# RELEAF: An Algorithm for Learning and Exploiting Relevance

arXiv: https://arxiv.org/abs/1502.01418 · HTML: https://mlsanity.com/paper/1502.01418/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Feb 2015.

## Built on by (most cited first, 7 of 7)

- [The Role of Contextual Information in Best Arm Identification](https://mlsanity.com/paper/2106.14077/) (2021)
- [Best Arm Identification with Contextual Information under a Small Gap](https://mlsanity.com/paper/2209.07330/) (2022)
- [Asymptotically Optimal Fixed-Budget Best Arm Identification with Variance-Dependent Bounds](https://mlsanity.com/paper/2302.02988/) (2023)
- [Generalized Translation and Scale Invariant Online Algorithm for Adversarial Multi-Armed Bandits](https://mlsanity.com/paper/2109.09212/) (2021)
- [Adaptive Experimental Design for Policy Learning](https://mlsanity.com/paper/2401.03756/) (2024)
- [Second Order Regret Bounds Against Generalized Expert Sequences under Partial Bandit Feedback](https://mlsanity.com/paper/2204.06660/) (2022)
- [Data Dependent Regret Guarantees Against General Comparators for Full or Bandit Feedback](https://mlsanity.com/paper/2303.06526/) (2023)

## Abstract (arXiv)

Recommender systems, medical diagnosis, network security, etc., require on-going learning and decision-making in real time. These -- and many others -- represent perfect examples of the opportunities and difficulties presented by Big Data: the available information often arrives from a variety of sources and has diverse features so that learning from all the sources may be valuable but integrating what is learned is subject to the curse of dimensionality. This paper develops and analyzes algorithms that allow efficient learning and decision-making while avoiding the curse of dimensionality. We formalize the information available to the learner/decision-maker at a particular time as a context vector which the learner should consider when taking actions. In general the context vector is very high dimensional, but in many settings, the most relevant information is embedded into only a few relevant dimensions. If these relevant dimensions were known in advance, the problem would be simple -- but they are not. Moreover, the relevant dimensions may be different for different actions. Our algorithm learns the relevant dimensions for each action, and makes decisions based in what it has learned. Formally, we build on the structure of a contextual multi-armed bandit by adding and exploiting a relevance relation. We prove a general regret bound for our algorithm whose time order depends only on the maximum number of relevant dimensions among all the actions, which in the special case where the relevance relation is single-valued (a function), reduces to tildeO(T^2(√2-1)); in the absence of a relevance relation, the best known contextual bandit algorithms achieve regret tildeO(T(D+1)/(D+2)), where D is the full dimension of the context vector.