On Local Equilibrium in Non-Concave Games
Primary Area: learning theory
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Keywords: non-concave games, learning in games, no-regret algorithms, local equilibrium
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TL;DR: We present a new solution concept for non-concave games that captures the convergence guarantee of online gradient descent and no-regret learning.
Abstract: While Online Gradient Descent and other no-regret learning procedures are known to efficiently converge to coarse correlated equilibrium in games where each agent's utility is concave in their own strategies, this is not the case when the utilities are non-concave, a situation that is common in machine learning applications where the agents' strategies are parametrized by deep neural networks, or the agents' utilities are computed by a neural network, or both. Indeed, non-concave games present a host of game-theoretic and optimization challenges: (i) Nash equilibria may fail to exist; (ii) local Nash equilibria exist but are intractable; and (iii) mixed Nash, correlated, and coarse correlated equilibria have infinite support, in general, and are intractable. To sidestep these challenges we propose a new solution concept, termed *local correlated equilibrium*, which generalizes local Nash equilibrium. Importantly, we show that this solution concept captures the convergence guarantees of Online Gradient Descent and no-regret learning, which we show efficiently converge to this type of equilibrium in non-concave games with smooth utilities.
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Submission Number: 8732
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