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Transfer Faster, Price Smarter: Minimax Dynamic Pricing under Cross-Market Preference Shift
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Proposes CM-TDP, a bias-corrected aggregate-then-debias transfer dynamic pricing algorithm that uses multiple source markets under utility-model shift, with regret bounds for linear (sparse difference) and RKHS utilities.
Problem
Contextual dynamic pricing for a data-poor target market that can leverage K auxiliary markets (offline logs or concurrent streams) whose mean utilities differ by a structured preference shift.
Approach
Aggregate source-market data with an unregularized MLE or kernel regression, then debias the aggregate on target data with an l1-regularized (or RKHS-norm) correction, and post prices optimistically from the resulting utility estimate; episodic doubling schedule for O2O-on and phased transfer for O2O-off.
Key results
- In simulations with T=2000, CM-TDP-O2O-on reduces cumulative regret by roughly 43-55% on average versus single-market learning (peaking at 75%).
- Learning speed up to 9x faster in reaching single-market final estimation error with K=10 sources (sparse-difference setting).
- Claimed minimax-optimal regret rates for linear (d/K + s0 up to log factors) and RKHS utilities, with matching lower bounds stated.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Transfer from live source markets | CM-TDP O2O_on Linear · Sparse-difference markets, averaged over d∈{10,15,20} | cumulative regret reduction: 54% | Helped |
| Transfer from live source markets | CM-TDP O2O_on RKHS · Sparse-difference markets, averaged over d∈{10,15,20} | cumulative regret reduction: 55% | Helped |
| Transfer from offline source data | CM-TDP O2O_off Linear · Sparse-difference markets, averaged over d∈{10,15,20} | cumulative regret reduction: 45% | Helped |
| Transfer from offline source data | CM-TDP O2O_off RKHS · Sparse-difference markets, averaged over d∈{10,15,20} | cumulative regret reduction: 43% | Helped |
| Increase the number of live source markets | CM-TDP O2O_on · Sparse-difference markets | cumulative regret reduction: 15% -> 71% (Linear); 17% -> 73% (RKHS) | Helped |
| Increase the offline source log size | CM-TDP O2O_off · Sparse-difference markets | cumulative regret reduction: 20% -> 56% (Linear); 15% -> 56% (RKHS) | Helped |
| Transfer from live source markets | CM-TDP O2O_on Linear · Sparse-difference markets, averaged over d∈{10,15,20} | standard error reduction: 31% | Helped |
| Transfer from live source markets | CM-TDP O2O_on RKHS · Sparse-difference markets, averaged over d∈{10,15,20} | standard error reduction: 29% | Helped |
| Transfer from offline source data | CM-TDP O2O_off Linear · Sparse-difference markets, averaged over d∈{10,15,20} | standard error reduction: 24% | Helped |
| Transfer from offline source data | CM-TDP O2O_off RKHS · Sparse-difference markets, averaged over d∈{10,15,20} | standard error reduction: 25% | Helped |
| Transfer from live source markets | CM-TDP O2O_on · Sparse-difference markets, averaged over d∈{10,15,20} | learning speed: 6.0$\times$ (Linear); 6.2$\times$ (RKHS) | Helped |
| Use concurrent source streams rather than offline source logs | CM-TDP Linear · Sparse-difference markets, averaged over d∈{10,15,20} | cumulative regret reduction: 45% -> 54% | Helped |
Limitations
- Assumes homogeneous covariate distributions across markets; covariate shift not handled.
- No mechanism to down-weight or exclude adversarial source markets with large parameter gaps.
- Evaluation is limited to synthetic simulations with logistic noise and T=2000.
Experimental setup
Datasets: simulated linear and RKHS demand data
Benchmarks: simulated pricing markets (identical, sparse-difference, dense-difference)
Metrics: cumulative regret standard error learning speed
Baselines: single-market (no transfer) dynamic pricing
Builds on: Meta Dynamic Pricing TLDP MOLAR
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