Fundamental Limits Of Learning In Data-Driven Problems
summary
Proves exact minimax rates for entropy estimation without a positive density lower bound and achieves them via a two-stage approximation that handles vanishing f regions; analyzes the profile MLE, proving it is optimal for group-invariant estimation but incurs an explicit penalty with a sharp n^{-1/3} threshold and requires a competitive analysis rather than classical expansions; develops bidding algorithms for first-price auctions that exploit the reward/feedback interplay, obtain optimal regret in many settings and are deployed by Verizon Media DSP.
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chapters (13)
- 0:00Intro
- 0:35Motivation
- 1:12Example: dynamic assortment optimization
- 1:35Why fundamental limit counts
- 3:45Example 1: nonparametric entropy estimation
- 4:08Rich line of prior research
- 5:00Our results
- 6:00Example II: theory of the profile MLE
- 7:03Profile and PMLE
- 8:09Questions and our answers
- 10:03Example III: learning to bid in first-price auctions
- 10:38Bidder's challenge
- 13:22My research picture
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