AlphaZero like implementation for Oware Abapa game (Codingame)

Marchete
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Differences between CGZero and Alphazero

Simple NN Model

Original AlphaZero NN design has many (80+) Convolutional layers, Fully Connected layers, Batch Normalization layers, skip connection layers (adding inputs again after each residual layer) and more. CGZero is a toy model. I haven't implemented neither Convolutional nor Batch Normalization layers. I have like 3 or 4 layers of Fully Connected layers, nothing more. Check https://adspassets.blob.core.windows.net/website/content/alpha_go_zero_cheat_sheet.png for some diagram of Alpha Zero networks. That can't fit on normal competitive games, and it won't have enough CPU time to do anything good.

Synchronous training

AlphaZero used 4 first-generation TPUs and 44 CPU cores. My setup is modest, just a single Intel Core i7, training while I do other stuff at the PC. I don't have distributed workers (can be really simple to delegate selfplay workers to external PC's though). So all the training pipeline is just linear, one task after another. I use threading to greatly improve selfplay game generation and pitplay winrate results.

Self-play generation

AlphaZero states 25000 games against itself. I just do around 400-1500 each generation. They always use the best model, I use 3 different options:

  1. Best1 vs Best1
  2. Best1 vs Best2
  3. Best1 or Best2 vs random generation (a recent one)

The amount of the third option is always a 10% of the games to generate. 1 and 2 will have variable percentage, depending on the result of the last training. Having winrate1 and winrate2 (winrates of candidate vs each best model) I'll generate more games to the lowest winrate.

Samples

Alphazero stores | Inputs | Policy | EndGame Value | as a sample. They store samples for the last 500k games, I just store last X00k samples (much less games).

My Samples have 4 parts:

| Inputs | SumPolicy | SumValue | Count |

Samples will be dictionaries with inputs as keys, so I make unique samples and sum the policy and values, and increase the count by 1. Dividing by Count will average samples. AlphaZero always uses EndGame Value for all samples. I mix what you can read on: https://medium.com/oracledevs/lessons-from-alphazero-part-4-improving-the-training-target-6efba2e71628 In that document they declare Z and Q as possible objectives for value training. Z is the endgame score (-1, 0 or 1) that will be used on all samples (taking into account that samples from the loser player has -endgameScore). Q is just the sumValue/visits you get while doing MCTS search (i.e. the mean Score of the root node). I use a mix of both. SampleValue = k * Z + (1-k)*Q . k will linearly increase each turn, so initial samples have some little EndGame Score (because I think it's too far to declare a position as good or bad), and final moves will have a big percentage of EndGame Score (it's more clear that this position is good or bad). I had many problems with the sign of the Samples value. I struggled to get the correct sign. It seems naive, but to evaluate a game state the root node have a -sum(childrenValues). This is not what I wanted. If as player 0 I have a sure win (1.0), then all children from root will have 1.0 as mean score. But as the way the score backpropagates the root node will have a -1.0 (it's seen as the enemy POV). I neeeded the score for the player 0, so I tested a lot with signs until I got what I expected.

Alphazero picks random minibatches of 2048 positions from last 500k games. I imagine it's just a random selection of 2048 samples. But according to my samples, without deduplication/averaging of samples you'll end up with a lot of repetitive initial samples, most of them having contradictory training targets.

My subset selection is much bigger, I take around 200k-800k samples from last 500k-N000k samples as a subset. Also the subset selection is weighted. I order samples by Count, on descending order. The 20% of my subset will come from the first 20% of that ordered sample list, the next 20% from the first 40% and so on. This way I ensure that most frequent samples usually appears on the subset. Finally I add some decay weight to older samples. I get all files, sortered by name descending (so higher generations are read first). For each file I reduce 0.02 the decay factor (starting with 1.0, limited to 0.7 as min decay). So samples from an old generation are counted but they add less to the final SumPolicy and SumValue

Training

Alphazero uses minibatches of 2048 samples. I use a big subset with M00k samples, and the training function does N passes (EPOCH between 5 and 20, depending on how much it takes). I do it on a synchronized way. AZ do the evaluation of the network each 1000 minisamples, I do after 1 training call (but that call has N passes as EPOCH).

The AZ loss function is Cross entropy loss + Mean squared loss + regularisation. I don't know exactly what that regularisation is, or how to calculate it, so I ignored it. Also the Cross entropy loss is completely incorrect for my approach. https://www.tensorflow.org/api_docs/python/tf/keras/losses/CategoricalCrossentropy or any other crossentropy loss in tensorflow seems to work for categorization (i.e. they expect only one true value, with a 1.0 on it and the rest with zero). In my tests I was getting huge losses as categorical crossentropy, even with near perfect predictions (0.0003 differences between the prediction and the expected policy values). Finally I used https://www.tensorflow.org/api_docs/python/tf/keras/metrics/kl_divergence , that is exactly what I was looking for (a measure of how one probability distribution is different from a second)

Evaluation

I evaluate against two best models, best1 and best2. When a new candidate have a winrate >55%, best1 is passed to best2, and the new candidate is promoted as best1

Move selection after MCTS Search ended

While training AlphaZero uses some temperature for selection. It seemed obscure and overly complicated.

I went to a simpler mode. I rely on dirichlet noise to have some randomness on visit count. Also for the first 11 turns I have some chance to randomly pick a move, regardless its stats. This random move invalidates the sample generation for that position, to avoid breaking the statistics. I don't pick the move with most visits. I used visits and score (similar to https://tech.io/playgrounds/55004/best-first-minimax-search-with-uct). SelectMoveScore = move's eval value + log(move's visits)

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