Solving Nash equilibrium is the key challenge in normal-form games with large strategy spaces, wherein open-ended learning framework provides an efficient approach. Previous studies invariably employ diversity as a conduit to foster the advancement of strategies. Nevertheless, diversity-based algorithms can only work in zero-sum games with cyclic dimensions, which lead to limitations in their applicability. Here, we propose an innovative unified open-ended learning framework SC-PSRO, i.e., Self-Confirming Policy Space Response Oracle, as a general framework for both zero-sum and general-sum games. In particular, we introduce the advantage function as an improved evaluation metric for strategies, allowing for a unified learning objective for agents in normal-form games. Concretely, SC-PSRO comprises three quintessential components: 1) A Diversity Module, aiming to avoid strategies to be constrained by the cyclic structure. 2) A LookAhead Module, devised for the promotion of strategy in the transitive dimension. This module is theoretically guaranteed to learn strategies in the direction of the Nash equilibrium. 3) A Confirming-based Population Clipping Module, contrived for tackling the equilibrium selection problem in general-sum games. This module can be applied to learn equilibria with optimal rewards, which to our knowledge is the first improvement for general-sum games. Our experiments indicate that SC-PSRO accomplishes a considerable decrease in exploitability in zero-sum games and an escalation in rewards in general-sum games, markedly surpassing antecedent methodologies. Code will be released upon acceptance.

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