# The Elliptical Potential Lemma Revisited

arXiv: https://arxiv.org/abs/2010.10182 · HTML: https://mlsanity.com/paper/2010.10182/

## Key facts

- Cited by 23 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Oct 2020.

## Built on by (most cited first, 23 of 23)

- [Model-free Representation Learning and Exploration in Low-rank MDPs](https://mlsanity.com/paper/2102.07035/) (2021)
- [Variance-Dependent Regret Bounds for Linear Bandits and Reinforcement Learning: Adaptivity and Computational Efficiency](https://mlsanity.com/paper/2302.10371/) (2023)
- [Towards Deployment-Efficient Reinforcement Learning: Lower Bound and Optimality](https://mlsanity.com/paper/2202.06450/) (2022)
- [Privacy Amplification via Shuffling for Linear Contextual Bandits](https://mlsanity.com/paper/2112.06008/) (2021)
- [Bandit Algorithms for Precision Medicine](https://mlsanity.com/paper/2108.04782/) (2021)
- [Federated Linear Contextual Bandits with User-level Differential Privacy](https://mlsanity.com/paper/2306.05275/) (2023)
- [Improved Algorithms for Contextual Dynamic Pricing](https://mlsanity.com/paper/2406.11316/) (2024)
- [Likelihood Ratio Confidence Sets for Sequential Decision Making](https://mlsanity.com/paper/2311.04402/) (2023)
- [Sample Complexity of Kernel-Based Q-Learning](https://mlsanity.com/paper/2302.00727/) (2023)
- [Anti-Concentrated Confidence Bonuses for Scalable Exploration](https://mlsanity.com/paper/2110.11202/) (2021)
- [Provably Efficient UCB-type Algorithms For Learning Predictive State Representations](https://mlsanity.com/paper/2307.00405/) (2023)
- [No-Regret Thompson Sampling for Finite-Horizon Markov Decision Processes with Gaussian Processes](https://mlsanity.com/paper/2510.20725/) (2025)
- [Augmenting Online RL with Offline Data is All You Need: A Unified Hybrid RL Algorithm Design and Analysis](https://mlsanity.com/paper/2505.13768/) (2025)
- [Effective Dimension in Bandit Problems under Censorship](https://mlsanity.com/paper/2302.06916/) (2023)
- [Follow-ups Also Matter: Improving Contextual Bandits via Post-serving Contexts](https://mlsanity.com/paper/2309.13896/) (2023)
- [f-Divergence Regularized RLHF: Two Tales of Sampling and Unified Analyses](https://mlsanity.com/paper/2605.06977/) (2026)
- [The Elliptical Potential Lemma for General Distributions with an Application to Linear Thompson Sampling](https://mlsanity.com/paper/2102.07987/) (2021)
- [Prior Diffusiveness and Regret in the Linear-Gaussian Bandit](https://mlsanity.com/paper/2601.02022/) (2026)
- [Adaptive Bandit Algorithms for Contextual Matching Markets](https://mlsanity.com/paper/2605.28290/) (2026)
- [Exploration and Online Transfer with Behavioral Foundation Models](https://mlsanity.com/paper/2606.29980/) (2026)
- [Posterior Sampling-based Online Learning for Episodic POMDPs](https://mlsanity.com/paper/2310.10107/) (2023)
- [Constrained Linear Thompson Sampling](https://mlsanity.com/paper/2503.02043/) (2025)
- [A Direct Approach for Handling Contextual Bandits with Latent State Dynamics](https://mlsanity.com/paper/2604.08149/) (2026)

## Abstract (arXiv)

This note proposes a new proof and new perspectives on the so-called Elliptical Potential Lemma. This result is important in online learning, especially for linear stochastic bandits. The original proof of the result, however short and elegant, does not give much flexibility on the type of potentials considered and we believe that this new interpretation can be of interest for future research in this field.