# Hidden Representation Clustering with Multi-Task Representation Learning towards Robust Online Budget Allocation

arXiv: https://arxiv.org/abs/2506.00959 · HTML: https://mlsanity.com/paper/2506.00959/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 22 of its 28 references that are in the map.
- First posted on arXiv 1 Jun 2025.

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

- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Adapting Neural Networks for the Estimation of Treatment Effects](https://mlsanity.com/paper/1906.02120/) (2019)
- [Melding the Data-Decisions Pipeline: Decision-Focused Learning for Combinatorial Optimization](https://mlsanity.com/paper/1809.05504/) (2018)
- [Differentiation of Blackbox Combinatorial Solvers](https://mlsanity.com/paper/1912.02175/) (2019)
- [Robust Learning with Jacobian Regularization](https://mlsanity.com/paper/1908.02729/) (2019)
- [Implicit MLE: Backpropagating Through Discrete Exponential Family Distributions](https://mlsanity.com/paper/2106.01798/) (2021)
- [Interior Point Solving for LP-based prediction+optimisation](https://mlsanity.com/paper/2010.13943/) (2020)
- [Decision-Focused Learning: Through the Lens of Learning to Rank](https://mlsanity.com/paper/2112.03609/) (2021)
- [VCNet and Functional Targeted Regularization For Learning Causal Effects of Continuous Treatments](https://mlsanity.com/paper/2103.07861/) (2021)
- [Uplift Modeling with Multiple Treatments and General Response Types](https://mlsanity.com/paper/1705.08492/) (2017)
- [E-Commerce Promotions Personalization via Online Multiple-Choice Knapsack with Uplift Modeling](https://mlsanity.com/paper/2108.13298/) (2021)
- [Direct Heterogeneous Causal Learning for Resource Allocation Problems in Marketing](https://mlsanity.com/paper/2211.15728/) (2022)
- [LBCF: A Large-Scale Budget-Constrained Causal Forest Algorithm](https://mlsanity.com/paper/2201.12585/) (2022)
- [Rankability-enhanced Revenue Uplift Modeling Framework for Online Marketing](https://mlsanity.com/paper/2405.15301/) (2024)
- [End-to-End Cost-Effective Incentive Recommendation under Budget Constraint with Uplift Modeling](https://mlsanity.com/paper/2408.11623/) (2024)
- [Decision Focused Causal Learning for Direct Counterfactual Marketing Optimization](https://mlsanity.com/paper/2407.13664/) (2024)
- [Benchmarking PtO and PnO Methods in the Predictive Combinatorial Optimization Regime](https://mlsanity.com/paper/2311.07633/) (2023)
- [Maximizing the Success Probability of Policy Allocations in Online Systems](https://mlsanity.com/paper/2312.16267/) (2023)
- [Uplift modeling with continuous treatments: A predict-then-optimize approach](https://mlsanity.com/paper/2412.09232/) (2024)
- [Metalearners for Ranking Treatment Effects](https://mlsanity.com/paper/2405.02183/) (2024)
- [Improve ROI with Causal Learning and Conformal Prediction](https://mlsanity.com/paper/2407.01065/) (2024)
- [Practical Marketplace Optimization at Uber Using Causally-Informed Machine Learning](https://mlsanity.com/paper/2407.19078/) (2024)

## Abstract (arXiv)

Marketing optimization, commonly formulated as an online budget allocation problem, has emerged as a pivotal factor in driving user growth. Most existing research addresses this problem by following the principle of 'first predict then optimize' for each individual, which presents challenges related to large-scale counterfactual prediction and solving complexity trade-offs. Note that the practical data quality is uncontrollable, and the solving scale tends to be tens of millions. Therefore, the existing approaches make the robust budget allocation non-trivial, especially in industrial scenarios with considerable data noise. To this end, this paper proposes a novel approach that solves the problem from the cluster perspective. Specifically, we propose a multi-task representation network to learn the inherent attributes of individuals and project the original features into high-dimension hidden representations through the first two layers of the trained network. Then, we divide these hidden representations into K groups through partitioning-based clustering, thus reformulating the problem as an integer stochastic programming problem under different total budgets. Finally, we distill the representation module and clustering model into a multi-category model to facilitate online deployment. Offline experiments validate the effectiveness and superiority of our approach compared to six state-of-the-art marketing optimization algorithms. Online A/B tests on the Meituan platform indicate that the approach outperforms the online algorithm by 0.53% and 0.65%, considering order volume (OV) and gross merchandise volume (GMV), respectively.