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Transfer Learning for Nonparametric Contextual Dynamic Pricing
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Proposes TLDP, a UCB-style adaptive partitioning (contextual zooming) algorithm for nonparametric contextual dynamic pricing with transfer from a source domain under covariate shift, with matching minimax upper and lower regret bounds under a Lipschitz reward.
Problem
Dynamic pricing with limited target data (new product or market) where the reward function is nonparametric and Lipschitz; the goal is to leverage pre-collected source data under covariate shift to reduce target-domain regret.
Approach
Extends contextual zooming/UCB to the joint covariate-price space, letting source data count toward node confidence and partition refinement thresholds, with transfer exponent and exploration coefficient quantifying how useful the source data is; derives minimax-optimal regret rates.
Key results
- Theory: TLDP regret is of order n_Q{n_Q+(kappa n_P)^{(d+3)/(d+3+gamma)}}^{-1/(d+3)} up to logs, matched by a minimax lower bound, and the target-only special case gives n_Q^{(d+2)/(d+3)}.
- Simulations show TLDP beats Target-Only TLDP, ABE and ExUCB in both scenarios; ExUCB is best in Scenario 1 (linear in covariates) while TLDP leads in Scenario 2.
- On the auto loan data (East South Central target), TLDP with all source data (n_P = n) reduces mean regret from 71.95 (no source) to 48.72 at Pacific source, versus ExUCB 64.91 and ABE 70.81.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add Mountain source data to TLDP (n_P = n) instead of using no source data | TLDP · Auto loan, East South Central target; Mountain source | cumulative regret: 71.95 (2.87) -> 50.23 (7.34) | Helped |
| Add East North Central source data to TLDP (n_P = n) instead of using no source data | TLDP · Auto loan, East South Central target; East North Central source | cumulative regret: 71.95 (2.87) -> 51.92 (7.09) | Helped |
| Add West South Central source data to TLDP (n_P = n) instead of using no source data | TLDP · Auto loan, East South Central target; West South Central source | cumulative regret: 71.95 (2.87) -> 49.85 (7.97) | Helped |
| Add Pacific source data to TLDP (n_P = n) instead of using no source data | TLDP · Auto loan, East South Central target; Pacific source | cumulative regret: 71.95 (2.87) -> 48.72 (8.27) | Helped |
Surprising findings
- ExUCB, despite a higher variance, achieves the lowest regret without source data on the auto loan dataset, while TLDP without source data is slightly worse than ABE and ExUCB.
Limitations
- Optimality requires prior knowledge of the transfer exponent gamma and exploration coefficient kappa, which are often unknown in practice.
- Analysis covers only a single source dataset; multiple sources are left for future work.
- Real-data evaluation approximates the true reward with a random forest trained on target data.
Experimental setup
Datasets: auto loan dataset (208,085 applications from an online US lender, 2002-2004) synthetic covariate-price data
Benchmarks: synthetic dynamic pricing scenarios auto loan dataset
Metrics: cumulative regret mean and standard deviation over 100 simulations
Baselines: Target-Only TLDP ABE ExUCB
Builds on: contextual zooming adaptive binning and exploration (ABE) transfer learning under covariate shift for contextual MAB
Closest papers by meaning
- Transfer Faster, Price Smarter: Minimax Dynamic Pricing under Cross-Market Preference Shift (NeurIPS 2025 · similarity 0.91)
- Learning to price with resource constraints: from full information to machine-learned prices (NeurIPS 2025 · similarity 0.88)
- Pricing with Contextual Elasticity and Heteroscedastic Valuation (ICML 2024 · similarity 0.88)
- Improved Algorithms for Contextual Dynamic Pricing (NeurIPS 2024 · similarity 0.87)
- Contextual Dynamic Pricing with Heterogeneous Buyers (NeurIPS 2025 · similarity 0.87)
- Optimal Contextual Pricing under Agnostic Non-Lipschitz Demand (NeurIPS 2026 · similarity 0.87)
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