# Bootstrap-Conditioned Action Selection with Tabular Foundation Models

arXiv: https://arxiv.org/abs/2608.06559 · HTML: https://mlsanity.com/paper/2608.06559/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Self-rewarding alignment and self-training, one of 13 directions in Synthetic data and self-improvement for LLMs.
- Builds on 22 of its 35 references that are in the map.
- First posted on arXiv 6 Aug 2026.

## Placed in

- Synthetic data and self-improvement for LLMs / [Self-rewarding alignment and self-training](https://mlsanity.com/synth/self-rewarding-alignment-and-self-training/)

## Builds on (most cited first, 22 of 22)

- [Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networks](https://mlsanity.com/paper/1703.03400/) (2017)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [An Explanation of In-context Learning as Implicit Bayesian Inference](https://mlsanity.com/paper/2111.02080/) (2021)
- [What Can Transformers Learn In-Context? A Case Study of Simple Function Classes](https://mlsanity.com/paper/2208.01066/) (2022)
- [Deep Exploration via Bootstrapped DQN](https://mlsanity.com/paper/1602.04621/) (2016)
- [RL2: Fast Reinforcement Learning via Slow Reinforcement Learning](https://mlsanity.com/paper/1611.02779/) (2016)
- [A Tutorial on Thompson Sampling](https://mlsanity.com/paper/1707.02038/) (2017)
- [TabTransformer: Tabular Data Modeling Using Contextual Embeddings](https://mlsanity.com/paper/2012.06678/) (2020)
- [On Kernelized Multi-armed Bandits](https://mlsanity.com/paper/1704.00445/) (2017)
- [SAINT: Improved Neural Networks for Tabular Data via Row Attention and Contrastive Pre-Training](https://mlsanity.com/paper/2106.01342/) (2021)
- [TabICL: A Tabular Foundation Model for In-Context Learning on Large Data](https://mlsanity.com/paper/2502.05564/) (2025)
- [Recasting Gradient-Based Meta-Learning as Hierarchical Bayes](https://mlsanity.com/paper/1801.08930/) (2018)
- [Finite-Time Analysis of Kernelised Contextual Bandits](https://mlsanity.com/paper/1309.6869/) (2013)
- [Deep Bayesian Bandits Showdown: An Empirical Comparison of Bayesian Deep Networks for Thompson Sampling](https://mlsanity.com/paper/1802.09127/) (2018)
- [Neural Thompson Sampling](https://mlsanity.com/paper/2010.00827/) (2020)
- [Instance-Dependent Complexity of Contextual Bandits and Reinforcement Learning: A Disagreement-Based Perspective](https://mlsanity.com/paper/2010.03104/) (2020)
- [Ensemble Sampling](https://mlsanity.com/paper/1705.07347/) (2017)
- [The End of Optimism? An Asymptotic Analysis of Finite-Armed Linear Bandits](https://mlsanity.com/paper/1610.04491/) (2016)
- [Garbage In, Reward Out: Bootstrapping Exploration in Multi-Armed Bandits](https://mlsanity.com/paper/1811.05154/) (2018)
- [Thompson sampling with the online bootstrap](https://mlsanity.com/paper/1410.4009/) (2014)
- [Active Exploration via Autoregressive Generation of Missing Data](https://mlsanity.com/paper/2405.19466/) (2024)
- [Contextual Thompson Sampling via Generation of Missing Data](https://mlsanity.com/paper/2502.07064/) (2025)

## Abstract (arXiv)

Contextual bandits offer a natural framework for sample-efficient personalization, but practical deployment remains difficult under sparse, biased interaction data, unreliable uncertainty estimates, and severe cold starts. We study whether pre-trained tabular foundation models with in-context learning can be turned into randomized policies for online decision making. We propose BC-ICL (Bootstrap-conditioned action selection using ICL), which at each round draws a bootstrap resample of the interaction history, conditions a frozen pre-trained ICL model on that resample, scores all actions, and selects the action with the highest sampled score. We further introduce an arm-context conditioning architecture that promotes shared statistical strength across actions and helps avoid common bootstrap failure modes of isolated-arm bandits. Empirically, this policy delivers strong early-round regret and regret performance on standard contextual bandit suites, outperforming established baselines under a strict online protocol.