Nonconvex Optimization

Finite-budget nonconvex optimization can benefit from treating stagnation as an event rather than only reducing local step sizes. A learned optimizer can combine structured local descent with memory and energy shaping to escape or redirect. A first-order optimizer can waste remaining oracle calls refining a nearby attractive stationary basin. The paper addresses fixed-budget nonconvex minimization in settings where local descent may fail by being too stable. The target problem minimizes an objective over a domain using oracle observations that may include values and several gradient types.