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1772:; It satisfies all the criteria in the "Self-published or questionable sources as sources on themselves". I'm not citing it as evidence of what expert players in general thought in 1995; I'm citing it as evidence of what Kit Woolsey thought was the best play in 1995, and this is not a self-serving or exceptional claim. That Kit Woolsey is a backgammon expert is established independently in the Knowledge article about him.
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completed game, and tweaking the evaluation function so it judges that board position to be closer in value to the following one. You can't do that until you have a board position with known value, and that's the final board position. To put that another way, what training value is there to back-propagate from if you don't know who won the game? —
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article). Note that the article states the w in the formula is the vector whose components are all the weights in the network, whereas the wiki page wording seems to imply that w is a single weight in the network (but then the formula wouldn't make sense, because the left-hand side would be a number and the right-hand side would be a vector).
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memory from the pre-TD-gammon 90s is that splitting play was generally already favored over slotting at most match scores. I'll search my backgammon library and see if I can find some citations for this. I also think the claim that everyone started playing the splitting move after TD-gammon is overstated. See for example
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suggests there are some inaccuracies in this article; specifically, the program was developed beyond its state in 1992, which appears to be what is described here, and incorporated features not described (a 3-ply search depth in some later versions). Also
Tesauro appears to have concluded that the
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with i in range 1..4, and the formula should sum over i, according to the sentence "In cases where there are multiple output units, the total weight change is given by the sum of the weight changes due to each individual output unit." (the article is apparently explaining about both TD-Learning in
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Let's make sure we understand what's being said. First, the current article does not speak of a miracle look into the future. It says that the algorithm is given a whole game transcript and uses the final board position to prime back-propagation of the weights in the neural net (working backward,
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that are specifically about the article's topic. You've certainly persuaded me that the source specifically about TD-Gammon overstates TD-Gammon's influence on tournament play. The topic-specific source isn't reliable about this particular fact. In lieu of an authoritative book or article about
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I was playing tournament backgammon in the 90's, and I find the claims of the effect of TD-gammon on how experts played the opening rolls to be greatly overstated. The splitting play was the recommended play at least as far back as
Magriel's book from 1976. Though fashions changed over time, my
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is the gradient of the function calculated by the network (the output of the network) with respect to the weights in the network. That function is noted Yk, and represents the possible outcome of game k (assumedly by giving that outcome a probability, though this isn't stated explicitly in the
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The latter interpretation agrees with my understanding of temporal-difference learning in general (though I am no expert). After re-reading those four paragraphs in the
Tesauro article several times, I'm now favoring thetter interpretation for TD-Gammon, too (even though it's weird because the
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Tesauro himself explains: At the end of each game, a final reward signal z (containing four components as described previously) is given, based on the outcome of the game. Once again equation 1 is used to change the weights, except that the difference (z − Yf) is used instead of (Yt+1 − Yt).
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Are you sure that contradicts the article? If the article is wrong, by all means fix it, but I understand the incremental update after each move to occur in relation to the known final board position of the game. Applying the TD rule "after each move" means looking at each board position of a
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come from? I've found the writing on the learning algorithm to be pretty unclear. The current
Knowledge article may well be wrong, but at least it's clear! Now, are you saying that the learning algorithm actually works forward, and on each turn, updates the weights in the neural net so its
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Uh oh, I just checked
Scholarpedia and Tesauro's article appears to be gone. I couldn't find any article by Tesauro there. Can you suggest another place to look for the information you mentioned above, especially the point about hand-crafted features not being necessary?
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evaluations of previous board positions are closer to its evaluation of the current position? The only exception would be the final board position, which gets a special evaluation that is independent of the weights in the neural net (that is, "who actually won").
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hand-crafted features to the input were not necessary; the 40-hidden-node network he had used before adding them appears to have been too small, and he did not train the system for long enough to see its potential before moving on to including them.
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Normally when I see claims I don't believe in WIkipedia, I add a "citation needed", but I'm not quite sure what to do when the incorrect claims in the article are supported by a citation from a reputable source that is nonetheless inaccurate.
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1669:. The page history says that the article "expired and reverted to proposed status". It looks like excellent info, but I don't think we can cite it until Scholarpedia makes it official again. I just asked about getting it re-approved. —
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algorithm spends most of its time adjusting the weights without any input that's known to be correct). If you also think that's right, I'd say go ahead and edit the page! I can do it if you'd rather not. —
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The gradient of a multiple-variable function is a vector whose components are the partial derivatives of that function. I think both the wikipedia page and the article at are pretty clear:
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1694:, where world-class player Kit Woolsey says in 1995, after looking at rollouts from TD-gammon and other programs, that the slotting and splitting plays with 2-1 are equal.
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Step 2 of TD-Gammon is wrong. It didn't have to wait until the end of each game. That's one of the major advantages over
Montecarlo-estimation. See
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for "Tesauro applied the nonlinear TD rule (11.1) fully incrementally, that is, after each individual move." —84.168.22.218, 20:51, June 12, 2010
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isn't really explained. I basically took
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Regarding correcting that, when I read the sources, the question in my mind is, where does the "reward signal" come from? In terms of
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1575:{\displaystyle w_{t+1}-w_{t}=\sum _{i=1}^{4}(\alpha (Y_{t+1}^{i}-Y_{t}^{i})\sum _{k=1}^{t}\lambda ^{t-k}\nabla _{w}Y_{k}^{i})}
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already states for general TD: predict the future (preferable very exactly) and change your "past" model accordingly.
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Lastly, the article is stating that there are four outputs from the network, not just one. So the notation
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1754:. Your thoughts? If you agree, please feel free to just dive in and add the source to the article. —
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computer backgammon's influence on tournament play and accepted theory, here are a couple options:
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on
Knowledge. If you would like to participate, please visit the project page, where you can join
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TD(lambda) does not take a miracle look into the future and looks at what the final result is.
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general and TD-Gammon specifically, hence the confusion). The complete formula would then be :
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I finally rewrote the description of the learning algorithm. Hopefully it's now both clear
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Thanks for spotting this. Normally, each
Knowledge article should only summarize
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http://www.scholarpedia.org/article/User:Gerald_Tesauro/Proposed/Td-gammon
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My feeling right now is that while citing the Usenet posting violates
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Fantastic! I'd say that
Scholarpedia meets our criteria for a
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is slightly misleading, it probably should be something like
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accurate. Actually, I know it's not entirely clear, because
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I don't think citing the Woolsey Usenet Post violates
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1737:(2) Cite the Usenet posting by Kit Woolsey.
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769:
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749:
747:
741:
738:
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733:
727:
724:
721:
719:
713:
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698:Hotline Miami
696:
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685:
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656:Dr Disrespect
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619:
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590:Kim Kitsuragi
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581:
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541:
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362:Covet Fashion
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35:
27:
23:
18:
17:
1792:
1748:Type I error
1701:— Preceding
1696:
1688:
1615:212.159.69.4
1607:
1604:Inaccuracies
1584:92.140.115.2
1193:
1150:
1056:
979:reassessment
957:
939:
927:
915:
903:
891:
855:
841:
827:
813:
799:
785:
771:
757:
743:
729:
715:
701:
687:
673:
659:
635:
621:
618:Pixel Piracy
607:
604:Miner 2049er
593:
549:
535:
521:
494:
482:
470:
448:
372:
369:participants
366:
353:
350:participants
347:
343:Ryo Sakazaki
334:
331:participants
328:
315:
309:
299:participants
296:
286:participants
283:
273:participants
270:
260:participants
257:
247:participants
244:
234:participants
231:
136:
96:
40:WikiProjects
1104:—Preceding
1003:screenshots
684:Async Corp.
518:Donkey Kong
398:Screen Rant
312:participant
167:Summary of
156:open tasks:
152:Summary of
112:Video games
103:video games
59:Video games
30:Start-class
1808:Categories
1756:Ben Kovitz
1671:Ben Kovitz
1651:Ben Kovitz
1634:Ben Kovitz
1255:Ben Kovitz
1170:Ben Kovitz
1147:figure 8.1
1068:Ben Kovitz
965:assessment
754:River Raid
471:The Sims 4
422:discussion
412:discussion
402:discussion
392:discussion
324:Butterfree
171:open tasks
1707:Andylatto
997:cover art
991:infoboxes
632:Ether One
580:Justin Yu
483:Smash Hit
227:GeneRally
1715:contribs
1703:unsigned
1106:unsigned
1021:creation
460:Ada Wong
374:relisted
355:relisted
336:relisted
317:relisted
305:Dokibird
292:Skycoach
1728:sources
1026:merging
1005:(8,822)
985:cleanup
852:Kleavor
782:Pikachu
201:vg talk
191:history
139:on the
1770:WP:SPS
1744:WP:SPS
1009:photos
940:Tetris
824:Meltan
206:alerts
36:scale.
1017:(190)
999:(251)
858:start
844:start
830:start
816:start
802:start
788:start
774:start
760:start
746:start
732:start
718:start
704:start
690:start
676:start
662:start
638:start
624:start
610:start
596:start
560:Birdo
552:start
538:start
524:start
211:purge
196:shell
181:watch
1778:talk
1760:talk
1711:talk
1675:talk
1655:talk
1638:talk
1619:talk
1608:The
1588:talk
1259:talk
1174:talk
1114:talk
1072:talk
1011:(66)
993:(19)
221:AfDs
186:edit
176:view
1194:and
987:(8)
981:(0)
971:) (
946:rev
933:rev
921:nom
909:nom
897:nom
650:nom
584:nom
574:nom
564:nom
500:nom
488:nom
476:nom
464:nom
454:nom
131:Low
1810::
1780:)
1762:)
1717:)
1713:•
1677:)
1657:)
1640:)
1621:)
1590:)
1546:∇
1537:−
1530:λ
1509:∑
1487:−
1460:α
1437:∑
1420:−
1288:∇
1261:)
1205:∇
1176:)
1116:)
1074:)
371:;
352:;
333:;
314:;
1776:(
1758:(
1709:(
1673:(
1653:(
1649:—
1636:(
1617:(
1586:(
1582:—
1570:)
1565:i
1560:k
1556:Y
1550:w
1540:k
1534:t
1524:t
1519:1
1516:=
1513:k
1505:)
1500:i
1495:t
1491:Y
1482:i
1477:1
1474:+
1471:t
1467:Y
1463:(
1457:(
1452:4
1447:1
1444:=
1441:i
1433:=
1428:t
1424:w
1415:1
1412:+
1409:t
1405:w
1379:i
1374:k
1370:Y
1347:k
1343:Y
1302:k
1298:Y
1292:w
1257:(
1241:k
1219:k
1215:Y
1209:w
1172:(
1151:r
1112:(
1070:(
975:)
973:2
969:1
967:(
948:)
944:(
935:)
931:(
923:)
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911:)
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862:)
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556:)
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410:(
404:)
400:(
394:)
390:(
377:)
367:8
364:(
358:)
348:4
345:(
339:)
329:7
326:(
320:)
310:1
307:(
301:)
297:3
294:(
288:)
284:2
281:(
275:)
271:2
268:(
262:)
258:4
255:(
249:)
245:3
242:(
236:)
232:0
229:(
143:.
42::
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