Thanks for writing this.
I wish you included an entry for your definition of 'mesa-optimizer'. When you use the term, do you mean the definition from the paper* (an algorithm that's literally doing search using the mesa objective as the criterion), or you do speak more loosely (e.g., a mesa-optimizer is an optimizer in the same sense as a human is an optimizer)?
A related question is: how would you describe a policy that's a bag of heuristics which, when executed, systematically leads to interesting (low-entopy) low-base-objective states?
*incidentally, looking back on the paper, it doesn't look like we explicitly defined things this way, but it's strongly implied that that's the definition, and appears to be how the term is used on AF.
Good point -- I think I wasn't thinking deeply enough about language modelling. I certainly agree that the model has to learn in the colloquial sense, especially if it's doing something really impressive that isn't well-explained by interpolating on dataset examples -- I'm imagining giving GPT-X some new mathematical definitions and asking it to make novel proofs.
I think my confusion was rooted in the fact that you were replying to a section that dealt specifically with learning an inner RL algorithm, and the above sense of 'learning' is a bit different from that one. 'Learning' in your sense can be required for a task without requiring an inner RL algorithm; or at least, whether it does isn't clear to me a priori.
I am quite confused. I wonder if we agree on the substance but not on the wording, but perhaps it’s worthwhile talking this through.
I follow your argument, and it is what I had in mind when I was responding to you earlier. If approximating π∗(ot) within the constraints requires computing f(ot), then any policy that approximates π∗ must compute f(ot). (Assuming appropriate constraints that preclude the policy from being a lookup table precomputed by SGD; not sure if that’s what you meant by “other similar”, though this may be trickier to do formally than we take it to be).
My point is that for f = ‘learning’, I can’t see how anything I would call learning could meaningfully happen inside a single timestep. ‘Learning’ in my head is something that suggests non-ephemeral change; and any lasting change has to feed into the agent’s next state, by which point SGD would have had its chance to make the same change.
Could you give an example of what you mean (this is partially why I wanted to taboo learning)? Or, could you give an example of a task that would require learning in this way? (Note the within-timestep restriction; without that I grant you that there are tasks that require learning).
I interpreted your previous point to mean you only take updates off-policy, but now I see what you meant. When I said you can update after every observation, I meant that you can update once you have made an environment transition and have an (observation, action, reward, observation) tuple. I now see that you meant the RL algorithm doesn't have the ability to update on the reward before the action is taken, which I agree with. I think I still am not convinced, however.
And can we taboo the word 'learning' for this discussion, or keep it to the standard ML meaning of 'update model weights through optimisation'? Of course, some domains require responsive policies that act differently depending on what they observe, which is what Rohin observes elsewhere in these comments. In complex tasks on the way to AGI, I can see the kind of responsiveness required become very sophisticated indeed, possessing interesting cognitive structure. But it doesn't have to be the same kind of responsiveness as the learning process of an RL agent; and it doesn't necessarily look like learning in the everyday sense of the word. Since the space of things that could be meant here is so big, it would be good to talk more concretely.
You can't update the model based on its action until its taken that action and gotten a reward for it.
Right, I agree with that.
Now, I understand that you argue that if a policy was to learn an internal search procedure, or an internal learning procedure, then it could predict the rewards it would get for different actions. It would then pick the action that scores best according to its prediction, thereby 'updating' based on returns it hasn't yet received, and actions it hasn't yet made. I agree that it's possible this is helpful, and it would be interesting to study existing meta-learners from this perspective (though my guess is that they don't do anything so sophisticated). It isn't clear to me a priori that from the point of view of the policy this is the best strategy to take.
But note that this argument means that to the extent learned responsiveness can do more than the RL algorithm's weight updates can, that cannot be due to recurrence. If it was, then the RL algorithm could just simulate the recurrent updates using the agent's weights, achieving performance parity. So for what you're describing to be the explanation for emergent learning-to-learn, you'd need the model to do all of its learned 'learning' within a single forward pass. I don't find that very plausible -- or rather, whatever advantageous responsive computation happens in the forward pass, I wouldn't be inclined to describe as learning.
You might argue that today's RL algorithms can't simulate the required recurrence using the weights -- but that is a different explanation to the one you state, and essentially the explanation I would lean towards.
if taking actions requires learning, then the model itself has to do that learning.
I'm not sure what you mean when you say 'taking actions requires learning'. Do you mean something other than the basic requirement that a policy depends on observations?
I've thought of two possible reasons so far.
Perhaps your outer RL algorithm is getting very sparse rewards, and so does not learn very fast. The inner RL could implement its own reward function, which gives faster feedback and therefore accelerates learning. This is closer to the story in Evan's mesa-optimization post, just replacing search with RL.
More likely perhaps (based on my understanding), the outer RL algorithm has a learning rate that might be too slow, or is not sufficiently adaptive to the situation. The inner RL algorithm adjusts its learning rate to improve performance.
I would be more inclined towards a more general version of the latter view, in which gradient updates just aren't a very effective way to track within-episode information.
The central example of learning-to-learn is a policy that effectively explores/exploits when presented with an unknown bandit from within the training distribution. An optimal policy essentially needs to keep track of sufficient statistics of the reward distributions for each action. If you're training a memoryless policy for a fixed bandit problem using RL, then the only way of tracking the sufficient stats you have is through your weights, which are changed through the gradient updates. But the weight-space might not be arranged in a way that's easily traversed by local jumps. On the other hand, a meta-trained recurrent agent can track sufficient stats in its activations, traversing the sufficient statistic space in whatever way it pleases -- its updates need not be local.
This has an interesting connection to MAML, because a converged memoryless MAML solution on a distribution of bandit tasks will presumably arrange the part of its weight-space that encodes bandit sufficient statistics in a way that makes it easy to traverse via SGD. That would be a neat (and not difficult) experiment to run.
I would propose a third reason, which is just that learning done by the RL algorithm happens after the agent has taken all of its actions in the episode, whereas learning done inside the model can happen during the episode.
This is not true of RL algorithms in general -- If I want, I can make weight updates after every observation. And yet, I suspect that if I meta-train a recurrent policy using such an algorithm on a distribution of bandit tasks, I will get a 'learning-to-learn' style policy.
So I think this is a less fundamental reason, though it is true in off-policy RL.
I had a similar confusion when I first read Evan's comment. I think the thing that obscures this discussion is the extent to which the word 'learning' is overloaded -- so I'd vote taboo the term and use more concrete language.
You might want to look into NMF, which, unlike PCA/SVD, doesn't aim to create an orthogonal projection. It works well for interpretability because its components cannot cancel each other out, which makes its features more intuitive to reason about. I think it is essentially what you want, although I don't think it will allow you to find directly the 'larger set of almost orthogonal vectors' you're looking for.
I think we basically agree. I would also prefer people to think more about the middle case. Indeed, when I use the term mesa-optimiser, I usually intend to talk about the middle picture, though strictly that’s sinful as the term is tied to Optimisers.
Re: inner alignment
I think it’s basically the right term. I guess in my mind I want to say something like, “Inner Alignment is the problem of aligning objectives across the Mesa≠Base gap”, which shows how the two have slightly different shapes. But the difference isn’t really important.
Inner alignment gap? Inner objective gap?
I’m not talking about finding on optimiser-less definition of goal-directedness that would support the distinction. As you say, that is easy. I am interested in a term that would just point to the distinction without taking a view on the nature of the underlying goals.
As a side note I think the role of the intentional stance here is more subtle than I see it discussed. The nature of goals and motivation in an agent isn’t just a question of applying the intentional stance. We can study how goals and motivation work in the brain neuroscientifically (or at least, the processes in the brain that resemble the role played by goals in the intentional stance picture), and we experience goals and motivations directly in ourselves. So, there is more to the concepts than just taking an interpretative stance, though of course to the extent that the concepts (even when refined by neuroscience) are pieces of a model being used to understand the world, they will form part of an interpretative stance.