# Local Optimum **Domain:** Optimization / Machine Learning **Doc Type:** Technical Concept Node **Maturity:** Foundational ## Definition A **local optimum** is a solution better than nearby alternatives within an [[wiki/Optimization Landscape|optimization landscape]] but not necessarily the best solution available across the full space. ## Historical Context The risk of hill-climbing becoming trapped at local maxima or minima was already an explicit concern in work by [[wiki/Shun-Ichi Amari|Shun-Ichi Amari]] and [[wiki/Geoffrey Hinton|Geoffrey Hinton]] before the later neural-network revival. ## Key Insight **Local improvement does not guarantee global adequacy.** ## See Also [[wiki/Gradient Descent|Gradient Descent]], [[wiki/Stochastic Gradient Descent|Stochastic Gradient Descent]], [[wiki/Optimization|Optimization]]