Wasn’t there a fairness/continuity condition in the original ADT paper that if there were two “agents” that converged to always taking the same action, then the embedder would assign them the same value? (more specifically, if Et(|At−Bt|)<δ, then Et(|Et(At)−Et(Bt)|)<ϵ ) This would mean that it’d be impossible to have Et(Et(ADTt,ϵ)) be low while Et(Et(straightt)) is high, so the argument still goes through.
Although, after this whole line of discussion, I’m realizing that there are enough substantial differences between the original formulation of ADT and the thing I wrote up that I should probably clean up this post a bit and clarify more about what’s different in the two formulations. Thanks for that.
Yes, the continuity condition on embedders in the ADT paper would eliminate the embedder I meant. Which means the answer might depend on whether ADT considers discontinuous embedders. (The importance of the continuity condition is that it is used in the optimality proof; the optimality proof can’t apply to chicken for this reason).
Wasn’t there a fairness/continuity condition in the original ADT paper that if there were two “agents” that converged to always taking the same action, then the embedder would assign them the same value? (more specifically, if Et(|At−Bt|)<δ, then Et(|Et(At)−Et(Bt)|)<ϵ ) This would mean that it’d be impossible to have Et(Et(ADTt,ϵ)) be low while Et(Et(straightt)) is high, so the argument still goes through.
Although, after this whole line of discussion, I’m realizing that there are enough substantial differences between the original formulation of ADT and the thing I wrote up that I should probably clean up this post a bit and clarify more about what’s different in the two formulations. Thanks for that.
Yes, the continuity condition on embedders in the ADT paper would eliminate the embedder I meant. Which means the answer might depend on whether ADT considers discontinuous embedders. (The importance of the continuity condition is that it is used in the optimality proof; the optimality proof can’t apply to chicken for this reason).