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A Unified Online-Offline Framework for Co-Branding Campaign Recommendations

Xiangxiang Dai, Xiaowei Sun, Jinhang Zuo, Xutong Liu, John C. S. Lui

TL;DR

The paper tackles co-branding campaign recommendations under budget constraints and market uncertainty by introducing a unified online-offline framework that couples online graph learning with budget-aware exploration and offline sub-brand budget optimization. It models co-branding opportunities as a bipartite graph with edges carrying budget-dependent success probabilities and target-brand market gains, optimizing expected rewards through online updates and offline planning. Theoretical results establish a near-optimal sublinear regret bound for online learning and a $1-1/e$ approximation for offline budget allocation, while extensive experiments on synthetic and real-world data demonstrate meaningful improvements in both short- and long-term returns. This framework provides a scalable, interpretable approach for brands seeking strategic, data-driven co-branding partnerships in dynamic markets.

Abstract

Co-branding has become a vital strategy for businesses aiming to expand market reach within recommendation systems. However, identifying effective cross-industry partnerships remains challenging due to resource imbalances, uncertain brand willingness, and ever-changing market conditions. In this paper, we provide the first systematic study of this problem and propose a unified online-offline framework to enable co-branding recommendations. Our approach begins by constructing a bipartite graph linking ``initiating'' and ``target'' brands to quantify co-branding probabilities and assess market benefits. During the online learning phase, we dynamically update the graph in response to market feedback, while striking a balance between exploring new collaborations for long-term gains and exploiting established partnerships for immediate benefits. To address the high initial co-branding costs, our framework mitigates redundant exploration, thereby enhancing short-term performance while ensuring sustainable strategic growth. In the offline optimization phase, our framework consolidates the interests of multiple sub-brands under the same parent brand to maximize overall returns, avoid excessive investment in single sub-brands, and reduce unnecessary costs associated with over-prioritizing a single sub-brand. We present a theoretical analysis of our approach, establishing a highly nontrivial sublinear regret bound for online learning in the complex co-branding problem, and enhancing the approximation guarantee for the NP-hard offline budget allocation optimization. Experiments on both synthetic and real-world co-branding datasets demonstrate the practical effectiveness of our framework, with at least 12\% improvement.

A Unified Online-Offline Framework for Co-Branding Campaign Recommendations

TL;DR

The paper tackles co-branding campaign recommendations under budget constraints and market uncertainty by introducing a unified online-offline framework that couples online graph learning with budget-aware exploration and offline sub-brand budget optimization. It models co-branding opportunities as a bipartite graph with edges carrying budget-dependent success probabilities and target-brand market gains, optimizing expected rewards through online updates and offline planning. Theoretical results establish a near-optimal sublinear regret bound for online learning and a approximation for offline budget allocation, while extensive experiments on synthetic and real-world data demonstrate meaningful improvements in both short- and long-term returns. This framework provides a scalable, interpretable approach for brands seeking strategic, data-driven co-branding partnerships in dynamic markets.

Abstract

Co-branding has become a vital strategy for businesses aiming to expand market reach within recommendation systems. However, identifying effective cross-industry partnerships remains challenging due to resource imbalances, uncertain brand willingness, and ever-changing market conditions. In this paper, we provide the first systematic study of this problem and propose a unified online-offline framework to enable co-branding recommendations. Our approach begins by constructing a bipartite graph linking ``initiating'' and ``target'' brands to quantify co-branding probabilities and assess market benefits. During the online learning phase, we dynamically update the graph in response to market feedback, while striking a balance between exploring new collaborations for long-term gains and exploiting established partnerships for immediate benefits. To address the high initial co-branding costs, our framework mitigates redundant exploration, thereby enhancing short-term performance while ensuring sustainable strategic growth. In the offline optimization phase, our framework consolidates the interests of multiple sub-brands under the same parent brand to maximize overall returns, avoid excessive investment in single sub-brands, and reduce unnecessary costs associated with over-prioritizing a single sub-brand. We present a theoretical analysis of our approach, establishing a highly nontrivial sublinear regret bound for online learning in the complex co-branding problem, and enhancing the approximation guarantee for the NP-hard offline budget allocation optimization. Experiments on both synthetic and real-world co-branding datasets demonstrate the practical effectiveness of our framework, with at least 12\% improvement.

Paper Structure

This paper contains 27 sections, 4 theorems, 7 equations, 9 figures, 1 table, 2 algorithms.

Table of Contents

  1. Introduction
  2. Model and Problem Formulation
  3. Co-Branding Bipartite Graph Model
  4. Online Feedback Mechanism
  5. Offline Strategic Budget Allocation
  6. Unified Problem Formulation
  7. Algorithmic Design
  8. Graph Learning via Online Feedback
  9. Budget Optimization via Offline Planning
  10. Theoretical Analysis
  11. Monotone Submodular Property
  12. Online Learning
  13. Offline Optimization
  14. Experiments
  15. Implementation Details
  16. ...and 12 more sections

Key Result

Lemma 1

For any graph $\mathcal{G}$, $r_{\mathcal{G}}(\cdot): \mathbb{N}_0^U \rightarrow \mathbb{R}$ is monotone and submodular, i.e., $r_{\mathcal{G}}(\bm{x \wedge y}) + r_{\mathcal{G}}(\bm{x \vee y}) \le r_{\mathcal{G}}(\bm{x}) + r_{\mathcal{G}}(\bm{y})$ for any $\bm{x},\bm{y} \in \mathbb{N}_0^U$, and $r_

Figures (9)

  • Figure 1: Co-Branding Bipartite Graph with Online-Offline Iterative Framework (with $U=4, V=5$ in this example).
  • Figure 2: Workflow of Hybrid Online-Offline Algorithm: It begins with the estimation of the co-branding bipartite graph, followed by offline budget allocation for selecting optimal co-branding pairs. After executing initial campaigns, market feedback is integrated to refine the estimations. These updated insights then guide the re-optimization of subsequent campaigns.
  • Figure 3: Comparison of average received market revenue.
  • Figure 4: Comparison of offline optimization across different total budgets on Synthetic dataset.
  • Figure 5: Influence of operational constraint $K$ under different $B$ on Diet and Apparel datasets.
  • ...and 4 more figures

Theorems & Definitions (4)

  • Lemma 1: Graph-based Lattice Submodularity
  • Theorem 1: Regret Bound
  • Theorem 2: Approximation
  • Lemma 3