Optimizing by Comparison
Normal direction descent · Scheinberg & Xiong,
arXiv:2604.26867
Match a color
Favorite shade
2D
3D
Undo
Restart
New colors
Computer answers
Reveal
Which side is closer to the target?
A
Target
B
A
←
Same
↓
B
→
40 more comparisons
Hidden objective
What the algorithm sees
better
worse
same
bracket
Algorithm
Settings
Planar bisection steps
Comparison radius
Comparison radius rule
Fixed h
Adaptive (Algorithm 3)
Stepsize
η_k = c/√k
Constant η
Comparison budget
20, then reveal
40, then reveal
60, then reveal
100, then reveal
No limit
Computer speed
Slow
Normal
Fast