# Off-Policy Evaluation of Slate Policies under Bayes Risk

arXiv: https://arxiv.org/abs/2101.02553 · HTML: https://mlsanity.com/paper/2101.02553/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 14 references that are in the map.
- First posted on arXiv 5 Jan 2021.

## Builds on (most cited first, 8 of 8)

- [Data-Efficient Off-Policy Policy Evaluation for Reinforcement Learning](https://mlsanity.com/paper/1604.00923/) (2016)
- [More Robust Doubly Robust Off-policy Evaluation](https://mlsanity.com/paper/1802.03493/) (2018)
- [Off-policy evaluation for slate recommendation](https://mlsanity.com/paper/1605.04812/) (2016)
- [Offline A/B testing for Recommender Systems](https://mlsanity.com/paper/1801.07030/) (2018)
- [Doubly robust off-policy evaluation with shrinkage](https://mlsanity.com/paper/1907.09623/) (2019)
- [Counterfactual Evaluation of Slate Recommendations with Sequential Reward Interactions](https://mlsanity.com/paper/2007.12986/) (2020)
- [An Efficient Bandit Algorithm for Realtime Multivariate Optimization](https://mlsanity.com/paper/1810.09558/) (2018)
- [Beyond Greedy Ranking: Slate Optimization via List-CVAE](https://mlsanity.com/paper/1803.01682/) (2018)

## Built on by (most cited first, 2 of 2)

- [Doubly Robust Off-Policy Evaluation for Ranking Policies under the Cascade Behavior Model](https://mlsanity.com/paper/2202.01562/) (2022)
- [Off-Policy Evaluation of Ranking Policies under Diverse User Behavior](https://mlsanity.com/paper/2306.15098/) (2023)

## Abstract (arXiv)

We study the problem of off-policy evaluation for slate bandits, for the typical case in which the logging policy factorizes over the slots of the slate. We slightly depart from the existing literature by taking Bayes risk as the criterion by which to evaluate estimators, and we analyze the family of 'additive' estimators that includes the pseudoinverse (PI) estimator of Swaminathan et al. (2017; arXiv:1605.04812). Using a control variate approach, we identify a new estimator in this family that is guaranteed to have lower risk than PI in the above class of problems. In particular, we show that the risk improvement over PI grows linearly with the number of slots, and linearly with the gap between the arithmetic and the harmonic mean of a set of slot-level divergences between the logging and the target policy. In the typical case of a uniform logging policy and a deterministic target policy, each divergence corresponds to slot size, showing that maximal gains can be obtained for slate problems with diverse numbers of actions per slot.