The existence of simple uncoupled noregret learning dynamics that converge to correlated equilibria in normalform games is a celebrated result in the theory of multiagent systems. Specifically, it has been known for more than 20 years that when all players seek to minimize their internal regret in a repeated normalform game, the empirical frequency of play converges to a normalform correlated equilibrium. Extensiveform games generalize normalform games by modeling both sequential and simultaneous moves, as well as imperfect information. Because of the sequential nature and presence of private information in the game, correlation in extensiveform games possesses significantly different properties than its counterpart in normalform games, many of which are still open research directions. Extensiveform correlated equilibrium (EFCE) has been proposed as the natural extensiveform counterpart to the classical notion of correlated equilibrium in normalform games. Compared to the latter, the constraints that define the set of EFCEs are significantly more complex, as the correlation device must keep into account the evolution of beliefs of each player as they make observations throughout the game. Due to that significant added complexity, the existence of uncoupled learning dynamics leading to an EFCE has remained a challenging open research question for a longmore »
Hindsight and Sequential Rationality of Correlated Play
Driven by recent successes in twoplayer, zerosum game solving and playing, artificial intelligence work on games has increasingly focused on algorithms that produce equilibriumbased strategies. However, this approach has been less effective at producing competent players in generalsum games or those with more than two players than in twoplayer, zerosum games. An appealing alternative is to consider adaptive algorithms that ensure strong performance in hindsight relative to what could have been achieved with modified behavior. This approach also leads to a gametheoretic analysis, but in the correlated play that arises from joint learning dynamics rather than factored agent behavior at equilibrium. We develop and advocate for this hindsight rationality framing of learning in general sequential decisionmaking settings. To this end, we reexamine mediated equilibrium and deviation types in extensiveform games, thereby gaining a more complete understanding and resolving past misconceptions. We present a set of examples illustrating the distinct strengths and weaknesses of each type of equilibrium in the literature, and prove that no tractable concept subsumes all others. This line of inquiry culminates in the definition of the deviation and equilibrium classes that correspond to algorithms in the counterfactual regret minimization (CFR) family, relating them to all others in more »
 Award ID(s):
 1761546
 Publication Date:
 NSFPAR ID:
 10290817
 Journal Name:
 Proceedings of the AAAI Conference on Artificial Intelligence
 ISSN:
 21595399
 Sponsoring Org:
 National Science Foundation
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The existence of simple, uncoupled noregret dynamics that converge to correlated equilibria in normalform games is a celebrated result in the theory of multiagent systems. Specifically, it has been known for more than 20 years that when all players seek to minimize their internal regret in a repeated normalform game, the empirical frequency of play converges to a normalform correlated equilibrium. Extensiveform (that is, treeform) games generalize normalform games by modeling both sequential and simultaneous moves, as well as private information. Because of the sequential nature and presence of partial information in the game, extensiveform correlation has significantly different properties than the normalform counterpart, many of which are still open research directions. Extensiveform correlated equilibrium (EFCE) has been proposed as the natural extensiveform counterpart to normalform correlated equilibrium. However, it was currently unknown whether EFCE emerges as the result of uncoupled agent dynamics. In this paper, we give the first uncoupled noregret dynamics that converge to the set of EFCEs in nplayer generalsum extensiveform games with perfect recall. First, we introduce a notion of trigger regret in extensiveform games, which extends that of internal regret in normalform games. When each player has low trigger regret, the empirical frequency of playmore »

The existence of simple, uncoupled noregret dynamics that converge to correlated equilibria in normalform games is a celebrated result in the theory of multiagent systems. Specifically, it has been known for more than 20 years that when all players seek to minimize their internal regret in a repeated normalform game, the empirical frequency of play converges to a normalform correlated equilibrium. Extensiveform (that is, treeform) games generalize normalform games by modeling both sequential and simultaneous moves, as well as private information. Because of the sequential nature and presence of partial information in the game, extensiveform correlation has significantly different properties than the normalform counterpart, many of which are still open research directions. Extensiveform correlated equilibrium (EFCE) has been proposed as the natural extensiveform counterpart to normalform correlated equilibrium. However, it was currently unknown whether EFCE emerges as the result of uncoupled agent dynamics. In this paper, we give the first uncoupled noregret dynamics that converge to the set of EFCEs in nplayer generalsum extensiveform games with perfect recall. First, we introduce a notion of trigger regret in extensiveform games, which extends that of internal regret in normalform games. When each player has low trigger regret, the empirical frequency of playmore »