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Correlated Equilibrium is a solution concept that is more general than NashEquilibrium (NE) and can lead to outcomes with better social welfare. However,its natural extension to the sequential setting, the \textit{Extensive FormCorrelated Equilibrium} (EFCE), requires a quadratic amount of space to solve,even in restricted settings without randomness in nature. To alleviate theseconcerns, we apply \textit{subgame resolving}, a technique extremely successfulin finding NE in zero-sum games to solving general-sum EFCEs. Subgame resolvingrefines a correlation plan in an \textit{online} manner: instead of solving forthe full game upfront, it only solves for strategies in subgames that arereached in actual play, resulting in significant computational gains. In thispaper, we (i) lay out the foundations to quantify the quality of a refinedstrategy, in terms of the \textit{social welfare} and \textit{exploitability}of correlation plans, (ii) show that EFCEs possess a sufficient amount ofindependence between subgames to perform resolving efficiently, and (iii)provide two algorithms for resolving, one using linear programming and theother based on regret minimization. Both methods guarantee \textit{safety},i.e., they will never be counterproductive. Our methods are the first time anonline method has been applied to the correlated, general-sum setting.

Safe Subgame Resolving for Extensive Form Correlated Equilibrium