# Learning to Allocate Resources with Censored Feedback

arXiv: https://arxiv.org/abs/2602.06565 · HTML: https://mlsanity.com/paper/2602.06565/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 16 of its 40 references that are in the map.
- First posted on arXiv 6 Feb 2026.

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

- [Introduction to Multi-Armed Bandits](https://mlsanity.com/paper/1904.07272/) (2019)
- [Context-Aware Attentive Knowledge Tracing](https://mlsanity.com/paper/2007.12324/) (2020)
- [Bandits with Knapsacks](https://mlsanity.com/paper/1305.2545/) (2013)
- [Bandits with concave rewards and convex knapsacks](https://mlsanity.com/paper/1402.5758/) (2014)
- [Cascading Bandits: Learning to Rank in the Cascade Model](https://mlsanity.com/paper/1502.02763/) (2015)
- [Multi-Armed Bandits for Intelligent Tutoring Systems](https://mlsanity.com/paper/1310.3174/) (2013)
- [Attribution Modeling Increases Efficiency of Bidding in Display Advertising](https://mlsanity.com/paper/1707.06409/) (2017)
- [A Nonparametric Delayed Feedback Model for Conversion Rate Prediction](https://mlsanity.com/paper/1802.00255/) (2018)
- [An adaptive stochastic optimization algorithm for resource allocation](https://mlsanity.com/paper/1902.04376/) (2019)
- [Combinatorial Multi-armed Bandits for Resource Allocation](https://mlsanity.com/paper/2105.04373/) (2021)
- [Optimal Resource Allocation with Semi-Bandit Feedback](https://mlsanity.com/paper/1406.3840/) (2014)
- [A Better Resource Allocation Algorithm with Semi-Bandit Feedback](https://mlsanity.com/paper/1803.10415/) (2018)
- [Display advertising: Estimating conversion probability efficiently](https://mlsanity.com/paper/1710.08583/) (2017)
- [Censored Semi-Bandits for Resource Allocation](https://mlsanity.com/paper/2104.05781/) (2021)
- [Dynamic Pricing with Adversarially-Censored Demands](https://mlsanity.com/paper/2502.06168/) (2025)
- [Multi-Armed Bandits with Censored Consumption of Resources](https://mlsanity.com/paper/2011.00813/) (2020)

## Abstract (arXiv)

We study the online resource allocation problem in which at each round, a budget B must be allocated across K arms under censored feedback. An arm yields a reward if and only if two conditions are satisfied: (i) the arm is activated according to an arm-specific Bernoulli random variable with unknown parameter, and (ii) the allocated budget exceeds a random threshold drawn from a parametric distribution with unknown parameter. Over T rounds, the learner must jointly estimate the unknown parameters and allocate the budget so as to maximize cumulative reward facing the exploration--exploitation trade-off. We prove an information-theoretic regret lower bound Omega(T1/3), demonstrating the intrinsic difficulty of the problem. We then propose RA-UCB, an optimistic algorithm that leverages non-trivial parameter estimation and confidence bounds. When the budget B is known at the beginning of each round, RA-UCB achieves a regret of order widetildeO(√T), and even O(poly-log T) under stronger assumptions. As for unknown, round dependent budget, we introduce MG-UCB, which allows within-round switching and infinitesimal allocations, and matches the regret guarantees of RA-UCB. We then validate our theoretical results through experiments on real-world datasets.