1. General Definition
- In multi-objective evaluation, one solution (recommendation list, model, or strategy) is said to dominate another if it is at least as good on all metrics and strictly better on at least one.
- This comes from Pareto dominance in decision theory / multi-objective optimization.
Formally:
Let system A and B be evaluated on metrics $(m_1, m_2, \dots, m_k)$.
- A dominates B if:
- $\forall j, \; m_j(A) \geq m_j(B) \quad \text{and} \quad \exists j, \; m_j(A) > m_j(B)$
2. Application in Recommender Systems
Recommender systems often balance multiple objectives:
- Accuracy (precision, recall, NDCG)
- Coverage (item coverage, user coverage, catalog coverage)
- Diversity (intra-list diversity)
- Novelty / Serendipity
- Fairness (across users or items)
When comparing algorithms:
- If Model A has equal or higher accuracy, diversity, and fairness compared to Model B, and strictly higher on at least one, then Model A dominates Model B.
- Dominated models can be discarded because there’s no reason to choose them.
3. Pareto Front
- In practice, very few models dominate others across all dimensions.
- Instead, we look for the Pareto front: the set of non-dominated models.
- Each model on the Pareto front represents a different trade-off.
- Example: One model may maximize accuracy but have lower coverage.
- Another may improve coverage but slightly reduce accuracy.
- Decision makers then pick a point on the Pareto front based on business goals.
4. Example
Suppose we evaluate two recommenders (Top-10 recommendations):
| Model | Precision@10 | Catalog Coverage | Diversity |
|---|---|---|---|
| A | 0.32 | 0.25 | 0.40 |
| B | 0.32 | 0.25 | 0.35 |
- Model A dominates Model B (same precision & coverage, but higher diversity).
Now consider:
| Model | Precision@10 | Catalog Coverage | Diversity |
|---|---|---|---|
| C | 0.35 | 0.15 | 0.30 |
| D | 0.30 | 0.30 | 0.45 |
- Neither C nor D dominates the other.
- Both are on the Pareto front, representing different trade-offs.
5. Why It Matters
- Research papers: domination analysis shows whether a proposed method truly improves over baselines.
- Industry deployment: helps pick models that maximize utility across goals (e.g., accuracy + fairness).
- Avoids cherry-picking a single metric like precision while ignoring coverage or fairness.
Summary:
In recommender systems, dominating means one model’s performance is at least as good on all evaluation metrics and strictly better on at least one. It comes from Pareto dominance and is used in multi-objective optimization. Models that are not dominated form the Pareto front, representing optimal trade-offs between competing goals like accuracy, coverage, diversity, and fairness.