# A Unified Model and Dimension for Interactive Estimation

arXiv: https://arxiv.org/abs/2306.06184 · HTML: https://mlsanity.com/paper/2306.06184/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 32 references that are in the map.
- First posted on arXiv 9 Jun 2023.

## Builds on (most cited first, 7 of 7)

- [The Statistical Complexity of Interactive Decision Making](https://mlsanity.com/paper/2112.13487/) (2021)
- [Taming the Monster: A Fast and Simple Algorithm for Contextual Bandits](https://mlsanity.com/paper/1402.0555/) (2014)
- [Beyond UCB: Optimal and Efficient Contextual Bandits with Regression Oracles](https://mlsanity.com/paper/2002.04926/) (2020)
- [Bilinear Classes: A Structural Framework for Provable Generalization in RL](https://mlsanity.com/paper/2103.10897/) (2021)
- [Model-based Reinforcement Learning and the Eluder Dimension](https://mlsanity.com/paper/1406.1853/) (2014)
- [Provable Model-based Nonlinear Bandit and Reinforcement Learning: Shelve Optimism, Embrace Virtual Curvature](https://mlsanity.com/paper/2102.04168/) (2021)
- [Statistical Queries and Statistical Algorithms: Foundations and Applications](https://mlsanity.com/paper/2004.00557/) (2020)

## Abstract (arXiv)

We study an abstract framework for interactive learning called interactive estimation in which the goal is to estimate a target from its "similarity'' to points queried by the learner. We introduce a combinatorial measure called dissimilarity dimension which largely captures learnability in our model. We present a simple, general, and broadly-applicable algorithm, for which we obtain both regret and PAC generalization bounds that are polynomial in the new dimension. We show that our framework subsumes and thereby unifies two classic learning models: statistical-query learning and structured bandits. We also delineate how the dissimilarity dimension is related to well-known parameters for both frameworks, in some cases yielding significantly improved analyses.