Blackwell approachability with approximation oracles for both players: the downward closure of α_X α_Y^{-1} S is efficiently approachable at rate O(1/sqrt(T)).
An analog of the minimax theorem for vector payoffs
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Blackwell's Approachability with Approximation Algorithms
Blackwell approachability with approximation oracles for both players: the downward closure of α_X α_Y^{-1} S is efficiently approachable at rate O(1/sqrt(T)).