# Online Pricing and Allocation with Demand Learning and Fulfillment Cost

arXiv: https://arxiv.org/abs/2501.18049 · HTML: https://mlsanity.com/paper/2501.18049/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 56 references that are in the map.
- First posted on arXiv 29 Jan 2025.

## Builds on (most cited first, 16 of 16)

- [Introduction to Online Convex Optimization](https://mlsanity.com/paper/1909.05207/) (2019)
- [Taming the Monster: A Fast and Simple Algorithm for Contextual Bandits](https://mlsanity.com/paper/1402.0555/) (2014)
- [Bandits with Knapsacks](https://mlsanity.com/paper/1305.2545/) (2013)
- [Dynamic Pricing in High-dimensions](https://mlsanity.com/paper/1609.07574/) (2016)
- [Dynamic Pricing with Demand Covariates](https://mlsanity.com/paper/1604.07463/) (2016)
- [Logarithmic Regret in Feature-based Dynamic Pricing](https://mlsanity.com/paper/2102.10221/) (2021)
- [Towards Agnostic Feature-based Dynamic Pricing: Linear Policies vs Linear Valuation with Unknown Noise](https://mlsanity.com/paper/2201.11341/) (2022)
- [A Re-solving Heuristic with Uniformly Bounded Loss for Network Revenue Management](https://mlsanity.com/paper/1802.06192/) (2018)
- [Semi-parametric dynamic contextual pricing](https://mlsanity.com/paper/1901.02045/) (2019)
- [Online Allocation and Pricing: Constant Regret via Bellman Inequalities](https://mlsanity.com/paper/1906.06361/) (2019)
- [Degeneracy is OK: Logarithmic Regret for Network Revenue Management with Indiscrete Distributions](https://mlsanity.com/paper/2210.07996/) (2022)
- [Multi-Product Dynamic Pricing in High-Dimensions with Heterogeneous Price Sensitivity](https://mlsanity.com/paper/1901.01030/) (2019)
- [On Dynamic Pricing with Covariates](https://mlsanity.com/paper/2112.13254/) (2021)
- [A Primal-dual Learning Algorithm for Personalized Dynamic Pricing with an Inventory Constraint](https://mlsanity.com/paper/1812.09234/) (2018)
- [Doubly Fair Dynamic Pricing](https://mlsanity.com/paper/2209.11837/) (2022)
- [Pricing with Contextual Elasticity and Heteroscedastic Valuation](https://mlsanity.com/paper/2312.15999/) (2023)

## Built on by (most cited first, 4 of 4)

- [Dynamic Pricing with Adversarially-Censored Demands](https://mlsanity.com/paper/2502.06168/) (2025)
- [Online Decision Making with Generative Action Sets](https://mlsanity.com/paper/2509.25777/) (2025)
- [Optimal Contextual Pricing under Agnostic Non-Lipschitz Demand](https://mlsanity.com/paper/2605.05609/) (2026)
- [Two-Timescale Hierarchical Reinforcement Learning for Resilient Operations](https://mlsanity.com/paper/2607.23434/) (2026)

## Abstract (arXiv)

We study online learning for a seller that jointly chooses per-period inventory positions and a uniform price, then fulfills realized demand through a downstream allocation. The main difficulty is not only demand learning: the price shifts demand and reshapes the transportation LP, making the population objective globally non-convex and non-smooth. To solve this problem, we propose OCSAA, an algorithm that exploits demand observations through counterfactual translation and proposes joint (price, inventory) decisions through lower-confidence optimism. OCSAA admits a polynomial-time additive-accuracy implementation for rational-polytope inventory sets. We prove a high-probability widetilde O(√ T) regret guarantee and establish a matching-in-T information-theoretic lower bound. Our results illustrate an effective integration of statistical learning methodologies with complex operations research problems.