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Consensus-Based Optimization for Saddle Point Problems
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Consensus-Based Optimization for Saddle Point Problems
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In this paper, we propose consensus-based optimization for saddle point problems (CBO-SP), a novel multi-particle metaheuristic derivative-free optimization method capable of provably finding global Nash equilibria. Following the idea of swarm intelligence, the method employs a group of interacting particles, which perform a minimization over one variable and a maximization over the other. This paradigm permits a passage to the mean-field limit, which makes the method amenable to theoretical analysis and allows to obtain rigorous convergence guarantees under reasonable assumptions about the initialization and the objective function, which most notably include nonconvex-nonconcave objectives.
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Cited by 1 Pith paper
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Consensus-Based Optimization with Truncated Noise
Truncating noise in CBO bounds higher moments of the particle law and enables a rigorous proof of convergence in expectation to the global minimizer via Wasserstein-2 distance analysis under minimal assumptions.
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