# Bandit Simulation for Average Reward Inference

arXiv: https://arxiv.org/abs/2606.00913 · HTML: https://mlsanity.com/paper/2606.00913/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 44 of its 67 references that are in the map.
- First posted on arXiv 30 May 2026.

## Builds on (most cited first, 30 of 44)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Brax -- A Differentiable Physics Engine for Large Scale Rigid Body Simulation](https://mlsanity.com/paper/2106.13281/) (2021)
- [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)
- [Time-uniform, nonparametric, nonasymptotic confidence sequences](https://mlsanity.com/paper/1810.08240/) (2018)
- [Double Reinforcement Learning for Efficient Off-Policy Evaluation in Markov Decision Processes](https://mlsanity.com/paper/1908.08526/) (2019)
- [Optimal and Adaptive Off-policy Evaluation in Contextual Bandits](https://mlsanity.com/paper/1612.01205/) (2016)
- [ChainQueen: A Real-Time Differentiable Physical Simulator for Soft Robotics](https://mlsanity.com/paper/1810.01054/) (2018)
- [Confidence Intervals for Policy Evaluation in Adaptive Experiments](https://mlsanity.com/paper/1911.02768/) (2019)
- [A Review of Off-Policy Evaluation in Reinforcement Learning](https://mlsanity.com/paper/2212.06355/) (2022)
- [Personalized HeartSteps: A Reinforcement Learning Algorithm for Optimizing Physical Activity](https://mlsanity.com/paper/1909.03539/) (2019)
- [CoinDICE: Off-Policy Confidence Interval Estimation](https://mlsanity.com/paper/2010.11652/) (2020)
- [Inference for Batched Bandits](https://mlsanity.com/paper/2002.03217/) (2020)
- [Statistical Inference with M-Estimators on Adaptively Collected Data](https://mlsanity.com/paper/2104.14074/) (2021)
- [Off-Policy Evaluation via Adaptive Weighting with Data from Contextual Bandits](https://mlsanity.com/paper/2106.02029/) (2021)
- [Accurate Inference for Adaptive Linear Models](https://mlsanity.com/paper/1712.06695/) (2017)
- [Post-Contextual-Bandit Inference](https://mlsanity.com/paper/2106.00418/) (2021)
- [Time-uniform central limit theory and asymptotic confidence sequences](https://mlsanity.com/paper/2103.06476/) (2021)
- [Near-optimal inference in adaptive linear regression](https://mlsanity.com/paper/2107.02266/) (2021)
- [UCB algorithms for multi-armed bandits: Precise regret and adaptive inference](https://mlsanity.com/paper/2412.06126/) (2024)
- [Statistical Inference After Adaptive Sampling for Longitudinal Data](https://mlsanity.com/paper/2202.07098/) (2022)
- [Inference with the Upper Confidence Bound Algorithm](https://mlsanity.com/paper/2408.04595/) (2024)
- [A Deployed Online Reinforcement Learning Algorithm In An Oral Health Clinical Trial](https://mlsanity.com/paper/2409.02069/) (2024)
- [Replicable Bandits for Digital Health Interventions](https://mlsanity.com/paper/2407.15377/) (2024)
- [Stable Thompson Sampling: Valid Inference via Variance Inflation](https://mlsanity.com/paper/2505.23260/) (2025)
- [Empirical Likelihood for Contextual Bandits](https://mlsanity.com/paper/1906.03323/) (2019)
- [Contextual Bandit Applications in Customer Support Bot](https://mlsanity.com/paper/2112.03210/) (2021)
- [Statistical Inference under Adaptive Sampling with LinUCB](https://mlsanity.com/paper/2512.00222/) (2025)
- [Did we personalize? Assessing personalization by an online reinforcement learning algorithm using resampling](https://mlsanity.com/paper/2304.05365/) (2023)
- [Adaptive Linear Estimating Equations](https://mlsanity.com/paper/2307.07320/) (2023)

## Abstract (arXiv)

Multi-arm bandit algorithms are increasingly used in online platforms, clinical trials, and social science experiments, but valid statistical inference on their performance remains an open challenge. After deploying bandits, a natural question is whether one can construct a confidence interval for its mean reward and assess whether it reliably outperforms a baseline policy. The total reward achieved in any single bandit deployment is random, and deploying a bandit twice on the same population typically yields different reward trajectories due to stochastic rewards. Standard statistical inference methods cannot be used because bandit algorithms introduce complex dependencies in the collected data, which violate the i.i.d. assumption underlying many classical approaches. Moreover, existing inference methods for adaptively collected data only apply to estimands that do not depend on the data-collection algorithm (such as the mean reward under a fixed action). We propose Bandit Simulation for Inference (BSI), a framework that fits a simulator of the bandit environment from observed data--either on-policy or off-policy--and uses it to estimate the mean reward under any evaluation policy, including adaptive blackbox algorithms. BSI formally propagates uncertainty in the estimated simulator parameters into the confidence interval construction. Furthermore, for BSI to be valid, it requires only weak exploration assumptions on the behavior policy and avoids importance weighting. We prove that BSI yields asymptotically valid confidence intervals, and demonstrate empirically that it maintains nominal coverage in settings where standard off-policy evaluation methods fail.