# Nonparametric Learning and Earning with One-Point Feedback under Nonstationarity

arXiv: https://arxiv.org/abs/2605.21263 · HTML: https://mlsanity.com/paper/2605.21263/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 19 of its 55 references that are in the map.
- First posted on arXiv 20 May 2026.

## Builds on (most cited first, 19 of 19)

- [Introduction to Online Convex Optimization](https://mlsanity.com/paper/1909.05207/) (2019)
- [Non-stationary Stochastic Optimization](https://mlsanity.com/paper/1307.5449/) (2013)
- [Tracking Slowly Moving Clairvoyant: Optimal Dynamic Regret of Online Learning with True and Noisy Gradient](https://mlsanity.com/paper/1605.04638/) (2016)
- [Efficient Contextual Bandits in Non-stationary Worlds](https://mlsanity.com/paper/1708.01799/) (2017)
- [Hedging the Drift: Learning to Optimize under Non-Stationarity](https://mlsanity.com/paper/1903.01461/) (2019)
- [Optimal Exploration-Exploitation in a Multi-Armed-Bandit Problem with Non-stationary Rewards](https://mlsanity.com/paper/1405.3316/) (2014)
- [Bandit Convex Optimization in Non-stationary Environments](https://mlsanity.com/paper/1907.12340/) (2019)
- [Tracking the Best Expert in Non-stationary Stochastic Environments](https://mlsanity.com/paper/1712.00578/) (2017)
- [Bandit learning in concave N-person games](https://mlsanity.com/paper/1810.01925/) (2018)
- [MetaGrad: Adaptation using Multiple Learning Rates in Online Learning](https://mlsanity.com/paper/2102.06622/) (2021)
- [Bandit Convex Optimization for Scalable and Dynamic IoT Management](https://mlsanity.com/paper/1707.09060/) (2017)
- [Distribution-free Contextual Dynamic Pricing](https://mlsanity.com/paper/2109.07340/) (2021)
- [On Abruptly-Changing and Slowly-Varying Multiarmed Bandit Problems](https://mlsanity.com/paper/1802.08380/) (2018)
- [Doubly Optimal No-Regret Online Learning in Strongly Monotone Games with Bandit Feedback](https://mlsanity.com/paper/2112.02856/) (2021)
- [Generalizing Gaussian Smoothing for Random Search](https://mlsanity.com/paper/2211.14721/) (2022)
- [Context-Based Dynamic Pricing with Online Clustering](https://mlsanity.com/paper/1902.06199/) (2019)
- [(Bandit) Convex Optimization with Biased Noisy Gradient Oracles](https://mlsanity.com/paper/1609.07087/) (2016)
- [Contextual Dynamic Pricing: Algorithms, Optimality, and Local Differential Privacy Constraints](https://mlsanity.com/paper/2406.02424/) (2024)
- [Learning When to Restart: Nonstationary Newsvendor from Uncensored to Censored Demand](https://mlsanity.com/paper/2509.18709/) (2025)

## Abstract (arXiv)

Firms increasingly rely on dynamic pricing to respond to evolving customer demand, yet in many applications they observe only the revenue generated by a single posted price in each period. At the same time, market conditions may shift gradually or abruptly due to changes in customer preferences, competition, or external shocks. These features create two intertwined challenges: learning the revenue--demand relationship from limited feedback and adapting pricing decisions to a changing environment. We study how a seller can learn and earn effectively under these constraints, without assuming a specific parametric form for demand. We develop a learning framework that updates prices using revenue-based gradient approximations constructed from one observation per period. To address environmental changes, we incorporate a restarting mechanism that periodically refreshes the learning process so that outdated information is discounted. When the degree of nonstationarity is unknown, we further introduce a meta-learning layer to adaptively hedge across multiple restarting schedules. We provide performance guarantees for our approach, showing how cumulative revenue loss relative to a fully informed benchmark depends on both the time horizon and the magnitude of market variation. Simulation experiments using synthetic and real-world data illustrate the effectiveness of the proposed procedures.