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Online Pricing with Offline Data: Phase Transition and Inverse Square Law
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Increase offline sample size n in the single-price setting when δ is sufficiently large | OPOD · Single historical price | optimal regret: \widetilde \Theta(\sqrt T) -> \widetilde \Theta(\frac{T}{n\delta^2}) -> \widetilde \Theta(\frac{\log T}{\delta^2}) | Helped |
| Increase offline sample size n when δ is small in the single-price setting | OPOD · Single historical price, δ \lesssim T^{-1/4} | optimal regret: \widetilde\Theta(\sqrt T) | No clear effect |
| Move the average historical price closer to the optimal price in the regular case | OPOD · Multiple historical prices, regular case | optimal regret: \frac{T}{n\sigma^2+(n\wedge T)\delta^2} | Hurt |
| Increase dispersion σ of the historical prices in the regular case | OPOD · Multiple historical prices, regular case | optimal regret: \widetilde \Theta \Big( \sqrt T \wedge \frac{T }{n\sigma^2+(n\wedge T) \delta^2}\Big) | Helped |
| Increase dispersion σ when δ is small enough for the corner case | OPOD · Multiple historical prices, corner case | optimal regret: \widetilde \Theta(T\delta^2) -> \widetilde \Theta(\frac{T}{n\sigma^2}) | Mixed |
| Use offline regression and charge its estimated optimal price when nσ² is large and δ is small | M-O3FU · Multiple historical prices | regret: \mathcal{O}(\frac{T}{n\sigma^2}) | Helped |
| Charge the average historical price instead of performing online exploration in the corner case | M-O3FU · Multiple historical prices, corner case | regret: \mathcal{O}(T\delta^2) | Helped |
| Use O3FU's optimistic-revenue decisions rather than a myopic policy without the stated self-exploration conditions | OPOD · Online pricing with offline data | regret | Mixed |
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