Optimization with delay-induced bifurcations

Area of Science:

• Nonlinear Dynamics
• Computational Optimization
• Analog Computing

Background:

• Optimization seeks the global minimum of cost functions, traditionally using digital or quantum computers with inherent limitations.
• Existing methods like simulated annealing and quantum computing employ noise or tunneling to escape local minima.
• Non-quantum analog devices offer potential for new optimization approaches but require novel principles.

Purpose of the Study:

• To propose and investigate a new optimization principle based on delay-induced bifurcations.
• To explore the potential of analog devices for deterministic optimization.
• To provide a method for overcoming local minima without relying on noise or quantum effects.

Main Methods:

• Investigating nonlinear delay-differential equations where the system's dynamics depend on a delayed variable.
• Utilizing delay-induced bifurcations to destroy local attractors in gradient descent settings.
• Formulating prerequisites for predictable bifurcation scenarios in dynamical systems.

Main Results:

• Delay-induced bifurcations can deterministically destroy local attractors, enabling exploration of all minima.
• Tuning the delay in a gradient descent setting forces the system to wander across potential energy landscape minima.
• This deterministic approach mimics noise-induced behavior but without randomness.

Conclusions:

• A novel, deterministic optimization principle is conceived using delay-induced bifurcations.
• This principle is potentially implementable in non-quantum analog devices.
• Tuning delay offers a new pathway for robust optimization, avoiding confinement to local minima.