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Matrix Multiplicative Weights Updates in Quantum Zero-Sum Games: Conservation Laws & Recurrence
Rahul Jain · Georgios Piliouras · Ryann Sim

Thu Dec 01 09:00 AM -- 11:00 AM (PST) @ Hall J #740

Recent advances in quantum computing and in particular, the introduction of quantum GANs, have led to increased interest in quantum zero-sum game theory, extending the scope of learning algorithms for classical games into the quantum realm. In this paper, we focus on learning in quantum zero-sum games under Matrix Multiplicative Weights Update (a generalization of the multiplicative weights update method) and its continuous analogue, Quantum Replicator Dynamics. When each player selects their state according to quantum replicator dynamics, we show that the system exhibits conservation laws in a quantum-information theoretic sense. Moreover, we show that the system exhibits Poincare recurrence, meaning that almost all orbits return arbitrarily close to their initial conditions infinitely often. Our analysis generalizes previous results in the case of classical games.

Author Information

Rahul Jain (National University of Singapore)
Georgios Piliouras (Singapore University of Technology and Design)
Ryann Sim (Singapore University of Technology and Design)

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