# Marginalized Operators for Off-policy Reinforcement Learning

arXiv: https://arxiv.org/abs/2203.16177 · HTML: https://mlsanity.com/paper/2203.16177/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 24 of its 49 references that are in the map.
- First posted on arXiv 30 Mar 2022.

## Builds on (most cited first, 24 of 24)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Addressing Function Approximation Error in Actor-Critic Methods](https://mlsanity.com/paper/1802.09477/) (2018)
- [Deep Reinforcement Learning with Double Q-learning](https://mlsanity.com/paper/1509.06461/) (2015)
- [OpenAI Gym](https://mlsanity.com/paper/1606.01540/) (2016)
- [DeepMind Control Suite](https://mlsanity.com/paper/1801.00690/) (2018)
- [IMPALA: Scalable Distributed Deep-RL with Importance Weighted Actor-Learner Architectures](https://mlsanity.com/paper/1802.01561/) (2018)
- [Data-Efficient Off-Policy Policy Evaluation for Reinforcement Learning](https://mlsanity.com/paper/1604.00923/) (2016)
- [Safe and Efficient Off-Policy Reinforcement Learning](https://mlsanity.com/paper/1606.02647/) (2016)
- [DualDICE: Behavior-Agnostic Estimation of Discounted Stationary Distribution Corrections](https://mlsanity.com/paper/1906.04733/) (2019)
- [Breaking the Curse of Horizon: Infinite-Horizon Off-Policy Estimation](https://mlsanity.com/paper/1810.12429/) (2018)
- [AlgaeDICE: Policy Gradient from Arbitrary Experience](https://mlsanity.com/paper/1912.02074/) (2019)
- [Minimax Weight and Q-Function Learning for Off-Policy Evaluation](https://mlsanity.com/paper/1910.12809/) (2019)
- [GenDICE: Generalized Offline Estimation of Stationary Values](https://mlsanity.com/paper/2002.09072/) (2020)
- [Towards Optimal Off-Policy Evaluation for Reinforcement Learning with Marginalized Importance Sampling](https://mlsanity.com/paper/1906.03393/) (2019)
- [Reinforcement Learning via Fenchel-Rockafellar Duality](https://mlsanity.com/paper/2001.01866/) (2020)
- [Off-Policy Evaluation via the Regularized Lagrangian](https://mlsanity.com/paper/2007.03438/) (2020)
- [Q(λ) with Off-Policy Corrections](https://mlsanity.com/paper/1602.04951/) (2016)
- [Understanding the Curse of Horizon in Off-Policy Evaluation via Conditional Importance Sampling](https://mlsanity.com/paper/1910.06508/) (2019)
- [Logistic Q-Learning](https://mlsanity.com/paper/2010.11151/) (2020)
- [Expected Eligibility Traces](https://mlsanity.com/paper/2007.01839/) (2020)
- [Adaptive Trade-Offs in Off-Policy Learning](https://mlsanity.com/paper/1910.07478/) (2019)
- [Black-box Off-policy Estimation for Infinite-Horizon Reinforcement Learning](https://mlsanity.com/paper/2003.11126/) (2020)
- [Conditional Importance Sampling for Off-Policy Learning](https://mlsanity.com/paper/1910.07479/) (2019)
- [SOPE: Spectrum of Off-Policy Estimators](https://mlsanity.com/paper/2111.03936/) (2021)

## Abstract (arXiv)

In this work, we propose marginalized operators, a new class of off-policy evaluation operators for reinforcement learning. Marginalized operators strictly generalize generic multi-step operators, such as Retrace, as special cases. Marginalized operators also suggest a form of sample-based estimates with potential variance reduction, compared to sample-based estimates of the original multi-step operators. We show that the estimates for marginalized operators can be computed in a scalable way, which also generalizes prior results on marginalized importance sampling as special cases. Finally, we empirically demonstrate that marginalized operators provide performance gains to off-policy evaluation and downstream policy optimization algorithms.