A Lower Bound on Swap Regret in Extensive-Form Games

Recent simultaneous works by Peng and Rubinstein 2024 and Dagan et al. 2024 have demonstrated the existence of a no-swap-regret learning algorithm that can reach average swap regret against an adversary in any extensive-form game within m^ O (1/) rounds, where m is the number of nodes in the game tree. However, the question of whether a poly (m, 1/) -round algorithm could exist remained open. In this paper, we show a lower bound that precludes the existence of such an algorithm. In particular, we show that achieving average swap regret against an oblivious adversary in general extensive-form games requires at least exp ( (\m^{1/14, ^-1/6\}) ) rounds.