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 obtained by different behavior policies --- under the model of nonstationary episodic Markov Decision Processes (MDP) with a long horizon and a large action space. Existing importance sampling (IS) methods often suffer from large variance that depends exponentially on the RL horizon $H$. To solve this problem, we consider a marginalized importance sampling (MIS) estimator that recursively estimates the state marginal distribution for the target policy at every step.

Originality: The main idea of the paper - avoiding the long horizon problem by computing IS over state distributions rather than trajectories - was already introduced in (Liu et. However, the approach the authors take to leveraging this idea is original. Additionally, there is not yet enough published work on leveraging this potentially important idea (IS over state distribution), and therefore even being the second paper in this direction is still charting new territory. Quality - To the extent I looked at it the theoretical work is solid. I did not go over every equality in the proofs to check for algebraic errors, but I did go through every step in the proofs found in the appendix.

The paper studies the important problem of off-policy policy evaluation in long-horizon MDPs. The setting focuses on small-state, large-action problems. A novel estimator is proposed, whose finite-sample statistical properties are studied. Empirical results show the method is useful, especially in partially observable problems. Reviewers feel the experiment section can be strengthened (e.g., using more domains).

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 obtained by different behavior policies --- under the model of nonstationary episodic Markov Decision Processes (MDP) with a long horizon and a large action space. Existing importance sampling (IS) methods often suffer from large variance that depends exponentially on the RL horizon H . To solve this problem, we consider a marginalized importance sampling (MIS) estimator that recursively estimates the state marginal distribution for the target policy at every step. The result matches the Cramer-Rao lower bound in [Jiang and Li, 2016] up to a multiplicative factor of H . To the best of our knowledge, this is the first OPE estimation error bound with a polynomial dependence on H .

Reinforcement Learning (RL) methods are typically sample-inefficient, making it challenging to train and deploy RL-policies in real world robots. Even a robust policy trained in simulation requires a real-world deployment to assess their performance. This paper proposes a new approach to evaluate the real-world performance of agent policies prior to deploying them in the real world. Our approach incorporates a simulator along with real-world offline data to evaluate the performance of any policy using the framework of Marginalized Importance Sampling (MIS). Existing MIS methods face two challenges: (1) large density ratios that deviate from a reasonable range and (2) indirect supervision, where the ratio needs to be inferred indirectly, thus exacerbating estimation error. Our approach addresses these challenges by introducing the target policy's occupancy in the simulator as an intermediate variable and learning the density ratio as the product of two terms that can be learned separately. The first term is learned with direct supervision and the second term has a small magnitude, thus making it computationally efficient. We analyze the sample complexity as well as error propagation of our two step-procedure. Furthermore, we empirically evaluate our approach on Sim2Sim environments such as Cartpole, Reacher, and Half-Cheetah. Our results show that our method generalizes well across a variety of Sim2Sim gap, target policies and offline data collection policies. We also demonstrate the performance of our algorithm on a Sim2Real task of validating the performance of a 7 DoF robotic arm using offline data along with the Gazebo simulator.

Marginalized importance sampling (MIS), which measures the density ratio between the state-action occupancy of a target policy and that of a sampling distribution, is a promising approach for off-policy evaluation. However, current state-of-the-art MIS methods rely on complex optimization tricks and succeed mostly on simple toy problems. We bridge the gap between MIS and deep reinforcement learning by observing that the density ratio can be computed from the successor representation of the target policy. The successor representation can be trained through deep reinforcement learning methodology and decouples the reward optimization from the dynamics of the environment, making the resulting algorithm stable and applicable to high-dimensional domains. We evaluate the empirical performance of our approach on a variety of challenging Atari and MuJoCo environments.

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 obtained by different behavior policies --- under the model of nonstationary episodic Markov Decision Processes (MDP) with a long horizon and a large action space. Existing importance sampling (IS) methods often suffer from large variance that depends exponentially on the RL horizon $H$. To solve this problem, we consider a marginalized importance sampling (MIS) estimator that recursively estimates the state marginal distribution for the target policy at every step. The result matches the Cramer-Rao lower bound in [Jiang and Li, 2016] up to a multiplicative factor of $H$. To the best of our knowledge, this is the first OPE estimation error bound with a polynomial dependence on $H$.