# Signature Approach for Contextual Bandits with Nonlinear and Path-dependent Rewards

arXiv: https://arxiv.org/abs/2605.10313 · HTML: https://mlsanity.com/paper/2605.10313/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 38 references that are in the map.
- First posted on arXiv 11 May 2026.

## Builds on (most cited first, 9 of 9)

- [On Kernelized Multi-armed Bandits](https://mlsanity.com/paper/1704.00445/) (2017)
- [Finite-Time Analysis of Kernelised Contextual Bandits](https://mlsanity.com/paper/1309.6869/) (2013)
- [Kernels for sequentially ordered data](https://mlsanity.com/paper/1601.08169/) (2016)
- [Deep Signature Transforms](https://mlsanity.com/paper/1905.08494/) (2019)
- [OSOM: A simultaneously optimal algorithm for multi-armed and linear contextual bandits](https://mlsanity.com/paper/1905.10040/) (2019)
- [A Stability Principle for Learning under Non-Stationarity](https://mlsanity.com/paper/2310.18304/) (2023)
- [Risk of Transfer Learning and its Applications in Finance](https://mlsanity.com/paper/2311.03283/) (2023)
- [Signature features with the visibility transformation](https://mlsanity.com/paper/2004.04006/) (2020)
- [Sig-DEG for Distillation: Making Diffusion Models Faster and Lighter](https://mlsanity.com/paper/2508.16939/) (2025)

## Abstract (arXiv)

We study contextual bandits with nonlinear and path-dependent rewards through a novel signature-transform-based approach. Leveraging the universal nonlinearity property of signatures, we approximate continuous path-dependent reward functionals by linear functionals in the signature space. This representation enables the use of efficient linear contextual bandit methods while preserving expressive sequential structure. Building on this framework, we propose textttDisSigUCB, a signature-based disjoint upper confidence bound (UCB) algorithm. Under boundedness and non-degeneracy assumptions, we prove a high-probability data-dependent sublinear regret bound of order (tildemathcal O(√(d+m)KT)) where (d) is the context dimension and (m) is the signature feature dimension. Synthetic experiments and numerical applications on temperature sensor monitoring, sleep-stage classification, and hospital nurse staffing demonstrate that textttDisSigUCB consistently outperforms classical linear and kernelized contextual bandit baselines in nonlinear and path-dependent settings.