# Gaussian Imagination in Bandit Learning

arXiv: https://arxiv.org/abs/2201.01902 · HTML: https://mlsanity.com/paper/2201.01902/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 34 references that are in the map.
- First posted on arXiv 6 Jan 2022.

## Builds on (most cited first, 21 of 21)

- [Learning to Optimize Via Posterior Sampling](https://mlsanity.com/paper/1301.2609/) (2013)
- [An Information-Theoretic Analysis of Thompson Sampling](https://mlsanity.com/paper/1403.5341/) (2014)
- [Learning to Optimize via Information-Directed Sampling](https://mlsanity.com/paper/1403.5556/) (2014)
- [Deep Exploration via Randomized Value Functions](https://mlsanity.com/paper/1703.07608/) (2017)
- [Reinforcement Learning, Bit by Bit](https://mlsanity.com/paper/2103.04047/) (2021)
- [Information-Directed Exploration for Deep Reinforcement Learning](https://mlsanity.com/paper/1812.07544/) (2018)
- [Information-Theoretic Confidence Bounds for Reinforcement Learning](https://mlsanity.com/paper/1911.09724/) (2019)
- [Bayesian decision-making under misspecified priors with applications to meta-learning](https://mlsanity.com/paper/2107.01509/) (2021)
- [An Information-Theoretic Approach to Minimax Regret in Partial Monitoring](https://mlsanity.com/paper/1902.00470/) (2019)
- [Information Directed Sampling for Linear Partial Monitoring](https://mlsanity.com/paper/2002.11182/) (2020)
- [Mirror Descent and the Information Ratio](https://mlsanity.com/paper/2009.12228/) (2020)
- [Satisficing in Time-Sensitive Bandit Learning](https://mlsanity.com/paper/1803.02855/) (2018)
- [An Information-Theoretic Analysis for Thompson Sampling with Many Actions](https://mlsanity.com/paper/1805.11845/) (2018)
- [Prior-free and prior-dependent regret bounds for Thompson Sampling](https://mlsanity.com/paper/1304.5758/) (2013)
- [Connections Between Mirror Descent, Thompson Sampling and the Information Ratio](https://mlsanity.com/paper/1905.11817/) (2019)
- [Exploration by Optimisation in Partial Monitoring](https://mlsanity.com/paper/1907.05772/) (2019)
- [Multi-scale exploration of convex functions and bandit convex optimization](https://mlsanity.com/paper/1507.06580/) (2015)
- [First-Order Bayesian Regret Analysis of Thompson Sampling](https://mlsanity.com/paper/1902.00681/) (2019)
- [The Fragility of Optimized Bandit Algorithms](https://mlsanity.com/paper/2109.13595/) (2021)
- [Bandit Phase Retrieval](https://mlsanity.com/paper/2106.01660/) (2021)
- [A Bit Better? Quantifying Information for Bandit Learning](https://mlsanity.com/paper/2102.09488/) (2021)

## Built on by (most cited first, 5 of 5)

- [Non-Stationary Bandit Learning via Predictive Sampling](https://mlsanity.com/paper/2205.01970/) (2022)
- [Lifting the Information Ratio: An Information-Theoretic Analysis of Thompson Sampling for Contextual Bandits](https://mlsanity.com/paper/2205.13924/) (2022)
- [Toward Efficient Exploration by Large Language Model Agents](https://mlsanity.com/paper/2504.20997/) (2025)
- [Meta-Learning for Simple Regret Minimization](https://mlsanity.com/paper/2202.12888/) (2022)
- [Overcoming Prior Misspecification in Online Learning to Rank](https://mlsanity.com/paper/2301.10651/) (2023)

## Abstract (arXiv)

Assuming distributions are Gaussian often facilitates computations that are otherwise intractable. We study the performance of an agent that attains a bounded information ratio with respect to a bandit environment with a Gaussian prior distribution and a Gaussian likelihood function when applied instead to a Bernoulli bandit. Relative to an information-theoretic bound on the Bayesian regret the agent would incur when interacting with the Gaussian bandit, we bound the increase in regret when the agent interacts with the Bernoulli bandit. If the Gaussian prior distribution and likelihood function are sufficiently diffuse, this increase grows at a rate which is at most linear in the square-root of the time horizon, and thus the per-timestep increase vanishes. Our results formalize the folklore that so-called Bayesian agents remain effective when instantiated with diffuse misspecified distributions.