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a knapsack riddle?

Posted in Books, pictures, R, Statistics, Travel with tags , , , , , , on February 13, 2017 by xi'an

gear

The [then current now past] riddle of the week is a sort of multiarmed bandits optimisation. Of sorts. Or rather a generalised knapsack problem. The question is about optimising the allocation of 100 undistinguishable units to 10 distinct boxes against a similarly endowed adversary, when the loss function is

L(x,y)=(x_1>y_1)-(x_1<y_1)+...+10((x_{10}>y_{10})-(x_{10}<y_{10}))

and the distribution q of the adversary is unknown. As usual (!), the phrasing of the riddle is somewhat ambiguous but I am under the impression that the game is played sequentially, hence that one can learn about the distribution of the adversary, at least when assuming this adversary keeps the same distribution q at all times. Continue reading