AMTLB

Atari Multitask & Transfer Learning Benchmark (AMTLB)

This is a library to test how a reinforcement learning architecture performs on all Atari games in OpenAI's gym. It performs two kinds of tests, one for transfer learning and one for multitask learning. Crucially, this benchmark tests how an architecture performs. Training the architecture on games is part of the test, so it does not aim to test how well a pre-trained network does, but rather how quickly an architecture can learn to play the games (but see note below for details).

Throughout this document, we'll refer to architecture as the system being tested irrespective of individual weight values. An instance will refer to the architecture instantiated with a particular set of weights (either trained or untrained). The benchmark trains several instances of the architecture to infer how well the architecture itself learns.

Transfer learning benchmark

The goal of the transfer learning benchmark is to see quickly an architecture can learn a new game it has never seen before, just using what it's learned from other games (so, how much knowledge is transferred from one game to another).

The way it works is first it creates a fresh instance of the architecture (call it instance F), and then measures its score over time as it learns on ten million frames of a random Atari game (call it game X). Next, we create another fresh instance of the architecture, but this one we train on bunch of other Atari games (but not on game X itself), we'll call it instance F_b. Finally, we let F_b play ten million frames of game X and measure its score over time.

For each time frame, we take the cumulative score of A and the cumulative score of B and get the ratio r = 1 - B / A.

• If r negative, then the architecture actually got worse from seeing other Atari games.
• If r is about 0, then the architecture didn't really transfer knowledge well from having seen the other Atari games.
• If r positive, then we're in the sweet spot and the architecture is successfully learning to play a new Atari game from other games.

We're not quite done though, because really this is just a measure of how well the architecture did on game X. Some games may transfer knowledge well, and other games may be so unlike other Atari games that it's hard to transfer much knowledge. What we could do to get around this is to then do the process above for each game in the entire collection and average the scores.

This would take a really long time though, so as a compromise, instead of just holding out one game in the above process, we hold out about 30% of all games as tests, and keep 70% of games for training. We then do the above process to test, except we create a fresh instance for each test game, and we save the state of network after it's been trained on the training set of games. We reset it to that "freshly trained" state before each test game (so it doesn't learn from the other testing games). Then we shuffle the training and testing sets up randomly and do this a few more times from scratch.

As an example, lets say there are five games S, U, V, X, and Y.

We'll measure the performance of a fresh instance on each of the games for 10 million frames, getting F(S), F(U), F(V), F(X), and F(Y) (F is for "fresh").

Then for the first trial, we'll randomly select X and Y as the test games. We'll train a new instance F on S, U, and V and save its weights as F_suv. Then we train F_suv on X for ten million frames, getting F_suv(X). Then we train F_suv on Y for ten million frames, getting F_suv(Y).

To get the score for the first trial, we average their ratios:

r_1 = (F_suv(X)/F(X) + F_suv(Y)/F(Y)) / 2

Now we do a couple more trials, maybe using S and V as the test games, then maybe for the third trial U and S as the tests.

r_2 = avg(F_uxy(S)/F(S) , F_uxy(V)/F(V))
r_3 = avg(F_vxy(U)/F(U) , F_vxy(S)/F(S))

Finally, we average the scores from all three trials:

r = avg(r_1, r_2, r_3)

r(t) is the final transfer learning score for the architecture for each time step, though we may simply use r(t_max) as a summary.

Multitask learning benchmark

The multitask learning benchmark is most similar to existing benchmarking that's been done on Atari games, in that we are concerned with an absolute score on the games. Since absolute scores aren't comparable across games, we have to keep each game's score separate in the results rather than aggregating them.

How it works is we once again train a fresh instance of the architecture for 10 million frames on each game separately, obtaining baseline scores for each game. These instances we call the "specialists" since they're trained on only one game a piece.

Then we train an instance of the architecture on every game in random order, so that the new architecture has seen 10 million frames of every game. This instance we call the "generalist".

We then compare the generalist's cumulative scores for each frame against the specialists' scores for the same game and time step. On the multitask benchmark, we're looking for the generalist to match the scores of the specialists in the best case. Since the architecture is the same, the presumption is that the specialist will nearly always have better performance, and we can only minimize how much the generalist loses. Though in practice, if the architecture transfers knowledge well, the generalist may actually outperform the specialists in some cases.

On the multitask benchmark, we also output the absolute scores for comparison with other benchmarks etc, though note that it should only be compared with scores that were obtained under the 10 million frame limit.

Note on pre-training

The benchmark doesn't have a strong opinion about how the weights are initialized in a fresh instance of an architecture. It's reasonable to not initialize the weights randomly, instead opting to come with some prior training so that (for example) a deep convolutional network doesn't waste part of its precious 10 million frames learning to recognize edges and shapes etc.

The transfer learning benchmark is somewhat robust to this kind of pre-training since it relies on measuring the amount of improvement in the architecture before and after it is able to see other games. If a "fresh" instance already has extensive training on Atari games beforehand, we should expect this to simply eat into the improvement.

Nevertheless, as a rule of thumb, it's best if a fresh instance of an architecture does not include any prior training on Atari games or images from Atari games, to eliminate confusion.