Swarm-Based Gradient Descent Method for Non-Convex Optimization
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We introduce a new Swarm-Based Gradient Descent (SBGD) method for non-convex optimization. The swarm consists of agents, each is identified with a position, x, and mass, m. The key to their dynamics is communication: masses are being transferred from agents at high ground to low(-est) ground. At the same time, agents change positions with step size, h=h(x,m), adjusted to their relative mass: heavier agents proceed with small time-steps in the direction of local gradient, while lighter agents take larger time-steps based on a backtracking protocol. Accordingly, the crowd of agents is dynamically divided between `heavier' leaders, expected to approach local minima, and `lighter' explorers. With their large-step protocol, explorers are expected to encounter improved position for the swarm; if they do, then they assume the role of `heavy' swarm leaders and so on. Convergence analysis and numerical simulations in one-, two-, and 20-dimensional benchmarks demonstrate the effectiveness of SBGD as a global optimizer.
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