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You're making a jump from "AlphaZero plays better than the best programs of its time" to "chess is close to being solved" but that's not justified without much

You're making a jump from "AlphaZero plays better than the best programs of its time" to "chess is close to being solved" but that's not justified without much more evidence. There are still a lot of improvements and new ideas added to the top programs and even if they reach a plateau, you'd have to show that increasing time per move 100x doesn't result in a significant improvement in playing strength. We don't know what would be the Elo difference between a 32-piece tablebase and the best existing program but I don't think anybody would bet that it's less than 200 Elo. Here is a graph of Stockfish's progress since the end of 2015: https://camo.githubusercontent.com/f169f774996346ad146f96f74d9f33da3f7d7b45597280309ec9b6423fb20898/68747470733a2f2f696d6775722e636f6d2f6e34456269386a2e706e67 https://camo.githubusercontent.com/f169f774996346ad146f96f74.... Self-play exaggerates strength differences but it's been a very good rate of progress, even without hardware improvements in the meantime.

tialaramex 6y ago
Right! A solved game is categorically different from merely teaching a machine to be better at it than humans are presently. Cepheus [0] is approximately a solution to Heads-Up (two player) Limit (ie the amount you can bet is specified in the game, you don't get to just bet arbitrary money) Texas Hold 'em poker. In contrast Libratus is an AI that plays Heads-Up No Limit Hold 'em very well against humans. You can examine the Cepheus strategy for yourself, if you could memorize it (it's too complicated) and were capable of making truly random decisions (Poker is a game of chance and so your strategy needs random action) you could reproduce it and be exactly as good at the game as Cepheus is. You can examine individual strategy elements and reason about them. For example if Cepheus gets an 8 and a 3 and you open with a bet, it will call your bet if they're the same suit, otherwise it will fold. On the other hand if those suited cards were an 8 and a Queen, it would raise a bit more than nine times out of ten. You can't do anything about it (you might be thinking surely knowing that e.g. Cepheus folds 8-3 off here is valuable so I can benefit from that, er, no, "hiding" that by sometimes playing it loses more money than Cepheus gives up by folding it that's why this is a perfect strategy), if playing Cepheus, even with an incrementally "more" approximate solution you're not going to win a significant amount of money reliably in reasonable time, that's why it's approximately solved. But Libratus isn't like that, it's playing some strategy that we know beat world class human players, but a further incrementally better AI might crush Libratus just as badly. [0] http://poker.srv.ualberta.ca/preflop http://poker.srv.ualberta.ca/preflop

tialaramex 6y ago

Right! A solved game is categorically different from merely teaching a machine to be better at it than humans are presently. Cepheus [0] is approximately a solution to Heads-Up (two player) Limit (ie the amount you can bet is specified in the game, you don't get to just bet arbitrary money) Texas Hold 'em poker. In contrast Libratus is an AI that plays Heads-Up No Limit Hold 'em very well against humans. You can examine the Cepheus strategy for yourself, if you could memorize it (it's too complicated) and were capable of making truly random decisions (Poker is a game of chance and so your strategy needs random action) you could reproduce it and be exactly as good at the game as Cepheus is. You can examine individual strategy elements and reason about them. For example if Cepheus gets an 8 and a 3 and you open with a bet, it will call your bet if they're the same suit, otherwise it will fold. On the other hand if those suited cards were an 8 and a Queen, it would raise a bit more than nine times out of ten. You can't do anything about it (you might be thinking surely knowing that e.g. Cepheus folds 8-3 off here is valuable so I can benefit from that, er, no, "hiding" that by sometimes playing it loses more money than Cepheus gives up by folding it that's why this is a perfect strategy), if playing Cepheus, even with an incrementally "more" approximate solution you're not going to win a significant amount of money reliably in reasonable time, that's why it's approximately solved. But Libratus isn't like that, it's playing some strategy that we know beat world class human players, but a further incrementally better AI might crush Libratus just as badly. [0] http://poker.srv.ualberta.ca/preflop http://poker.srv.ualberta.ca/preflop