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I am reading the paper Regret Minimization in Games with Incomplete Information on CFR algorithm.

On page 4, the paper defines $R^{T,+}_{i,\text{imm}}=\max\{R^{T}_{i,\text{imm}}, 0\}$ after equation (5). I am confused why it is necessary? It seems to me that since in the definition of $R^{T}_{i,\text{imm}}$ the regret is computed with respect to the optimal action.

  • As everything is in expectation, is mixed-action going to make any difference?

Isn't $R^{T}_{i,\text{imm}}$ always nonzero already?

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