Interactive lesson~20 minAdvanced
Optimization Theory
Optimization is the art of moving through a landscape without seeing the whole terrain. Gradients point locally; geometry decides whether that is enough.
ConvexityLagrangiansConvergence
Mental model
Training is navigation under limited visibility.
Convexity, constraints, learning-rate schedules, and saddle points explain why some training runs glide and others thrash.
Progress speed
balanced63% modeled signal
Stability
balanced59% modeled signal
Final fit
balanced55% modeled signal
Concept pipeline
Build the idea in four moves
Interactive lab
Stabilize a difficult optimization run.
Objective
Define what “better” means as a scalar loss.
Focus lens
The part that usually clicks late
Convexity
Convex losses make local improvement globally trustworthy.
Progress speed
63
Stability
59
Final fit
55
Knowledge check
Why can a high learning rate fail on sharp curvature?
Next horizon
Where this topic is headed
Second-order methods
Sharpness-aware minimization
Constrained optimization