Optimizing Data-to-Learning-to-Action by Steven Flinn

Author:Steven Flinn
Language: eng
Format: epub, pdf
Publisher: Apress, Berkeley, CA

So, again, there is still a priori uncertainty because we have a clairvoyant, not a wizard, helping us. But in this case, we (or our model) make the bid-price decision after the prediction of the competitor’s bid is received, and the prediction is guaranteed to be accurate. So, it is optimal to always just bid a bit below the competitor bid that the clairvoyant predicts, as is shown for a given prediction slice, k, in Figure 6-5. Unlike the original case, with perfect predictability our optimal bids now always win the deal and deliver a profit, although in some instances the profit may be relatively small because the predicted competitor bid is low. The total expected value of the learning in this case of perfect predictability (where the “learning” here is having the services of the clairvoyant) is simply the sum of all these individual profits weighted by the probability function of the competitor’s bid price, which the clairvoyant’s predictions necessarily obey, minus the expected profit from the original case. Or, in equation form, if we have n prediction slices:

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