David Blackwell: Teacher And Colleague And A Sample Of His Work
summary
Generalizes Von Neumann to vector payoffs and proves: any closed convex target set S is either approachable or excludable. Strategy is explicit and dynamic — at each round compute the average payoff, project to the closest point in S, and pick the mixed action whose reachable payoff polytope meets that supporting hyperplane; a projection-to-nearest-point rule plus a submartingale-style drift yields almost-sure convergence. Blackwell exhibits a nonconvex counterexample; a weaker probabilistic notion of approachability is later settled by Villeneuve 1992.
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chapters (9)
- 0:00Introduction to David Blackwell
- 1:48Blackwell's life and career
- 5:50Note on Bayes estimates
- 8:16Vector minimax theorem
- 13:32Proof of the theorem
- 20:14Approachability analysis
- 28:19Conjectures and conclusions
- 31:04Q&A and discussion
- 37:23Closing remarks
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