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devised and introduced by [[Kunihito Hoki]] and [[Tomoyuki Kaneko]] <ref>[[Kunihito Hoki]], [[Tomoyuki Kaneko]] ('''2014'''). ''[https://www.jair.org/papers/paper4217.html Large-Scale Optimization for Evaluation Functions with Minimax Search]''. [https://www.jair.org/vol/vol49.html JAIR Vol. 49], [https://pdfs.semanticscholar.org/eb9c/173576577acbb8800bf96aba452d77f1dc19.pdf pdf]</ref>.
A MMTO predecessor, the initial '''Bonanza-Method''' was used in Hoki's [[Shogi]] engine [[Bonanaza]] in 2006, winning the [[WCSC16]] <ref>[[Kunihito Hoki]] ('''2006'''). ''Optimal control of minimax search result to learn positional evaluation''. [[Conferences#GPW|11th Game Programming Workshop]] (Japanese)</ref>.
The further improved MMTO version of Bonanaza won the [[WCSC23]] in 2013 <ref>[[Takenobu Takizawa]], [[Takeshi Ito]], [[Takuya Hiraoka]], [[Kunihito Hoki]] ('''2015'''). ''[https://link.springer.com/referenceworkentry/10.1007/978-3-319-08234-9_22-1 Contemporary Computer Shogi]''. [https://link.springer.com/referencework/10.1007/978-3-319-08234-9 Encyclopedia of Computer Graphics and Games]</ref>..
=Move Adaptation=
=MMTO=
MMTO improved by performing a [[Minimax|minimax search]] (One or two [[Ply|ply]] plus [[Quiescence Search|quiescence]]), by grid-adjacent update, and using [https://en.wikipedia.org/wiki/Constraint_(mathematics) equality constraint] and [https://en.wikipedia.org/wiki/Regularization_(mathematics) L1 regularization] to achieve [https://en.wikipedia.org/wiki/Scalability scalability] and [https://en.wikipedia.org/wiki/Stability stability].
==Objective Function==
MMTO's [https://en.wikipedia.org/wiki/Loss_function objective function] consists of the sum of three terms, where the first term J(P,ω) on the right side is the main part.
