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A Unified Framework for Marketing Budget Allocation
Kui Zhao, Junhao Hua, Ling Yan, Qi Zhang, Huan Xu, Cheng Yang
TL;DR
Online marketing allocation is dynamic and complex, while segment-specific logit fitting cannot share information across sparse segments. The paper combines a context-aware semi-black-box response model with efficient optimization; in Taopiaopiao, sales improved over 6% with 40% less marketing spend.
Problem
Online marketing requires frequent budget readjustment, while separately fitted logit models cannot share information across segments with sparse historical budget values.
Source: §1 · p. 1, §2.2 · p. 3Method
A neural network estimates market-response elasticity from segment context, and the learned response models feed an optimizer using dual-variable bisection.
Source: §1 · p. 2Results
Over 6% sales improvement with 40% less marketing spend was reported for the Taopiaopiao example.
Source: §4.3.2 · p. 8Takeaways & Limitations
The approach handled billions of decision variables in several real-world scenarios.
Source: §1 · p. 2The response model assumes market-cost elasticity depends on contextual variables; boundary constraints and discrete-setting approximation error remain future-work topics.
Source: §2.2 · p. 3, §6 · p. 9
Abstract
from arXiv · showhide
While marketing budget allocation has been studied for decades in traditional business, nowadays online business brings much more challenges due to the dynamic environment and complex decision-making process. In this paper, we present a novel unified framework for marketing budget allocation. By leveraging abundant data, the proposed data-driven approach can help us to overcome the challenges and make more informed decisions. In our approach, a semi-black-box model is built to forecast the dynamic market response and an efficient optimization method is proposed to solve the complex allocation task. First, the response in each market-segment is forecasted by exploring historical data through a semi-black-box model, where the capability of logit demand curve is enhanced by neural networks. The response model reveals relationship between sales and marketing cost. Based on the learned model, budget allocation is then formulated as an optimization problem, and we design efficient algorithms to solve it in both continuous and discrete settings. Several kinds of business constraints are supported in one unified optimization paradigm, including cost upper bound, profit lower bound, or ROI lower bound. The proposed framework is easy to implement and readily to handle large-scale problems. It has been successfully applied to many scenarios in Alibaba Group. The results of both offline experiments and online A/B testing demonstrate its effectiveness.
1 INTRODUCTION
Online marketing allocation must respond to a dynamic, complex environment, and separate black-box forecasts or segment-specific logit curves leave decision-making or information-sharing gaps. The paper proposes a unified framework that learns market responses and optimizes budgets, reporting a five-week Taopiaopiao A/B test and large-scale applications.
1 INTRODUCTION
- Online marketing budgets require frequent readjustment, while black-box forecasts are difficult to translate into allocation decisions and separate logit fits cannot share segment information.The paper notes that this is especially challenging for companies with large, diversified markets.Source: §1 · p. 1
- The framework learns semi-black-box market-response models, using neural networks to share information across segments while retaining explicit sales–cost relationships.It estimates elasticity at market cost from contextual variables and learns a segment-specific sensitivity coefficient.Source: §1 · p. 2
- The allocation optimizer reformulates a non-convex problem as an equivalent convex one and uses bisection on a dual variable, with O(N) work per iteration.The framework supports cost upper bounds, profit lower bounds, and ROI lower bounds, and extends to discrete budget choices.Source: §1 · p. 2
- The framework has been applied to Alibaba Group scenarios spanning daily marketing, shopping festivals, and interest discounts.The listed examples include Taopiaopiao, Tmall, Lazada, Credit Pay, and Cash Now.Source: §1 · p. 2
- Five-week Taopiaopiao A/B testing showed remarkable improvements, and the approach handled billions of decision variables in several scenarios.The introduction describes the online test as a typical example and reports that the approach handled those large-scale scenarios well.Source: §1 · p. 2
2 MARKET RESPONSE
Online commerce data enable granular market segmentation, and the section develops response models from the logit demand curve to a neural-network extension that shares information across segments while retaining explicit sales–cost relationships.
2 MARKET RESPONSE
- Online commerce data support granular market segments formed around specific commodities, customers, and consumption times.Examples include black wool sweaters for children and movie tickets at a particular cinema on Saturday evening.Source: §2 · p. 2
2.1 Logit Response Model
- The logit curve relates segment sales to marketing cost, with sensitivity highest at market cost and diminishing as cost moves away from it.At market cost, the logit response model's elasticity is −ai/2.Source: §2.1 · pp. 2–3
2.2 Semi-black-box Model
- The semi-black-box model assumes market-cost elasticity depends on contextual variables, estimates it with a neural network, and retains an explicit sales–cost relationship.The shared elasticity information addresses sparse historical budget values across segments; segment-specific sensitivity coefficients are also learned.Source: §2.2 · p. 3
3 BUDGET ALLOCATION
The section formulates sales-maximizing budget allocation across market segments and develops continuous and discrete methods that accommodate budget and ROI constraints. Its continuous method uses convex reformulation and a one-dimensional bisection search; discrete costs are handled through a knapsack formulation.
3.1 Problem Formulation
- The allocation problem maximizes total sales across N market-segments subject to a budget bound, where positive B limits cost and negative B imposes a profit lower bound.The decision variables are the unit costs assigned to each segment.Source: §3.1 · p. 3
- Because the original formulation is non-convex in segment costs, the authors reformulate it as an equivalent convex problem in market shares.The constraint function in the reformulation is strongly convex.Source: §3.1 · p. 3
3.2 Algorithm
- KKT conditions reduce the continuous allocation to finding a dual variable λ whose root yields the optimal segment allocations.The segment variables can be represented using the same dual variable, and the paper uses the Lambert W function in deriving the conditions.Source: §3.2 · p. 4, §3.2.1 · p. 4
3.2.2 Bisection method.
- When Assumption 2 holds, bisection can find a root satisfying the allocation constraint, with early termination also allowed by an objective-gap condition.The root is defined by д(λ)=0; the cited figure plots objective and exceeded budget against λ.Source: §3.2.2 · p. 4, Figure 3 · p. 5
3.2.3 Time complexity.
- In practice, the algorithm converges in a few iterations and each iteration has O(N) complexity, supporting large-scale problems.Source: §3.2.3 · p. 5
3.3.1 ROI.
- An ROI lower bound can replace the specific budget bound B, and the resulting optimization remains solvable by Algorithm 1 with a modified segment-allocation expression.The input B is no longer required.Source: §3.3.1 · p. 5
3.3.2 Discrete settings.
- For discrete segment costs, the authors construct a Multiple Choice Knapsack Problem with market-segments as classes and budget B as capacity.The paper also describes an O(N)-time Dyer-Zemel approximation algorithm and notes that ROI-constrained discrete settings can be supported with adaptations.Source: §3.3.2 · p. 5
4 EXPERIMENT
Offline experiments evaluate market-response prediction and allocation algorithms, while a cinema-based A/B test compares uniform budget allocation with the proposed approach. The reported real-world results show improved sales with less marketing spend.
4.1.1 Datasets. •
- On Breakfast (4,000 market-segments over 156 weeks) and Taopiaopiao (60,000 market-segments over 152 days), results were measured using Relative Mean Absolute Error (RMAE).Source: §4.1.1 · pp. 5–6, §4.1.3 · p. 6
4.1.3 Results.
- The semi-black-box model significantly outperformed the logit model, especially with limited training data, across the evaluated partition ratios.The authors attribute this to information sharing across segments, which relieves data sparseness.Source: §4.1.3 · p. 6, Figure 4 · p. 6
4.2.1 Setups.
- In synthetic simulations with 100 market-segments, the proposed allocation algorithm converged in usually fewer than 10 iterations.As g(λ) approached zero, the objective value approached its maximum; the convergence examples are grouped by column.Source: §4.2.2 · p. 6, Figure 5 · p. 6, §4.2.1 · p. 6
4.2.3 Parameter sensitivity.
- The parameter-sensitivity simulations introduced random relative biases to a_i or b_i and assessed objective error and exceeded budget over more than 1,000 runs.The bias was sampled from U(−0.2, 0.2) for each group of parameters.Source: §4.2.3 · p. 6
- Objective error remained below 1% even with 20% estimation bias, while budget was more sensitive than the objective and the algorithm was less sensitive to a_i than b_i.Exceeded budget stayed below 5% when estimation biases of a_i and b_i were below 10% and 5%, respectively; more than 1,000 Monte Carlo simulations were conducted.Source: §4.2.3 · pp. 6–7, Figure 6 · p. 7
4.2.4 Discrete settings.
- For discrete options spaced less than 1 apart, the reported upper bound on approximation error was no more than 1%.As options became sparser, the upper bound increased; the authors note that the actual error is unknown, and recommend Dyer-Zemel directly when options are few and runtime is not a bottleneck.Source: §4.2.4 · p. 7, Table 1 · p. 7
4.3.1 Setups.
- The cinema A/B test compared uniform allocation with the proposed approach across matched groups of 400 cinemas over five weeks, under equal weekly cost upper bounds.The real-world setting updates the cost upper bound weekly and readjusts allocation daily; discrete constraints address customers’ preference for 99-ending prices.Source: §4.3.1 · p. 7, §4.3 · p. 7
4.3.2 Results.
- The proposed approach achieved average weekly sales improvement above 6% while spending 40% less on marketing by allocating budget to the right market segments, with average ROI improvement above 40%.Source: §4.3.2 · p. 8
5 RELATED WORK
Marketing allocation has a long research history, but online markets add dynamic challenges; prior work addresses forecasting and optimization, while this paper combines a data-sharing response model with allocation optimization.
5 RELATED WORK
- Online business brings dynamic, complex marketing conditions, and improving allocation efficiency has practical benefits.Prior data-driven work includes forecasting and optimization.Source: §5 · p. 8
- Neural networks can forecast accurately, but black-box models obscure cost-sales relationships and are difficult to optimize; demand curves provide explicit relationships.The paper focuses on logit demand curves, whose separate segment fitting can cause data sparseness, and extends them with neural networks.Source: §5 · p. 8
- The paper combines information-sharing logit response curves with an equivalent convex reformulation for budget allocation.Earlier works address product pricing without budget constraints.Source: §5 · p. 8
- Prior marketing and pricing optimization uses integer programming, relaxations, sequential decision models, and robust optimization.For discrete decisions, the paper constructs an MCKP from the relaxed continuous solution, with 99-ending display prices as one motivation.Source: §5 · p. 8
6 CONCLUSION
The paper presents a unified framework that forecasts segment responses and optimizes budget allocation under varied constraints. It reports improved Taopiaopiao sales with lower marketing spend and identifies further modeling and optimization topics for future work.
6 CONCLUSION
- Sales improve over 6% while marketing spend falls 40% in Taopiaopiao daily marketing.The paper also reports offline experiments and online A/B testing as evidence of effectiveness.Source: §6 · p. 9
- The framework forecasts segment responses with a neural-network-enhanced logit model, then optimizes allocation using binary search on a dual variable with O(N) work per iteration.The framework supports cost upper bounds, profit lower bounds, ROI lower bounds, and discrete constraints with minor adaptations.Source: §6 · p. 9
- Future work includes modeling the relationship between market cost and contextual variables and supporting boundary constraints on decision variables.The paper also identifies theoretical analysis of discrete-setting approximation error as a future topic.Source: §6 · p. 9
A.1 Implementation
The implementation appendix introduces additional details to improve reproducibility, including deployment and experiment tooling.
A.1 Implementation
- The appendix presents implementation details with the stated aim of improving reproducibility.Source: §A.1 · p. 10
- The section frames these details as supplementary implementation information rather than a description of the allocation method.Source: §A.1 · p. 10, §A.1.1 · p. 10
- The implementation details cover languages, packages, and frameworks used in deployment and experiments.Source: §A.1.1 · p. 10
A.1.1 Software versions. •
The appendix reports software versions and notes implementation choices for large-scale forecasting and distributed optimization.
A.1.1 Software versions. •
- The listed software includes Python 2.7.15, Cython 0.28.5, SQL, NumPy 1.15.4, SciPy 1.1.0, Tensorflow 1.11.0, MaxCompute, and Spark 2.3.0.Source: §A.1.1 · p. 10
- For extremely large forecasting training sets, use batch gradient descent rather than gradient descent, and GPUs are preferred.Source: §A.1.2 · p. 10
- Inference can be parallelized, while optimization can run across market segments in a distributed framework such as Spark.Source: §A.1.2 · p. 10
A.1.3 Other tips. •
The appendix gives implementation guidance for the semi-black-box model and optimization algorithm, alongside proof excerpts establishing convexity and monotonicity properties.
A.1.3 Other tips. •
- Semi-black-box model results are described as insensitive to neural-network hyperparameters; more layers or higher dimensions are unnecessary.Source: §A.1.3 · p. 10
- High-precision computation of q in Eq. (15b) may prevent exponent overflow when ϵ is very small, a setting usually unnecessary.Source: §A.1.3 · p. 10
- The appendix points to the Dyer-Zemel pseudocode in as an implementation reference and notes two misprints.Source: §A.1.3 · p. 10
A.2.2 Theorem 2.
- Theorem 2's Hessian bound establishes strict convexity of g(q) for the stated positive parameters and 0 < q_i < 1.Source: §A.2.2 · p. 10
A.2.4 Theorem 4.
- Under the stated positive-parameter and domain conditions, Theorem 4 says f(λ) and g(λ) are strictly decreasing.Source: §A.2.4 · pp. 10–11
A.2.5 Theorem 5.
- Theorem 5 establishes strong convexity of g′(q) and strict decrease of g′(λ) under its stated conditions.Source: §A.2.5 · p. 11