# Optimality of Thompson Sampling with Noninformative Priors for Pareto Bandits

arXiv: https://arxiv.org/abs/2302.01544 · HTML: https://mlsanity.com/paper/2302.01544/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 49 references that are in the map.
- First posted on arXiv 3 Feb 2023.

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

- [A Tutorial on Thompson Sampling](https://mlsanity.com/paper/1707.02038/) (2017)
- [An Information-Theoretic Analysis of Thompson Sampling](https://mlsanity.com/paper/1403.5341/) (2014)
- [Thompson Sampling for 1-Dimensional Exponential Family Bandits](https://mlsanity.com/paper/1307.3400/) (2013)
- [A minimax and asymptotically optimal algorithm for stochastic bandits](https://mlsanity.com/paper/1702.07211/) (2017)
- [Optimal Thompson Sampling strategies for support-aware CVaR bandits](https://mlsanity.com/paper/2012.05754/) (2020)
- [Prior-free and prior-dependent regret bounds for Thompson Sampling](https://mlsanity.com/paper/1304.5758/) (2013)
- [Regret Minimization in Heavy-Tailed Bandits](https://mlsanity.com/paper/2102.03734/) (2021)
- [On Bayesian index policies for sequential resource allocation](https://mlsanity.com/paper/1601.01190/) (2016)

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

- [Thompson Exploration with Best Challenger Rule in Best Arm Identification](https://mlsanity.com/paper/2310.00539/) (2023)
- [The Choice of Noninformative Priors for Thompson Sampling in Multiparameter Bandit Models](https://mlsanity.com/paper/2302.14407/) (2023)
- [Approximate information maximization for bandit games](https://mlsanity.com/paper/2310.12563/) (2023)

## Abstract (arXiv)

In the stochastic multi-armed bandit problem, a randomized probability matching policy called Thompson sampling (TS) has shown excellent performance in various reward models. In addition to the empirical performance, TS has been shown to achieve asymptotic problem-dependent lower bounds in several models. However, its optimality has been mainly addressed under light-tailed or one-parameter models that belong to exponential families. In this paper, we consider the optimality of TS for the Pareto model that has a heavy tail and is parameterized by two unknown parameters. Specifically, we discuss the optimality of TS with probability matching priors that include the Jeffreys prior and the reference priors. We first prove that TS with certain probability matching priors can achieve the optimal regret bound. Then, we show the suboptimality of TS with other priors, including the Jeffreys and the reference priors. Nevertheless, we find that TS with the Jeffreys and reference priors can achieve the asymptotic lower bound if one uses a truncation procedure. These results suggest carefully choosing noninformative priors to avoid suboptimality and show the effectiveness of truncation procedures in TS-based policies.