACT

Original: Off-policy evaluation (OPE) holds the promise of being able to leverage large, ofﬂine datasets for both evaluating and selecting complex policies for decision making.
Revised: Off-policy evaluation (OPE) holds the promise of being able to leverage large, ofﬂine datasets for both evaluating and selecting complex policies for decision making.

Original: The ability to learn ofﬂine is particularly important in many real-world domains, such as in healthcare, recommender systems, or robotics, where online data collection is an expensive and potentially dangerous process.
Revised: The ability to learn ofﬂine is particularly important in many real-world domains, such as in healthcare, recommender systems, or robotics, where online data collection is an expensive and potentially dangerous process.

Original: Being able to accurately evaluate and select high-performing policies without requiring online interaction could yield signiﬁcant beneﬁts in safety, time, and cost for these applications.
Revised: Being able to accurately evaluate and select high-performing policies without requiring online interaction could yield signiﬁcant beneﬁts in safety, time, and cost for these applications.

Original: While many OPE methods have been proposed in recent years, comparing results between works is difﬁcult because currently there is a lack of a comprehensive and uniﬁed benchmark, and measuring algorithmic progress has been challenging due to the lack of difﬁcult evaluation tasks.
Revised: While many OPE methods have been proposed in recent years, comparing results between papers is difﬁcult because currently there is a lack of a comprehensive and uniﬁed benchmark, and measuring algorithmic progress has been challenging due to the lack of difﬁcult evaluation tasks.

Original: In order to address this gap, we propose a new benchmark for  off-policy evaluation which includes tasks on a range of challenging, high-dimensional  control problems, with wide selections of datasets and policies for performing policy selection.
Revised: In order to address this gap, we present a collection of policies that in conjunction with existing ofﬂine datasets can be used for benchmarking off-policy evaluation. Our tasks include a range of challenging high-dimensional continuous control problems, with wide selections of datasets and policies for performing policy selection.

Original: The goal of our benchmark is to provide a standardized measure of progress that is motivated from a set of principles designed to challenge and test the limits of existing OPE methods.
Revised: The goal of our benchmark is to provide a standardized measure of progress that is motivated from a set of principles designed to challenge and test the limits of existing OPE methods.

Original: We perform an evaluation of state-of-the-art algorithms, and we provide open-source access to all data and code to foster future research in this area.
Revised: We perform an evaluation of state-of-the-art algorithms, and we provide open-source access to all data and code to foster future research in this area.

Original:  I NTRODUCTION
Revised:  I NTRODUCTION

Original: Reinforcement learning algorithms can acquire effective policies for a wide range of problems through active online interaction, such as in robotics (Kober et al., 2013), board games and video games (Tesauro, 1995;
Revised: Reinforcement learning algorithms can acquire effective policies for a wide range of problems through active online interaction, such as in robotics (Kober et al., 2013), board games and video games (Tesauro, 1995;

Original: Mnih et al., 2013; Vinyals et al., 2019), and recommender systems (Aggarwal et al., 2016).
Revised: Mnih et al., 2013; Vinyals et al., 2019), and recommender systems (Aggarwal et al., 2016).

Original: However, this sort of active online interaction is often impractical for real-world problems, where active data collection can be costly (Li et al., 2010), dangerous (Hauskrecht & Fraser, 2000; Kendall et al., 2019), or time consuming (Gu et al., 2017).
Revised: However, this sort of active online interaction is often impractical for real-world problems, where active data collection can be costly (Li et al., 2010), dangerous (Hauskrecht & Fraser, 2000; Kendall et al., 2019), or time consuming (Gu et al., 2017).

Original: Batch (or ofﬂine) reinforcement learning, has been studied extensively in domains such as healthcare (Thapa et al., 2005; Raghu et al., 2018), recommender systems (Dudík et al., 2014;
Revised: Batch (or ofﬂine) reinforcement learning, has been studied extensively in domains such as healthcare (Thapa et al., 2005; Raghu et al., 2018), recommender systems (Dudík et al., 2014;

Original: Theocharous et al., 2015; Swaminathan et al., 2017), education (Mandel et al., 2014), and robotics (Kalashnikov et al., 2018).
Revised: Theocharous et al., 2015; Swaminathan et al., 2017), education (Mandel et al., 2014), and robotics (Kalashnikov et al., 2018).

Original: A major challenge with such methods is the off-policy evaluation (OPE) problem, where one must evaluate the expected performance of policies solely from ofﬂine data.
Revised: A major challenge with such methods is the off-policy evaluation (OPE) problem, where one must evaluate the expected performance of policies solely from ofﬂine data.

Original: This is critical for several reasons, including providing high-conﬁdence guarantees prior to deployment (Thomas et al., 2015), and performing policy improvement and model selection (Bottou et al., 2013; Doroudi et al., 2017).
Revised: This is critical for several reasons, including providing high-conﬁdence guarantees prior to deployment (Thomas et al., 2015), and performing policy improvement and model selection (Bottou et al., 2013; Doroudi et al., 2017).

Original: The goal of this paper is to provide a standardized benchmark for evaluating OPE methods.
Revised: The goal of this paper is to provide a standardized benchmark for evaluating OPE methods.

Original: Although considerable theoretical (Thomas & Brunskill, 2016; Swaminathan & Joachims, 2015; Jiang & Li, 2015; Wang et al., 2017; Yang et al., 2020) and practical progress (Gilotte et al., 2018; Nie et al., 2019; Kalashnikov et al., 2018) on OPE algorithms has been made in a range of different domains, there are few broadly accepted evaluation tasks that combine complex, high-dimensional problems commonly explored by modern deep reinforcement learning algorithms (Bellemare et al., 2013;
Revised: Although considerable theoretical (Thomas & Brunskill, 2016; Swaminathan & Joachims, 2015; Jiang & Li, 2015; Wang et al., 2017; Yang et al., 2020) and practical progress (Gilotte et al., 2018; Nie et al., 2019; Kalashnikov et al., 2018) on OPE algorithms has been made in a range of different domains, there are few broadly accepted evaluation tasks that combine complex, high-dimensional problems commonly explored by modern deep reinforcement learning algorithms (Bellemare et al., 2013;

Original: Brockman et al., 2016) with standardized evaluation protocols and metrics.
Revised: Brockman et al., 2016) with standardized evaluation protocols and metrics.

Original: Our goal is to provide a set of tasks with a range of difﬁculty, excercise a variety of design properties, and provide policies with different behavioral patterns in order to establish a standardized framework for comparing OPE algorithms.
Revised: Our goal is to provide a set of tasks with a range of difﬁculty, excercise a variety of design properties, and provide policies with different behavioral patterns in order to establish a standardized framework for comparing OPE algorithms.

Original: We put particular emphasis on large datasets, long-horizon tasks, and task complexity to facilitate the development of scalable algorithms that can solve high-dimensional problems.
Revised: We put particular emphasis on large datasets, long-horizon tasks, and task complexity to facilitate the development of scalable algorithms that can solve high-dimensional problems.

Original: Our primary contribution is the D eep
Revised: Our primary contribution is the D eep

Original: O ff-
Revised: O ff-

Original: P olicy E valuation (DOPE) benchmark.
Revised: P olicy E valuation (DOPE) benchmark.

Original: DOPE is designed to measure the performance of OPE methods by 1) evaluating on challenging control tasks with properties known to be difﬁcult for OPE methods, but which occur in real-world scenarios, 2) evaluating across a range of policies with different values, to directly measure performance on policy evaluation, ranking and selection, and 3) evaluating in ideal and adversarial settings in terms of dataset coverage and support.
Revised: DOPE is designed to measure the performance of OPE methods by 1) evaluating on challenging control tasks with properties known to be difﬁcult for OPE methods, but which occur in real-world scenarios, 2) evaluating across a range of policies with different values, to directly measure performance on policy evaluation, ranking and selection, and 3) evaluating in ideal and adversarial settings in terms of dataset coverage and support.

Original: These factors are independent of task difﬁculty, but are known to have a large impact on OPE performance.
Revised: These factors are independent of task difﬁculty, but are known to have a large impact on OPE performance.

Original: To achieve 1, we selected tasks on a set of design principles outlined in
Revised: To achieve 1, we selected tasks on a set of design principles outlined in

Original: Section 3.1.
Revised: Section 3.1.

Original: To achieve 2, for each task we include 10 to 96 policies for evaluation and devise an evaluation protocol that measures policy evaluation, ranking, and selection as outlined in Section 3.2, and to achieve 3, we provide two domains with differing dataset coverage and support properties described in Section 4.
Revised: To achieve 2, for each task we include 10 to 96 policies for evaluation and devise an evaluation protocol that measures policy evaluation, ranking, and selection as outlined in Section 3.2, and to achieve 3, we provide two domains with differing dataset coverage and support properties described in Section 4.

Original: Finally, to build an easy-to-use research platform, we provide a uniﬁed API training and evaluation API across all tasks, as well as a performance evaluation for state-of-the-art algorithms in Section 5.
Revised: Finally, to build an easy-to-use research platform, we provide a uniﬁed API training and evaluation API across all tasks, as well as a performance evaluation for state-of-the-art algorithms in Section 5.

Original: Our code for loading all datasets, tasks, and policies presented in this paper are included in the supplementary material.
Revised: Our code for loading all datasets, tasks, and policies presented in this paper are included in the supplementary material.

Original:  B ACKGROUND
Revised:  B ACKGROUND

Original: the goal is to estimate the value of a single policy given only data.
Revised: the goal is to estimate the value of a single policy given only data.

Original: Ofﬂine Policy
Revised: Ofﬂine Policy

Original: Selection (bottom) is a closely related problem: given a set of N policies, attempt to pick the best given only data.
Revised: Selection (bottom) is a closely related problem: given a set of N policies, attempt to pick the best given only data.

Original: We consider Markov decision processes (MDPs), deﬁned by a tuple ( S , A , T , R, ρ 0 , γ ) , with state space S , action space A , transition distribution T ( s (cid:48) | s, a ) , initial state distribution ρ 0 ( s ) , reward function R ( s, a ) and discount factor γ ∈ (0 , 1] .
Revised: We consider Markov decision processes (MDPs), deﬁned by a tuple ( S , A , T , R, ρ 0 , γ ) , with state space S , action space A , transition distribution T ( s (cid:48) | s, a ) , initial state distribution ρ 0 ( s ) , reward function R ( s, a ) and discount factor γ ∈ (0 , 1] .

Original: In reinforcement learning, we are typically concerned with optimizing or estimating the performance of a policy π ( a | s ) .
Revised: In reinforcement learning, we are typically concerned with optimizing or estimating the performance of a policy π ( a | s ) .

Original: The performance of a policy is commonly measured by the  valuefunction V π , deﬁned as the expected sum of discounted rewards:
Revised: The performance of a policy is commonly measured by the policy value V π , deﬁned as the expected sum of discounted rewards:

Original: [Equation]
Revised: [Equation]

Original: If we have access to state and action samples collected from a policy π , then we can use the sample mean of observed returns to estimate the value function above.
Revised: If we have access to state and action samples collected from a policy π , then we can use the sample mean of observed returns to estimate the value function above.

Original: However, in off-policy evaluation we are typically interested in estimating the value of a policy when the data is collected from a separate behavior policy π B ( a | s ) .
Revised: However, in off-policy evaluation we are typically interested in estimating the value of a policy when the data is collected from a separate behavior policy π B ( a | s ) .

Original: This setting can arise, for example, when data is being generated online from some process that we cannot control, or in the purely ofﬂine case when a ﬁxed dataset is given and additional samples cannot be collected.
Revised: This setting can arise, for example, when data is being generated online from some process that we cannot control, or in the purely ofﬂine case when a ﬁxed dataset is given and additional samples cannot be collected.

Original: In this work we consider the latter, purely ofﬂine setting.
Revised: In this work we consider the latter, purely ofﬂine setting.

Original: The typical setup for this problem formulation is that we are provided with a discount γ , ﬁxed samples collected from a behavior policy
Revised: The typical setup for this problem formulation is that we are provided with a discount γ , ﬁxed samples collected from a behavior policy

Original: D = { ( s t , a t , r t ) } , and optionally the action probabilities for the behavior policy π B ( a t | s t ) .
Revised: D = { ( s t , a t , r t ) } , and optionally the action probabilities for the behavior policy π B ( a t | s t ) .

Original: The objective can take multiple ﬂavors, as shown in Fig.
Revised: The objective can take multiple ﬂavors, as shown in Fig.

Original: A common task in OPE is to estimate the performance, or value, of a policy π (which may not be the same as π B ) so that the estimated value is as close as possible to V π under a metric such as MSE or absolute error.
Revised: A common task in OPE is to estimate the performance, or value, of a policy π (which may not be the same as π B ) so that the estimated value is as close as possible to V π under a metric such as MSE or absolute error.

Original: A second task is to perform policy selection, where the goal is to select the best policy or set of policies out of a group of candidates.
Revised: A second task is to perform policy selection, where the goal is to select the best policy or set of policies out of a group of candidates.

Original: This setup corresponds to how OPE is commonly used in practice, which is to ﬁnd the best performing strategy out of a pool when online evaluation is too expensive to be feasible.
Revised: This setup corresponds to how OPE is commonly used in practice, which is to ﬁnd the best performing strategy out of a pool when online evaluation is too expensive to be feasible.

Original:  DOPE: D EEP O FF -P OLICY E VALUATION
Revised:  DOPE: D EEP O FF -P OLICY E VALUATION

Original: The goal of the Deep Off-Policy Evaluation (DOPE) benchmark is to provide tasks that are challenging and effective measures of progress for OPE methods, yet is easy to use in order to better facilitate research.
Revised: The goal of the Deep Off-Policy Evaluation (DOPE) benchmark is to provide tasks that are challenging and effective measures of progress for OPE methods, yet is easy to use in order to better facilitate research.

Original: Therefore, we design our benchmark around a set of properties which are known to be difﬁcult for existing OPE methods in order to gauge their shortcomings, and keep all tasks amenable to simulation in order for the benchmark to be accessible and easy to evaluate.
Revised: Therefore, we design our benchmark around a set of properties which are known to be difﬁcult for existing OPE methods in order to gauge their shortcomings, and keep all tasks amenable to simulation in order for the benchmark to be accessible and easy to evaluate.

Original: 3. T ASK P ROPERTIES
Revised: 3. T ASK P ROPERTIES

Original: We describe our motivating properties for selecting tasks for the benchmark as follows:
Revised: We describe our motivating properties for selecting tasks for the benchmark as follows:

Original: High Dimensional Spaces (H) High-dimensionality is a key-feature in many real-world domains where it is difﬁcult to perform feature engineering, such as in robotics, autonomous driving, and more.
Revised: High Dimensional Spaces (H) High-dimensionality is a key-feature in many real-world domains where it is difﬁcult to perform feature engineering, such as in robotics, autonomous driving, and more.

Original: In these problems, it becomes challenging to accurately estimate quantities such as the value function without the use of high-capacity models such a neural networks and large datasets with wide state coverage.
Revised: In these problems, it becomes challenging to accurately estimate quantities such as the value function without the use of high-capacity models such a neural networks and large datasets with wide state coverage.

Original: Our benchmark is primarily composed of complex continuous-space tasks which exercise these challenges.
Revised: Our benchmark is primarily composed of complex continuous-space tasks which exercise these challenges.

Original: Long Time-Horizon (L) Long time horizon tasks are known to present difﬁcult challenges for OPE algorithms.
Revised: Long Time-Horizon (L) Long time horizon tasks are known to present difﬁcult challenges for OPE algorithms.

Original: Some algorithms have difﬁculty doing credit assignment for these tasks.
Revised: Some algorithms have difﬁculty doing credit assignment for these tasks.

Original: This can be made worse as the state dimension or action dimension increases.
Revised: This can be made worse as the state dimension or action dimension increases.

Original: Sparse Rewards (R) Sparse reward tasks increase the difﬁculty of credit assignment and add exploration challenges, which may interact with data coverage in the ofﬂine setting.
Revised: Sparse Rewards (R) Sparse reward tasks increase the difﬁculty of credit assignment and add exploration challenges, which may interact with data coverage in the ofﬂine setting.

Original: We include a range robotics and navigation tasks which are difﬁcult to solve due to reward sparsity.
Revised: We include a range robotics and navigation tasks which are difﬁcult to solve due to reward sparsity.

Original: Temporally extended control (T)
Revised: Temporally extended control (T)

Original: The ability to make decisions hierarchically is major challenge in many reinforcement learning applications.
Revised: The ability to make decisions hierarchically is major challenge in many reinforcement learning applications.

Original: We include two navigation tasks which require high-level planning in addition to low-level control in order to simulate the difﬁculty in such problems.
Revised: We include two navigation tasks which require high-level planning in addition to low-level control in order to simulate the difﬁculty in such problems.

Original: 3. E VALUATION P ROTOCOL
Revised: 3. E VALUATION P ROTOCOL

Original: The goal of DOPE to provide metrics for policy ranking, evaluation and selection.
Revised: The goal of DOPE to provide metrics for policy ranking, evaluation and selection.

Original: Many existing OPE methods only evaluate on point estimates such as MSE, but policy selection in domains where it is expensive to perform live deployment is one of the main practical use-cases of OPE.
Revised: Many existing OPE methods only evaluate on point estimates such as MSE, but policy selection in domains where it is expensive to perform live deployment is one of the main practical use-cases of OPE.

Original: In order to explicitly measure the quality of using OPE for policy selection we provide a set of policies with varying value, and devise two metrics that measure how well OPE methods can rank policies.
Revised: In order to explicitly measure the quality of using OPE for policy selection we provide a set of policies with varying value, and devise two metrics that measure how well OPE methods can rank policies.

Original: For each task we include a dataset of logged experiences
Revised: For each task we include a dataset of logged experiences

Original: D , and a set of policies { π 1 , π 2 , ..., π N } with varying values.
Revised: D , and a set of policies { π 1 , π 2 , ..., π N } with varying values.

Original: For each policy, OPE algorithms must produce an estimate of its value.
Revised: For each policy, OPE algorithms must produce an estimate of its value.

Original: In order to compute metrics, for each policy we provide "ground truth values" { V π 1 , V π 2 , ..., V π N } that are computed by running the policy for at least 1000 episodes, and ran as many additional episodes required to lower the error bar to .666.
Revised: In order to compute metrics, for each policy we provide "ground truth values" { V π 1 , V π 2 , ..., V π N } that are computed by running the policy for at least 1000 episodes, and ran as many additional episodes required to lower the error bar to .666.

Original: The estimated values will then be compared to the ground truth values using three different metrics (illustrated in Figure 2).
Revised: The estimated values will then be compared to the ground truth values using three different metrics (illustrated in Figure 2).

Original: Absolute Error
Revised: Absolute Error

Original: This metric measures estimate accuracy instead of its usefulness for ranking.
Revised: This metric measures estimate accuracy instead of its usefulness for ranking.

Original: Error is the most commonly used metric to assess performance of OPE algorithms.
Revised: Error is the most commonly used metric to assess performance of OPE algorithms.

Original: Rank correlation This metric directly measures how well estimated values rank policies, by computing the correlation between ranking according by the OPE estimates and ranking according to the ground truth values.

Original: Regret@k
Revised: Regret@k

Original: This metric measures how much worse the best policies identiﬁed by the estimates are than the best policy in the entire set.
Revised: This metric measures how much worse the best policies identiﬁed by the estimates are than the best policy in the entire set.

Original: It is computed by identifying the top-k policies according to the estimated returns.
Revised: It is computed by identifying the top-k policies according to the estimated returns.

Original: Regret @
Revised: Regret @

Original: k is the difference between the actual expected return of the best policy in the entire set, and the actual value of the best policy in the top-k set.
Revised: k is the difference between the actual expected return of the best policy in the entire set, and the actual value of the best policy in the top-k set.

Revised: Rank correlation This metric directly measures how well estimated values rank policies, by computing the correlation between ranking according by the OPE estimates and ranking according to the ground truth values.

Original:  D OMAINS
Revised:  D OMAINS

Original: DOPE contains two domains designed to provide a more comprehensive picture of how well OPE methods perform in different settings.
Revised: DOPE contains two domains designed to provide a more comprehensive picture of how well OPE methods perform in different settings.

Original: These two domains are constructed using two benchmarks
Revised: These two domains are constructed using two benchmarks

Original: [Table]
Revised: [Table]

Original: previously proposed for ofﬂine reinforcement learning: RL Unplugged (Gulcehre et al., 2020) and
Revised: previously proposed for ofﬂine reinforcement learning: RL Unplugged (Gulcehre et al., 2020) and

Original: D4RL (Fu et al., 2020), and reﬂect the challenges found within them.
Revised: D4RL (Fu et al., 2020), and reﬂect the challenges found within them.

Original: The DOPE RL Unplugged domain is constrained in two important ways: 1) the data is always generated using online RL training, ensuring there is adequate coverage of the state-action space, and 2) the policies are generated using ofﬂine RL algorithms on the same dataset we use for evaluation, ensuring the dataset and policies have some mutual support.
Revised: The DOPE RL Unplugged domain is constrained in two important ways: 1) the data is always generated using online RL training, ensuring there is adequate coverage of the state-action space, and 2) the policies are generated using ofﬂine RL algorithms on the same dataset we use for evaluation, ensuring the dataset and policies have some mutual support.

Original: Using it we hope to measure how well
Revised: Using it we hope to measure how well

Original: OPE methods work on more challenging tasks, but with otherwise ideal settings.
Revised: OPE methods work on more challenging tasks, but with otherwise ideal settings.

Original: The DOPE D4RL domain is less constrained in those ways: 1) the data comes from various sources (including random exploration, human teleoperation
Revised: The DOPE D4RL domain is less constrained in those ways: 1) the data comes from various sources (including random exploration, human teleoperation

Original: [Table]
Revised: [Table]

Original: and expert learned policies with limited exploration), which results in varying levels of coverage of the state-action space, and 2) the policies are generated using online RL algorithms, making it much less likely the dataset and policies will have mutual support.
Revised: and expert learned policies with limited exploration), which results in varying levels of coverage of the state-action space, and 2) the policies are generated using online RL algorithms, making it much less likely the dataset and policies will have mutual support.

Original: Both these issues are known to be challenging for OPE methods, even in simple tasks.
Revised: Both these issues are known to be challenging for OPE methods, even in simple tasks.

Original: So, using it we hope to measure how well OPE methods work in adversarial settings.
Revised: So, using it we hope to measure how well OPE methods work in adversarial settings.

Original: 4. DOPE RL U NPLUGGED
Revised: 4. DOPE RL U NPLUGGED

Original: DeepMind Control Suite (Tassa et al., 2018) is a set of control tasks implemented in MuJoCo (Todorov et al., 2012).
Revised: DeepMind Control Suite (Tassa et al., 2018) is a set of control tasks implemented in MuJoCo (Todorov et al., 2012).

Original: We consider the subset included in RL Unplugged.
Revised: We consider the subset included in RL Unplugged.

Original: This subset includes tasks that cover a range of difﬁculties.
Revised: This subset includes tasks that cover a range of difﬁculties.

Original: From Cartpole swingup, a simple task with a single degree of freedom, to Humanoid run which involves control of a complex bodies with 21 degrees of freedom.
Revised: From Cartpole swingup, a simple task with a single degree of freedom, to Humanoid run which involves control of a complex bodies with 21 degrees of freedom.

Original: All tasks use the default feature representation of the system state, including proprioceptive information such as joint positions and velocity, and additional sensor information and target position where appropriate.
Revised: All tasks use the default feature representation of the system state, including proprioceptive information such as joint positions and velocity, and additional sensor information and target position where appropriate.

Original: The observation dimension ranges from 5 to 67.
Revised: The observation dimension ranges from 5 to 67.

Original: Datasets and policies We train four ofﬂine RL algorithms (D4PG (Barth-Maron et al., 2018),
Revised: Datasets and policies We train four ofﬂine RL algorithms (D4PG (Barth-Maron et al., 2018),

Original: ABM (Siegel et al., 2020), CRR (Wang et al., 2020) and behavior cloning) varying their hyperparameters and for each algorithm-task-hyperparameter combination we train an agent with 3 random seeds on the DM Control Suite dataset from RL Unplugged and record policy snapshots at exponentially increasing intervals (after 25k learner steps, 50k, 100K, 200K, etc).
Revised: ABM (Siegel et al., 2020), CRR (Wang et al., 2020) and behavior cloning) varying their hyperparameters and for each algorithm-task-hyperparameter combination we train an agent with 3 random seeds on the DM Control Suite dataset from RL Unplugged and record policy snapshots at exponentially increasing intervals (after 25k learner steps, 50k, 100K, 200K, etc).

Original: Following Gulcehre et al.
Revised: Following Gulcehre et al.

Original: (2020), we consider a deterministic policy for D4PG and stochastic policies for BC, ABM and CRR.
Revised: (2020), we consider a deterministic policy for D4PG and stochastic policies for BC, ABM and CRR.

Original: The datasets are taken from RL Unplugged benchmark.
Revised: The datasets are taken from RL Unplugged benchmark.

Original: To create the datasets, for every environment they trained multiple (online) RL agents and collected both successful and unsuccessful episodes from different stages of training.
Revised: To create the datasets, for every environment they trained multiple (online) RL agents and collected both successful and unsuccessful episodes from different stages of training.

Original: All ofﬂine RL algorithms are implemented using the Acme framework (Hoffman et al., 2020).
Revised: All ofﬂine RL algorithms are implemented using the Acme framework (Hoffman et al., 2020).

Original: 4. DOPE
Revised: 4. DOPE

Original: D4RL
Revised: D4RL

Original: Gym-MuJoCo tasks.
Revised: Gym-MuJoCo tasks.

Original: Gym-MuJoCo consists of several continuous control tasks implemented within the MuJoCo simulator (Todorov et al., 2012) and provided in the OpenAI Gym (Brockman et al.,
Revised: Gym-MuJoCo consists of several continuous control tasks implemented within the MuJoCo simulator (Todorov et al., 2012) and provided in the OpenAI Gym (Brockman et al.,

Original: [Figure]
Revised: [Figure]

Original: insert ball
Revised: insert ball

Original: 2016) benchmark for online RL.
Revised: 2016) benchmark for online RL.

Original: We include the HalfCheetah, Hopper, Walker2D, and Ant tasks.
Revised: We include the HalfCheetah, Hopper, Walker2D, and Ant tasks.

Original: We include this domain primarily for comparison with past works, as a vast array of popular RL methods have been evaluated and developed on these tasks (Schulman et al., 2015;
Revised: We include this domain primarily for comparison with past works, as a vast array of popular RL methods have been evaluated and developed on these tasks (Schulman et al., 2015;

Original: Lillicrap et al., 2015; Schulman et al., 2017; Fujimoto et al., 2018; Haarnoja et al., 2018).
Revised: Lillicrap et al., 2015; Schulman et al., 2017; Fujimoto et al., 2018; Haarnoja et al., 2018).

Original: Gym-MuJoCo datasets and policies.
Revised: Gym-MuJoCo datasets and policies.

Original: For each task, in order to explore the effect of varying distributions, we include 5 datasets originally proposed by Fu et al.
Revised: For each task, in order to explore the effect of varying distributions, we include 5 datasets originally proposed by Fu et al.

Original: 3 correspond to different performance levels of the agent – “random”, “medium”, and “expert”.
Revised: 3 correspond to different performance levels of the agent – “random”, “medium”, and “expert”.

Original: We additionally include a mixture of medium and expert dataset, labeled “medium-expert”, and data collected from a replay buffer until the policy reaches the medium level of performance, labeled “medium-replay”.
Revised: We additionally include a mixture of medium and expert dataset, labeled “medium-expert”, and data collected from a replay buffer until the policy reaches the medium level of performance, labeled “medium-replay”.

Original: For policies, we selected 11 policies collected from evenly-spaced snapshots of training a Soft Actor-Critic agent (Haarnoja et al., 2018), which covers a range of performance between random and expert.
Revised: For policies, we selected 11 policies collected from evenly-spaced snapshots of training a Soft Actor-Critic agent (Haarnoja et al., 2018), which covers a range of performance between random and expert.

Original: Maze2D and AntMaze tasks.
Revised: Maze2D and AntMaze tasks.

Original: Maze2D and AntMaze are two maze navigation tasks originally proposed in
Revised: Maze2D and AntMaze are two maze navigation tasks originally proposed in

Original: D4RL (Fu et al., 2020).
Revised: D4RL (Fu et al., 2020).

Original: The domain consists of 3 mazes ranging from easy to hard (“umaze”, “medium”, “large”), and two morphologies: a 2D ball in Maze2D and the “Ant” robot of the Gym benchmark in AntMaze.
Revised: The domain consists of 3 mazes ranging from easy to hard (“umaze”, “medium”, “large”), and two morphologies: a 2D ball in Maze2D and the “Ant” robot of the Gym benchmark in AntMaze.

Original: For the Maze2D environment, we provide a less challenging reward computed base on distance to a ﬁxed goal.
Revised: For the Maze2D environment, we provide a less challenging reward computed base on distance to a ﬁxed goal.

Original: The
Revised: The

Original: AntMaze environment is a challenging sparse reward task, with a reward given only upon reaching the ﬁxed goal.
Revised: AntMaze environment is a challenging sparse reward task, with a reward given only upon reaching the ﬁxed goal.

Original: Maze2D and AntMaze datasets and policies.
Revised: Maze2D and AntMaze datasets and policies.

Original: Datasets for both morphologies consists of undirect data navigating randomly to different goal locations.
Revised: Datasets for both morphologies consists of undirect data navigating randomly to different goal locations.

Original: The datasets for Maze2D are collected by using a high-level planner to command waypoints to a low-level PID controller in order to reach randomly selected goals.
Revised: The datasets for Maze2D are collected by using a high-level planner to command waypoints to a low-level PID controller in order to reach randomly selected goals.

Original: The dataset in AntMaze is generated using the same high-level planner, but the lowlevel planner is replaced with a goal-conditioned policy trained to reach arbitrary waypoints.
Revised: The dataset in AntMaze is generated using the same high-level planner, but the lowlevel planner is replaced with a goal-conditioned policy trained to reach arbitrary waypoints.

Original: Both of these datasets are generated from non-Markovian policies, as the high-level controller maintains a history of waypoints reached in order to construct a plan to the goal.
Revised: Both of these datasets are generated from non-Markovian policies, as the high-level controller maintains a history of waypoints reached in order to construct a plan to the goal.

Original: We provide policies for all environments except “antmaze-large” by taking training snapshots obtained while running the
Revised: We provide policies for all environments except “antmaze-large” by taking training snapshots obtained while running the

Original: DAPG algorithm (Fu et al., 2020).
Revised: DAPG algorithm (Fu et al., 2020).

Original: Because obtaining high-performing policies for “antmaze-large” was challenging, we instead used imitation learning on a large amount of expert data to generate evaluation policies.
Revised: Because obtaining high-performing policies for “antmaze-large” was challenging, we instead used imitation learning on a large amount of expert data to generate evaluation policies.

Original: Adroit tasks.
Revised: Adroit tasks.

Original: The Adroit domain is a realistic simulation based on the
Revised: The Adroit domain is a realistic simulation based on the

Original: Shadow Hand robot, ﬁrst proposed by Rajeswaran et al.
Revised: Shadow Hand robot, ﬁrst proposed by Rajeswaran et al.

Original: There are 4 tasks in this domain: opening a door (“door”), pen twirling (“pen”), moving a ball to a target location (“relocate”), and hitting a nail with a hammer (“hammer”).
Revised: There are 4 tasks in this domain: opening a door (“door”), pen twirling (“pen”), moving a ball to a target location (“relocate”), and hitting a nail with a hammer (“hammer”).

Original: These tasks all contain sparse rewards and are difﬁcult to optimize directly using reinforcement learning.
Revised: These tasks all contain sparse rewards and are difﬁcult to optimize directly using reinforcement learning.

Original: Adroit datasets and policies.
Revised: Adroit datasets and policies.

Original: We include 3 datasets for each task.
Revised: We include 3 datasets for each task.

Original: The “human” dataset consists of a small amount of human demonstrations performing the task.
Revised: The “human” dataset consists of a small amount of human demonstrations performing the task.

Original: The “expert” dataset consists of data collected from an expert trained via
Revised: The “expert” dataset consists of data collected from an expert trained via

Original: DAPG (Rajeswaran et al., 2017).
Revised: DAPG (Rajeswaran et al., 2017).

Original: Finally, the “cloned” dataset contains a mixture of human demonstrations and data collected from an imitation learning algorithm trained on the demonstrations.
Revised: Finally, the “cloned” dataset contains a mixture of human demonstrations and data collected from an imitation learning algorithm trained on the demonstrations.

Original: For policies, we include 11 policies collected from snapshots while running the DAPG algorithm, which range from random performance to expert performance.
Revised: For policies, we include 11 policies collected from snapshots while running the DAPG algorithm, which range from random performance to expert performance.

Original:  B ASELINES AND R ESULTS
Revised:  B ASELINES AND R ESULTS

Original: The goal of our evaluation is two-fold.
Revised: The goal of our evaluation is two-fold.

Original: First, we wish to measure the performance of a variety of existing algorithms to provide baselines and reference numbers for future research.
Revised: First, we wish to measure the performance of a variety of existing algorithms to provide baselines and reference numbers for future research.

Original: Second, we wish to identify shortcomings in these approaches to reveal promising directions for future research.
Revised: Second, we wish to identify shortcomings in these approaches to reveal promising directions for future research.

Original: 5. B ASELINES
Revised: 5. B ASELINES

Original: We selected six methods to evaluate, which cover a variety of approaches that have been explored for the OPE problem.
Revised: We selected six methods to evaluate, which cover a variety of approaches that have been explored for the OPE problem.

Original: Fitted Q-Evaluation (FQE)
Revised: Fitted Q-Evaluation (FQE)

Original: As in Le et al.
Revised: As in Le et al.

Original: (2019), we train a neural network to estimate the value of the evaluation policy π e by bootstrapping from Q ( s (cid:48) , π e ( s (cid:48) )) .
Revised: (2019), we train a neural network to estimate the value of the evaluation policy π e by bootstrapping from Q ( s (cid:48) , π e ( s (cid:48) )) .

Original: We tried two different implementations, one from Kostrikov & Nachum (2020) and another from Paine et al.
Revised: We tried two different implementations, one from Kostrikov & Nachum (2020) and another from Paine et al.

Original: labeled FQE-L2 and
Revised: labeled FQE-L2 and

Original: FQE-D respectively to reﬂect different choices in loss function and parameterization.
Revised: FQE-D respectively to reﬂect different choices in loss function and parameterization.

Original: Model-Based (MB) Similar to Paduraru (2007), we train dynamics and reward models on transitions from the ofﬂine dataset D .
Revised: Model-Based (MB) Similar to Paduraru (2007), we train dynamics and reward models on transitions from the ofﬂine dataset D .

Original: Our models are deep neural networks trained to maximize the log likelihood of the next state and reward given the current state and action, similar to models from successful model-based RL algorithms (Chua et al., 2018; Janner et al., 2019).
Revised: Our models are deep neural networks trained to maximize the log likelihood of the next state and reward given the current state and action, similar to models from successful model-based RL algorithms (Chua et al., 2018; Janner et al., 2019).

Original: We follow the setup detailed in Anonymous (2021).
Revised: We follow the setup detailed in Anonymous (2021).

Original: To evaluate a policy, we compute the return using simulated trajectories generated by the policy under the learned dynamics model.
Revised: To evaluate a policy, we compute the return using simulated trajectories generated by the policy under the learned dynamics model.

Original: Importance Sampling (IS)
Revised: Importance Sampling (IS)

Original: We perform importance sampling with a learned behavior policy.
Revised: We perform importance sampling with a learned behavior policy.

Original: We use the implementation from Kostrikov & Nachum (2020), which uses self-normalized (also known as weighted) step-wise importance sampling (Liu et al., 2018; Nachum et al., 2019).
Revised: We use the implementation from Kostrikov & Nachum (2020), which uses self-normalized (also known as weighted) step-wise importance sampling (Liu et al., 2018; Nachum et al., 2019).

Original: Since the behavior policy is not known explicitly, we learn an estimate of it via a max-likelihood objective over the dataset D , as advocated by Hanna et al.
Revised: Since the behavior policy is not known explicitly, we learn an estimate of it via a max-likelihood objective over the dataset D , as advocated by Hanna et al.

Original: In order to be able to compute log-probabilities when the target policy is deterministic, we add artiﬁcial Gaussian noise with standard deviation 0 .
Revised: In order to be able to compute log-probabilities when the target policy is deterministic, we add artiﬁcial Gaussian noise with standard deviation 0 .

Original: 01 for all deterministic target policies.
Revised: 01 for all deterministic target policies.

Original: Doubly-Robust (DR)
Revised: Doubly-Robust (DR)

Original: We perform weighted doubly-robust policy evaluation based on Thomas &
Revised: We perform weighted doubly-robust policy evaluation based on Thomas &

Original: Brunskill (2016) and using the implementation of Kostrikov & Nachum (2020).
Revised: Brunskill (2016) and using the implementation of Kostrikov & Nachum (2020).

Original: Speciﬁcally, this method combines the IS technique above with a value estimator for variance reduction.
Revised: Speciﬁcally, this method combines the IS technique above with a value estimator for variance reduction.

Original: The value estimator is learned according to Kostrikov & Nachum (2020), using deep FQE with an L2 loss function.
Revised: The value estimator is learned according to Kostrikov & Nachum (2020), using deep FQE with an L2 loss function.

Original: DICE This method uses a saddle-point objective to estimate marginalized importance weights
Revised: DICE This method uses a saddle-point objective to estimate marginalized importance weights

Original: d π ( s, a ) /d
Revised: d π ( s, a ) /d

Original: π B ( s, a ) ; these weights are then used to compute a weighted average of reward over the ofﬂine dataset, and this serves as an estimate of the policy’s value in the MDP.
Revised: π B ( s, a ) ; these weights are then used to compute a weighted average of reward over the ofﬂine dataset, and this serves as an estimate of the policy’s value in the MDP.

Original: We use the implementation from Yang et al.
Revised: We use the implementation from Yang et al.

Original: (2020) corresponding to the algorithm BestDICE .
Revised: (2020) corresponding to the algorithm BestDICE .

Original: Variational Power Method (VPM)
Revised: Variational Power Method (VPM)

Original: This method runs a variational power iteration algorithm to estimate the importance weights
Revised: This method runs a variational power iteration algorithm to estimate the importance weights

Original: d π ( s, a ) /d
Revised: d π ( s, a ) /d

Original: π B ( s, a ) without the knowledge of the behavior policy.
Revised: π B ( s, a ) without the knowledge of the behavior policy.

Original: It then estimates the target policy value using weighted average of rewards similar to the DICE method.
Revised: It then estimates the target policy value using weighted average of rewards similar to the DICE method.

Original: Our implementation is based on the same network and hyperparameters for OPE setting as in Wen et al.
Revised: Our implementation is based on the same network and hyperparameters for OPE setting as in Wen et al.

Original: We further tune the hyper-parameters including the regularization parameter λ , learning rates α θ
Revised: We further tune the hyper-parameters including the regularization parameter λ , learning rates α θ

Original: and α v , and number of iterations on the Cartpole swingup task using ground-truth policy value, and then ﬁx them for all other tasks.
Revised: and α v , and number of iterations on the Cartpole swingup task using ground-truth policy value, and then ﬁx them for all other tasks.

Original: 5. R ESULTS
Revised: 5. R ESULTS

Original: We present results averaged across DOPE RL Unplugged in Fig. 4, and results for DOPE D4RL in Fig.
Revised: We present results averaged across DOPE RL Unplugged in Fig. 4, and results for DOPE D4RL in Fig.

Original: Overall, no evaluated algorithm attains near-maximum performance under any metric (absolute error, regret, or rank correlation).
Revised: Overall, no evaluated algorithm attains near-maximum performance under any metric (absolute error, regret, or rank correlation).

Original: This suggests that the benchmark provides signiﬁcant room for improvement, making it suitable for driving further future progress on OPE methods and facilitating the development of OPE algorithms that can provide reliable estimates on the types of high-dimensional problems that we consider.
Revised: This suggests that the benchmark provides signiﬁcant room for improvement, making it suitable for driving further future progress on OPE methods and facilitating the development of OPE algorithms that can provide reliable estimates on the types of high-dimensional problems that we consider.

Original: Out of all algorithms evaluated, FQE performs the best overall, attaining the best absolute error, rank correlation, and regret on DOPE RL Unplugged, and the best absolute error and regret on DOPE
Revised: Out of all algorithms evaluated, FQE performs the best overall, attaining the best absolute error, rank correlation, and regret on DOPE RL Unplugged, and the best absolute error and regret on DOPE

Original: D4RL.
Revised: D4RL.

Original: While FQE does well in general, differences in implementation details between FQE-L2 and
Revised: While FQE does well in general, differences in implementation details between FQE-L2 and

Original: FQE-D can create a signiﬁcant difference in performance.
Revised: FQE-D can create a signiﬁcant difference in performance.

Original: There are cases, however, where other methods outperform FQE.
Revised: There are cases, however, where other methods outperform FQE.

Original: Notably, importance sampling and doubly-robust estimators outperform
Revised: Notably, importance sampling and doubly-robust estimators outperform

Original: FQE under the rank correlation metric for DOPE D4RL (arguably the more important metric for model selection), but FQE still produces competitive numbers.
Revised: FQE under the rank correlation metric for DOPE D4RL (arguably the more important metric for model selection), but FQE still produces competitive numbers.

Original: Rank correlation is comparable between domains (absolute error and regret are not, due to different reward scales and different distributions of policies).
Revised: Rank correlation is comparable between domains (absolute error and regret are not, due to different reward scales and different distributions of policies).

Original: From this metric it is clear that algorithms perform better on these challenging tasks under the more ideal conditions of DOPE RL Unplugged (near 0.6) than under the challenging conditions of DOPE D4RL (near 0.2), but there is still signiﬁcant room for improvement.
Revised: From this metric it is clear that algorithms perform better on these challenging tasks under the more ideal conditions of DOPE RL Unplugged (near 0.6) than under the challenging conditions of DOPE D4RL (near 0.2), but there is still signiﬁcant room for improvement.

Original: FQE-D performs very poorly on Manipulator Insert Peg, even with good coverage and support (see Figure A.2), and is unreliable for other tasks such as Fish Swim and
Revised: FQE-D performs very poorly on Manipulator Insert Peg, even with good coverage and support (see Figure A.2), and is unreliable for other tasks such as Fish Swim and

Original: Cheetah Run.
Revised: Cheetah Run.

Original: We present more detailed results, separated by task, in Appendix A. Note in particular how in
Revised: We present more detailed results, separated by task, in Appendix A. Note in particular how in

Original: Figure A.6, which shows the regret@1 metric for different D4RL tasks, the particular choice of dataset for the Gym-MuJoCo, Adroit, and AntMaze domains causes a signiﬁcant difference in the performance of OPE methods.
Revised: Figure A.6, which shows the regret@1 metric for different D4RL tasks, the particular choice of dataset for the Gym-MuJoCo, Adroit, and AntMaze domains causes a signiﬁcant difference in the performance of OPE methods.

Original: This indicates the importance of evaluating multiple distinct datasets, with different data distribution properties (e.g., more narrow datasets, such as expert data, vs. broader datasets, such as random data), as no tested method is reliably robust to the effects of dataset variation.
Revised: This indicates the importance of evaluating multiple distinct datasets, with different data distribution properties (e.g., more narrow datasets, such as expert data, vs. broader datasets, such as random data), as no tested method is reliably robust to the effects of dataset variation.

Original: High-dimensional tasks requiring temporally extended control were also challenging, as highlighted by the performance on the AntMaze domain.
Revised: High-dimensional tasks requiring temporally extended control were also challenging, as highlighted by the performance on the AntMaze domain.

Original: No algorithm was able to achieve a good absolute error value on such tasks, and importance sampling was the only method able to achieve a correlation consistently above zero, suggesting that these more complex tasks are a particularly important area for future methods to focus on.
Revised: No algorithm was able to achieve a good absolute error value on such tasks, and importance sampling was the only method able to achieve a correlation consistently above zero, suggesting that these more complex tasks are a particularly important area for future methods to focus on.

Original:  R ELATED W ORK
Revised:  R ELATED W ORK

Original: Off-policy evaluation (OPE) has been studied extensively across a range of different domains, from healthcare (Thapa et al., 2005; Raghu et al., 2018; Nie et al., 2019), to recommender systems (Li et al., 2010; Dudík et al., 2014; Theocharous et al., 2015), and robotics (Kalashnikov et al., 2018).
Revised: Off-policy evaluation (OPE) has been studied extensively across a range of different domains, from healthcare (Thapa et al., 2005; Raghu et al., 2018; Nie et al., 2019), to recommender systems (Li et al., 2010; Dudík et al., 2014; Theocharous et al., 2015), and robotics (Kalashnikov et al., 2018).

Original: While a full survey of OPE methods is outside the scope of this article, broadly speaking we can categories OPE methods into groups based the use of importance sampling (Precup, 2000), value functions (Sutton et al., 2009; Migliavacca et al., 2010; Sutton et al., 2016; Yang et al., 2020), and learned transition models (Paduraru, 2007), though a number of methods combine two or more of these components (Jiang & Li, 2015; Thomas & Brunskill, 2016; Munos et al., 2016).
Revised: While a full survey of OPE methods is outside the scope of this article, broadly speaking we can categories OPE methods into groups based the use of importance sampling (Precup, 2000), value functions (Sutton et al., 2009; Migliavacca et al., 2010; Sutton et al., 2016; Yang et al., 2020), and learned transition models (Paduraru, 2007), though a number of methods combine two or more of these components (Jiang & Li, 2015; Thomas & Brunskill, 2016; Munos et al., 2016).

Original: A signiﬁcant body of work in OPE is also concerned with providing statistical guarantees (Thomas et al., 2015).
Revised: A signiﬁcant body of work in OPE is also concerned with providing statistical guarantees (Thomas et al., 2015).

Original: Our focus instead is on empirical evaluation – while theoretical analysis is likely to be a critical part of future OPE research, combining such analysis with empirical demonstration on broadly accepted and standardized benchmarks is likely to facilitate progress toward practically useful algorithms.
Revised: Our focus instead is on empirical evaluation – while theoretical analysis is likely to be a critical part of future OPE research, combining such analysis with empirical demonstration on broadly accepted and standardized benchmarks is likely to facilitate progress toward practically useful algorithms.

Original: Current evaluation of OPE methods is based around several metrics, including error in predicting the true return of the evaluated policy (Voloshin et al., 2019), correlation between the evaluation output and actual returns (Irpan et al., 2019), and ranking and model selection metrics (Doroudi et al., 2017).
Revised: Current evaluation of OPE methods is based around several metrics, including error in predicting the true return of the evaluated policy (Voloshin et al., 2019), correlation between the evaluation output and actual returns (Irpan et al., 2019), and ranking and model selection metrics (Doroudi et al., 2017).

Original: As there is no single accepted metric used by the entire community, we provide a set of candidate metrics along with our benchmark, with a detailed justiﬁcation in Section 5.
Revised: As there is no single accepted metric used by the entire community, we provide a set of candidate metrics along with our benchmark, with a detailed justiﬁcation in Section 5.

Original: Our work is closely related to (Paine et al., 2020) which studies OPE in a similar setting, however in our work we present a benchmark for the community and compare a range of OPE methods.
Revised: Our work is closely related to (Paine et al., 2020) which studies OPE in a similar setting, however in our work we present a benchmark for the community and compare a range of OPE methods.

Original: Outside of OPE, standardized benchmark suites have led to considerable standardization and progress in RL (Stone & Sutton, 2001;
Revised: Outside of OPE, standardized benchmark suites have led to considerable standardization and progress in RL (Stone & Sutton, 2001;

Original: Dutech et al., 2005; Riedmiller et al., 2007).
Revised: Dutech et al., 2005; Riedmiller et al., 2007).

Original: The Arcade Learning Environment (ALE) (Bellemare et al., 2013) and OpenAI Gym (Brockman et al., 2016) have been widely used to compare online
Revised: The Arcade Learning Environment (ALE) (Bellemare et al., 2013) and OpenAI Gym (Brockman et al., 2016) have been widely used to compare online

Original: RL algorithms to good effect.
Revised: RL algorithms to good effect.

Original: More recently, Gulcehre et al.
Revised: More recently, Gulcehre et al.

Original: Fu et al.
Revised: Fu et al.

Original: (2020) proposed benchmark tasks for ofﬂine RL.
Revised: (2020) proposed benchmark tasks for ofﬂine RL.

Original: Our benchmark is based on the tasks and environments described in these two benchmarks, which we augment with a set of standardized policies for evaluation, results for a number of existing OPE methods, and standardized evaluation metrics and protocols.
Revised: Our benchmark is based on the tasks and environments described in these two benchmarks, which we augment with a set of standardized policies for evaluation, results for a number of existing OPE methods, and standardized evaluation metrics and protocols.

Original: Voloshin et al.
Revised: Voloshin et al.

Original: (2019) have recently proposed benchmarking for OPE methods on a variety of tasks ranging from tabular problems to image-based tasks in Atari.
Revised: (2019) have recently proposed benchmarking for OPE methods on a variety of tasks ranging from tabular problems to image-based tasks in Atari.

Original: However, all of their evaluations are performed using the MSE metric, and they do not provide standardized datasets.
Revised: However, all of their evaluations are performed using the MSE metric, and they do not provide standardized datasets.

Original: In contrast, we provide a variety of policies for each problem which enables one to evaluate metrics such as ranking for policy selection, and a wide range of standardized datasets for reproducbility and the ability to study the effect of varying the dataset distribution.
Revised: In contrast, we provide a variety of policies for each problem which enables one to evaluate metrics such as ranking for policy selection, and a wide range of standardized datasets for reproducbility and the ability to study the effect of varying the dataset distribution.

Original:  C ONCLUSION
Revised:  C ONCLUSION

Original: We have presented the Deep Off-Policy Evaluation (DOPE) benchmark, which aims to provide a platform for studying policy evaluation and selection across a wide range of challenging tasks and datasets.
Revised: We have presented the Deep Off-Policy Evaluation (DOPE) benchmark, which aims to provide a platform for studying policy evaluation and selection across a wide range of challenging tasks and datasets.

Original: Our tasks are motivated from a set of properties designed to challenge existing OPE methods, such as high dimensionality and distributional mismatch between datasets and policies.
Revised: Our tasks are motivated from a set of properties designed to challenge existing OPE methods, such as high dimensionality and distributional mismatch between datasets and policies.

Original: In contrast to prior benchmarks, DOPE provides multiple datasets and policies, allowing researchers to study how data distributions affect performance and to evaluate a wide variety of metrics, including those that are relevant for ofﬂine policy selection.
Revised: In contrast to prior benchmarks, DOPE provides multiple datasets and policies, allowing researchers to study how data distributions affect performance and to evaluate a wide variety of metrics, including those that are relevant for ofﬂine policy selection.

Original: In comparing existing OPE methods, we generally ﬁnd that no existing algorithms consistently perform very well across all of the tasks, which further reinforces the importance of standardized and challenging OPE benchmarks.
Revised: In comparing existing OPE methods, we generally ﬁnd that no existing algorithms consistently perform very well across all of the tasks, which further reinforces the importance of standardized and challenging OPE benchmarks.

Original: Moreover, algorithms that perform poorly under one metric, such as absolute error, may perform better on other metrics, such as correlation, which provides insight into what algorithms to use depending on the use case (e.g., policy evaluation vs. policy selection).
Revised: Moreover, algorithms that perform poorly under one metric, such as absolute error, may perform better on other metrics, such as correlation, which provides insight into what algorithms to use depending on the use case (e.g., policy evaluation vs. policy selection).

Original: Overall, we believe that OPE is an exciting area for future research, as it allows RL agents to learn from large and abundant datasets in domains where online RL methods are otherwise infeasible.
Revised: Overall, we believe that OPE is an exciting area for future research, as it allows RL agents to learn from large and abundant datasets in domains where online RL methods are otherwise infeasible.

Original: We hope that our benchmark will enable further progress in this ﬁeld, though important evaluation challenges remain.
Revised: We hope that our benchmark will enable further progress in this ﬁeld, though important evaluation challenges remain.

Original: As the key beneﬁt of OPE is the ability to utilize real-world datasets, a promising direction for future evaluation efforts is to devise effective ways to use such data, where a key challenge is to develop evaluation protocols that are both reproducible and accessible.
Revised: As the key beneﬁt of OPE is the ability to utilize real-world datasets, a promising direction for future evaluation efforts is to devise effective ways to use such data, where a key challenge is to develop evaluation protocols that are both reproducible and accessible.

Original: This could help pave the way towards developing intelligent decision making agents that can leverage vast banks of logged information to solve important real-world problems.
Revised: This could help pave the way towards developing intelligent decision making agents that can leverage vast banks of logged information to solve important real-world problems.

Original: A A PPENDIX
Revised: A A PPENDIX

Original: Additional results ﬁgures and tables are presented here.
Revised: Additional results ﬁgures and tables are presented here.

Original: We show results by task in both tabular and chart form, as well as scatter plots which compare the estimated returns against the ground truth returns for every policy.
Revised: We show results by task in both tabular and chart form, as well as scatter plots which compare the estimated returns against the ground truth returns for every policy.

Original: [Figure] [Figure]
Revised: [Figure] [Figure]

Original: [Table] [Table]
Revised: [Table] [Table]

Original: [Table] [Table]
Revised: [Table] [Table]

Original: [Table] [Table]
Revised: [Table] [Table]

Original: [Figure] [Figure]
Revised: [Figure] [Figure]

Original: [Figure] [Figure]
Revised: [Figure] [Figure]

Original: [Figure] [Figure]
Revised: [Figure] [Figure]

Original: [Table]
Revised: [Table]

Original: [Table] [Table]
Revised: [Table] [Table]

Original: [Figure] [Figure]
Revised: [Figure] [Figure]

Original: n c
Revised: n c

Original: [Figure]
Revised: [Figure]

Original: [Figure] [Figure]
Revised: [Figure] [Figure]

Original: [Equation]
Revised: [Equation]

Original: [Figure] [Figure]
Revised: [Figure] [Figure]

Original: [Figure] [Figure]
Revised: [Figure] [Figure]