# SPEED: Experimental Design for Policy Evaluation in Linear Heteroscedastic Bandits

arXiv: https://arxiv.org/abs/2301.12357 · HTML: https://mlsanity.com/paper/2301.12357/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 30 of its 83 references that are in the map.
- First posted on arXiv 29 Jan 2023.

## Builds on (most cited first, 30 of 30)

- [Nearly Minimax Optimal Reinforcement Learning for Linear Mixture Markov Decision Processes](https://mlsanity.com/paper/2012.08507/) (2020)
- [Doubly Robust Policy Evaluation and Optimization](https://mlsanity.com/paper/1503.02834/) (2015)
- [Optimal and Adaptive Off-policy Evaluation in Contextual Bandits](https://mlsanity.com/paper/1612.01205/) (2016)
- [Off-policy evaluation for slate recommendation](https://mlsanity.com/paper/1605.04812/) (2016)
- [Sequential Experimental Design for Transductive Linear Bandits](https://mlsanity.com/paper/1906.08399/) (2019)
- [Doubly robust off-policy evaluation with shrinkage](https://mlsanity.com/paper/1907.09623/) (2019)
- [Information Directed Sampling and Bandits with Heteroscedastic Noise](https://mlsanity.com/paper/1801.09667/) (2018)
- [Computationally Efficient Horizon-Free Reinforcement Learning for Linear Mixture MDPs](https://mlsanity.com/paper/2205.11507/) (2022)
- [An Empirical Process Approach to the Union Bound: Practical Algorithms for Combinatorial and Linear Bandits](https://mlsanity.com/paper/2006.11685/) (2020)
- [Improved Variance-Aware Confidence Sets for Linear Bandits and Linear Mixture MDP](https://mlsanity.com/paper/2101.12745/) (2021)
- [Minimal Exploration in Structured Stochastic Bandits](https://mlsanity.com/paper/1711.00400/) (2017)
- [Residual Weighted Learning for Estimating Individualized Treatment Rules](https://mlsanity.com/paper/1508.03179/) (2015)
- [Optimal Off-Policy Evaluation from Multiple Logging Policies](https://mlsanity.com/paper/2010.11002/) (2020)
- [Data-Efficient Policy Evaluation Through Behavior Policy Search](https://mlsanity.com/paper/1706.03469/) (2017)
- [Efficient-UCBV: An Almost Optimal Algorithm using Variance Estimates](https://mlsanity.com/paper/1711.03591/) (2017)
- [Nearly Optimal Algorithms for Level Set Estimation](https://mlsanity.com/paper/2111.01768/) (2021)
- [ReVar: Strengthening Policy Evaluation via Reduced Variance Sampling](https://mlsanity.com/paper/2203.04510/) (2022)
- [Improved Algorithms for Agnostic Pool-based Active Classification](https://mlsanity.com/paper/2105.06499/) (2021)
- [Robust On-Policy Sampling for Data-Efficient Policy Evaluation in Reinforcement Learning](https://mlsanity.com/paper/2111.14552/) (2021)
- [Safe Exploration for Efficient Policy Evaluation and Comparison](https://mlsanity.com/paper/2202.13234/) (2022)
- [Deep Jump Learning for Off-Policy Evaluation in Continuous Treatment Settings](https://mlsanity.com/paper/2010.15963/) (2020)
- [Chernoff Sampling for Active Testing and Extension to Active Regression](https://mlsanity.com/paper/2012.08073/) (2020)
- [Structured Best Arm Identification with Fixed Confidence](https://mlsanity.com/paper/1706.05198/) (2017)
- [Online Learning to Sample](https://mlsanity.com/paper/1506.09016/) (2015)
- [Taking the Counterfactual Online: Efficient and Unbiased Online Evaluation for Ranking](https://mlsanity.com/paper/2007.12719/) (2020)
- [Fast Rates for Bandit Optimization with Upper-Confidence Frank-Wolfe](https://mlsanity.com/paper/1702.06917/) (2017)
- [Active Learning for Accurate Estimation of Linear Models](https://mlsanity.com/paper/1703.00579/) (2017)
- [Variance-Optimal Augmentation Logging for Counterfactual Evaluation in Contextual Bandits](https://mlsanity.com/paper/2202.01721/) (2022)
- [An Affine Invariant Linear Convergence Analysis for Frank-Wolfe Algorithms](https://mlsanity.com/paper/1312.7864/) (2013)
- [Safe Data Collection for Offline and Online Policy Learning](https://mlsanity.com/paper/2111.04835/) (2021)

## Built on by (most cited first, 3 of 3)

- [Multi-task Representation Learning for Pure Exploration in Bilinear Bandits](https://mlsanity.com/paper/2311.00327/) (2023)
- [SaVeR: Optimal Data Collection Strategy for Safe Policy Evaluation in Tabular MDP](https://mlsanity.com/paper/2406.02165/) (2024)
- [Safety by Design: Realized-Cost Constraints for Contextual Bandits with Continuous Actions](https://mlsanity.com/paper/2608.26755/) (2026)

## Abstract (arXiv)

In this paper, we study the problem of optimal data collection for policy evaluation in linear bandits. In policy evaluation, we are given a target policy and asked to estimate the expected reward it will obtain when executed in a multi-armed bandit environment. Our work is the first work that focuses on such optimal data collection strategy for policy evaluation involving heteroscedastic reward noise in the linear bandit setting. We first formulate an optimal design for weighted least squares estimates in the heteroscedastic linear bandit setting that reduces the MSE of the value of the target policy. We then use this formulation to derive the optimal allocation of samples per action during data collection. We then introduce a novel algorithm SPEED (Structured Policy Evaluation Experimental Design) that tracks the optimal design and derive its regret with respect to the optimal design. Finally, we empirically validate that SPEED leads to policy evaluation with mean squared error comparable to the oracle strategy and significantly lower than simply running the target policy.