# Quotient DAGs for Off-Policy Evaluation:Forward-Flow Importance Sampling and Exact Slate Propensities

arXiv: https://arxiv.org/abs/2605.29500 · HTML: https://mlsanity.com/paper/2605.29500/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 34 references that are in the map.
- First posted on arXiv 28 May 2026.

## Builds on (most cited first, 28 of 28)

- [Self-Attentive Sequential Recommendation](https://mlsanity.com/paper/1808.09781/) (2018)
- [BERT4Rec: Sequential Recommendation with Bidirectional Encoder Representations from Transformer](https://mlsanity.com/paper/1904.06690/) (2019)
- [Recommendation as Language Processing (RLP): A Unified Pretrain, Personalized Prompt & Predict Paradigm (P5)](https://mlsanity.com/paper/2203.13366/) (2022)
- [Is ChatGPT Good at Search? Investigating Large Language Models as Re-Ranking Agents](https://mlsanity.com/paper/2304.09542/) (2023)
- [Doubly Robust Off-policy Value Evaluation for Reinforcement Learning](https://mlsanity.com/paper/1511.03722/) (2015)
- [Data-Efficient Off-Policy Policy Evaluation for Reinforcement Learning](https://mlsanity.com/paper/1604.00923/) (2016)
- [DualDICE: Behavior-Agnostic Estimation of Discounted Stationary Distribution Corrections](https://mlsanity.com/paper/1906.04733/) (2019)
- [Stochastic Beams and Where to Find Them: The Gumbel-Top-k Trick for Sampling Sequences Without Replacement](https://mlsanity.com/paper/1903.06059/) (2019)
- [Recommender Systems with Generative Retrieval](https://mlsanity.com/paper/2305.05065/) (2023)
- [RankZephyr: Effective and Robust Zero-Shot Listwise Reranking is a Breeze!](https://mlsanity.com/paper/2312.02724/) (2023)
- [M6-Rec: Generative Pretrained Language Models are Open-Ended Recommender Systems](https://mlsanity.com/paper/2205.08084/) (2022)
- [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)
- [Counterfactual Off-Policy Evaluation with Gumbel-Max Structural Causal Models](https://mlsanity.com/paper/1905.05824/) (2019)
- [Off-policy evaluation for slate recommendation](https://mlsanity.com/paper/1605.04812/) (2016)
- [KuaiRec: A Fully-observed Dataset and Insights for Evaluating Recommender Systems](https://mlsanity.com/paper/2202.10842/) (2022)
- [Understanding the Curse of Horizon in Off-Policy Evaluation via Conditional Importance Sampling](https://mlsanity.com/paper/1910.06508/) (2019)
- [Off-Policy Evaluation of Slate Bandit Policies via Optimizing Abstraction](https://mlsanity.com/paper/2402.02171/) (2024)
- [Off-Policy Evaluation of Ranking Policies under Diverse User Behavior](https://mlsanity.com/paper/2306.15098/) (2023)
- [Conditional Importance Sampling for Off-Policy Learning](https://mlsanity.com/paper/1910.07479/) (2019)
- [Control Variates for Slate Off-Policy Evaluation](https://mlsanity.com/paper/2106.07914/) (2021)
- [Learning-to-Rank with Partitioned Preference: Fast Estimation for the Plackett-Luce Model](https://mlsanity.com/paper/2006.05067/) (2020)
- [Effective Off-Policy Evaluation and Learning in Contextual Combinatorial Bandits](https://mlsanity.com/paper/2408.11202/) (2024)
- [Scaling Marginalized Importance Sampling to High-Dimensional State-Spaces via State Abstraction](https://mlsanity.com/paper/2212.07486/) (2022)
- [Policy-Gradient Training of Language Models for Ranking](https://mlsanity.com/paper/2310.04407/) (2023)
- [Abstract Reward Processes: Leveraging State Abstraction for Consistent Off-Policy Evaluation](https://mlsanity.com/paper/2410.02172/) (2024)
- [Concept-driven Off Policy Evaluation](https://mlsanity.com/paper/2411.19395/) (2024)

## Built on by (most cited first, 1 of 1)

- [What a Data Release Must Preserve for Off-Policy Evaluation](https://mlsanity.com/paper/2610.15283/) (2026)

## Abstract (arXiv)

Off-policy evaluation estimates how a target policy would perform using data collected by a different behavior policy, which is crucial when online testing is costly or risky, such as in recommendation or healthcare. Standard importance sampling reweights each logged trajectory, but it can treat details of the generation process as meaningful even when the evaluation target ignores them: for example, an autoregressive slate recommender may generate an ordered sequence of items while the reward and downstream estimator depend only on the unordered slate. This creates nuisance variance and a computational gap, since exact unordered slate propensities require summing over all generation orders. We introduce a quotient-DAG view that merges histories equivalent for evaluation and assigns weights using target-to-behavior forward-flow ratios on the merged graph. For slate recommendation under a set-sufficient next-item interface, this yields Forward-DP, a subset-DAG dynamic program that computes exact unordered propensities without factorial enumeration. The resulting propensity primitive enables practical propensity-based evaluation and model selection for context-dependent autoregressive slate loggers.