Aspiration+Windows

toc =Gradual Widening= Some programs, such as Crafty, also use a gradual widening on re-searches. For instance, if the window is, in pawns: > math [g - 1/4, g + 1/4] math
 * Home * Search * Alpha-Beta * Aspiration Windows**
 * [[image:TheNon-EuclideanWindow.JPG]] ||~  || **Aspiration windows** are a way to reduce the search space in an alpha-beta search. The technique is to use a guess of the expected value (usually from the last iteration in iterative deepening), and use a window around this as the alpha-beta bounds. Because the window is narrower, more beta cutoffs are achieved, and the search takes a shorter time. The drawback is that if the true score is outside this window, then a costly re-search must be made. Typical window sizes are 1/2 to 1/4 of a pawn on either side of the guess. ||
 * The Non-Euclidean Window ||~  ||^   ||

and the search fails high, the next search would be > math [g - 1/4, g + 1] math

It's important to note that the bound that didn't fail is unchanged. In a basic alpha-beta without search instability, one could have done the next search on > math [g + 1/4, g + 1] math > instead. However, a fully fledged search is typically full of search instability, and it will often happen that the above re-search will fail low! This is why it is best to only widen the bound that fails, and leave the other bound unchanged.

Modern engines, like Robbolito or Stockfish, start with a rather small aspiration window, and increase the bound that fails in an exponential fashion.

=PVS and Aspiration= Using aspiration windows together with the principal variation search (PVS) causes some additional complications.
 * PVS and Aspiration

=See also=
 * Null Window
 * Scoring Root Moves
 * Search Instability
 * Window

=Publications=
 * Hermann Kaindl, Reza Shams, Helmut Horacek (**1991**). //[|Minimax Search Algorithms with and without Aspiration Windows].// IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 13, No. 12
 * Reza Shams, Hermann Kaindl, Helmut Horacek (**1991**). //Using Aspiration Windows for Minimax Algorithms//. IJCAI 1991, [|pdf]

=Forum Posts=

1995 ...

 * [|Question about aspiration window] by Werner Inmann, CCC, August 14, 1998
 * [|aspiration windows] by James Long, CCC, November 27, 1998
 * [|Aspiration Rules...] by Chris Pile, rgcc, February 5, 1999
 * [|Aspiration search] by James Robertson, CCC, April 20, 1999
 * [|Aspiration search] by Scott Gasch, CCC, August 13, 1999

2000 ...

 * [|Aspiration window] by Bas Hamstra, CCC, January 20, 2002
 * [|Exact value of second best move in AlphaBeta with aspiration Window] by Martin Bauer, CCC, August 01, 2002
 * [|Aspiration search, PVS] by Russell Reagan, CCC, December 28, 2002
 * [|Unstable aspiration search] by Sune Fischer, CCC, February 10, 2003
 * [|Question about aspiration search] by Jaime Benito de Valle Ruiz, CCC, March 23, 2004
 * [|What is a common Aspiration window?] by Joachim Rang, CCC, March 26, 2004
 * [|aspiration search question] by Daniel Shawul, CCC, May 13, 2004
 * [|Q. Aspiration, PVS, Fail-Soft] by David B. Weller, CCC, July 02, 2004
 * [|PVS and aspiration windows] by Tord Romstad, CCC, August 06, 2004

2005 ...

 * [|Aspiration Window sizes] by Renze Steenhuisen, CCC, March 14, 2005
 * [|Bounds for aspiration window re-search] by Sven Schüle, CCC, March 17, 2009
 * [|A way to improve PVS] by Sergei S. Markoff, CCC, September 07, 2009

2010 ...

 * [|Apiration window] by Don Dailey, CCC, March 27, 2010
 * [|A few general questions...] by Bill Henry, CCC, January 29, 2012 » Root, Exact Score
 * [|optimal aspiration window for stockfish question] by Uri Blass, CCC, March 12, 2012 » Stockfish
 * [|Aspiration Windows: Rubbish!] by Matthew R. Brades, CCC, July 16, 2012
 * [|Aspiration window - effect? Issue with hashtables?!] by Jens Bæk Nielsen, CCC, December 28, 2012
 * [|Aspiration Windows] by Jerry Donald, CCC, January 11, 2013
 * [|Aspiration windows] by Marco Pampaloni, CCC, May 14, 2013
 * [|Your experience with PVS + Aspiration window] by Fabio Gobbato, CCC, October 07, 2014 » Principal Variation Search, PVS and aspiration
 * [|Solving a fail low situation at the root] by Alberto Sanjuan, CCC, November 03, 2014 » Fail-Low

2015 ...

 * [|Parallel aspiration windows] by Giuseppe Cannella, CCC, July 29, 2015
 * [|Restarting iterative deepening] by Harm Geert Muller, CCC, December 09, 2015 » Fail-Low, Iterative Deepening
 * 2016**
 * [|Dynamic aspiration window] by Sergei S. Markoff, CCC, May 26, 2016
 * [|Aspiration Windows on the root search -- Determining margin] by Andrew Grant, CCC, June 08, 2016
 * [|Iterative Deepening Question] by David Cimbalista, CCC, July 23, 2016 » Iterative Deepening
 * [|Aspiration window with TT question] by sandermvdb, OpenChess Forum, August 01, 2016 » Transposition Table
 * 2016**
 * [|Conceptual question on aspiration windows] by Jacob Wilkins, CCC, April 09, 2017
 * [|(I)ID and PV dropout] by Harm Geert Muller, CCC, June 17, 2017 » Fail-Low, Internal Iterative Deepening, Iterative Deepening
 * [|Aspiration window problem] by Sander Maassen vd Brink, CCC, October 30, 2017

=External Links= > media type="youtube" key="qrw8kA6jaDk"
 * [|Aspiration Windows] from Bruce Moreland's Programming Topics
 * [|Aspiration from Wikipedia]
 * [|aspiration - Wiktionary]
 * [|aspire - Wiktionary]
 * [|Aspire] - [|Break Down These Walls], [|YouTube] Video

=References= =What links here?= include page="Aspiration Windows" component="backlinks" limit="300"
 * Up one level**