# Online Mixture of Experts: No-Regret Learning for Optimal Collective Decision-Making

arXiv: https://arxiv.org/abs/2510.21788 · HTML: https://mlsanity.com/paper/2510.21788/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in MoE theory and gating functions, one of 12 directions in Mixture-of-experts.
- Builds on 20 of its 42 references that are in the map.
- First posted on arXiv 19 Oct 2025.

## Placed in

- Mixture-of-experts / [MoE theory and gating functions](https://mlsanity.com/moe/moe-theory-and-gating-functions/)

## Builds on (most cited first, 20 of 20)

- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Outrageously Large Neural Networks: The Sparsely-Gated Mixture-of-Experts Layer](https://mlsanity.com/paper/1701.06538/) (2017)
- [BoolQ: Exploring the Surprising Difficulty of Natural Yes/No Questions](https://mlsanity.com/paper/1905.10044/) (2019)
- [Mixtral of Experts](https://mlsanity.com/paper/2401.04088/) (2024)
- [CommonsenseQA: A Question Answering Challenge Targeting Commonsense Knowledge](https://mlsanity.com/paper/1811.00937/) (2018)
- [DeepSeekMoE: Towards Ultimate Expert Specialization in Mixture-of-Experts Language Models](https://mlsanity.com/paper/2401.06066/) (2024)
- [A Review of Sparse Expert Models in Deep Learning](https://mlsanity.com/paper/2209.01667/) (2022)
- [Contextual Dueling Bandits](https://mlsanity.com/paper/1502.06362/) (2015)
- [Improving Regret Bounds for Combinatorial Semi-Bandits with Probabilistically Triggered Arms and Its Applications](https://mlsanity.com/paper/1703.01610/) (2017)
- [Getting MoRE out of Mixture of Language Model Reasoning Experts](https://mlsanity.com/paper/2305.14628/) (2023)
- [Online Learning via Offline Greedy Algorithms: Applications in Market Design and Optimization](https://mlsanity.com/paper/2102.11050/) (2021)
- [Satisficing in Time-Sensitive Bandit Learning](https://mlsanity.com/paper/1803.02855/) (2018)
- [BlackMamba: Mixture of Experts for State-Space Models](https://mlsanity.com/paper/2402.01771/) (2024)
- [Parameter-Efficient Mixture-of-Experts Architecture for Pre-trained Language Models](https://mlsanity.com/paper/2203.01104/) (2022)
- [Multi-Head Mixture-of-Experts](https://mlsanity.com/paper/2404.15045/) (2024)
- [Top-k Combinatorial Bandits with Full-Bandit Feedback](https://mlsanity.com/paper/1905.12624/) (2019)
- [Batch-Size Independent Regret Bounds for the Combinatorial Multi-Armed Bandit Problem](https://mlsanity.com/paper/1905.03125/) (2019)
- [Consistency of weighted majority votes](https://mlsanity.com/paper/1312.0451/) (2013)
- [Who Reviews The Reviewers? A Multi-Level Jury Problem](https://mlsanity.com/paper/2211.08494/) (2022)

## Built on by (most cited first, 2 of 2)

- [Truthful Online Preference Aggregation for LLM Fine-Tuning in Mobile Crowdsourcing](https://mlsanity.com/paper/2605.24052/) (2026)
- [AdaWeather: Adaptively Mixing Probabilistic Weather Forecasts with Logarithmic Regret](https://mlsanity.com/paper/2606.02663/) (2026)

## Abstract (arXiv)

We explore the use of expert-guided bandit learning, which we refer to as online mixture-of-experts (OMoE). In this setting, given a context, a candidate committee of experts must determine how to aggregate their outputs to achieve optimal results in terms of aggregate accuracy. We propose two algorithms to address this problem. The first algorithm combines aggregate voting with UCB-driven successive elimination, efficiently pruning suboptimal exploration actions. The second algorithm employs an online weighted-majority-voting mechanism, leveraging the respective voting power of each expert proportional to their predictive power. We derive theoretical guarantees for the regret properties in the bandit setting under ideal circumstances, and empirical results are provided accordingly. As a modern study on applications, these methods are applied to the online fine-tuning of a set of expert large language models (LLMs), where after each response, the generative LLM dynamically reweighs its set of experts and/or selects the optimal committee of experts to generate the most accurate response. Our results introduce new methodologies and no-regret guarantees for combining multiple experts to improve on the performance of the an aggregate model overall.