We can modify the population game setting to study superrationality. In order to do this, we can allow the agents to see a fixed size finite portion of the their opponents’ histories. This should lead to superrationality for the same reasons I discussedbefore. More generally, we can probably allow each agent to submit a finite state automaton of limited size, s.t. the opponent history is processed by the automaton and the result becomes known to the agent.
What is unclear about this is how to define an analogous setting based on source code introspection. While arguably seeing the entire history is equivalent to seeing the entire source code, seeing part of the history, or processing the history through a finite state automaton, might be equivalent to some limited access to source code, but I don’t know to define this limitation.
EDIT: Actually, the obvious analogue is processing the source code through a finite state automaton.
Instead of postulating access to a portion of the history or some kind of limited access to the opponent’s source code, we can consider agents with full access to history / source code but finite memory. The problem is, an agent with fixed memory size usually cannot have regret going to zero, since it cannot store probabilities with arbitrary precision. However, it seems plausible that we can usually get learning with memory of size O(log11−γ). This is because something like “counting pieces of evidence” should be sufficient. For example, if consider finite MDPs, then it is enough to remember how many transitions of each type occurred to encode the belief state. There question is, does assuming O(log11−γ) memory (or whatever is needed for learning) is enough to reach superrationality.
What do you mean by equivalent? The entire history doesn’t say what the opponent will do later or would do against other agents, and the source code may not allow you to prove what the agent does if it involves statements that are true but not provable.
For a fixed policy, the history is the only thing you need to know in order to simulate the agent on a given round. In this sense, seeing the history is equivalent to seeing the source code.
The claim is: In settings where the agent has unlimited memory and sees the entire history or source code, you can’t get good guarantees (as in the folk theorem for repeated games). On the other hand, in settings where the agent sees part of the history, or is constrained to have finite memory (possibly of size O(log11−γ)?), you can (maybe?) prove convergence to Pareto efficient outcomes or some other strong desideratum that deserves to be called “superrationality”.
We can modify the population game setting to study superrationality. In order to do this, we can allow the agents to see a fixed size finite portion of the their opponents’ histories. This should lead to superrationality for the same reasons I discussed before. More generally, we can probably allow each agent to submit a finite state automaton of limited size, s.t. the opponent history is processed by the automaton and the result becomes known to the agent.
What is unclear about this is how to define an analogous setting based on source code introspection. While arguably seeing the entire history is equivalent to seeing the entire source code, seeing part of the history, or processing the history through a finite state automaton, might be equivalent to some limited access to source code, but I don’t know to define this limitation.
EDIT: Actually, the obvious analogue is processing the source code through a finite state automaton.
Instead of postulating access to a portion of the history or some kind of limited access to the opponent’s source code, we can consider agents with full access to history / source code but finite memory. The problem is, an agent with fixed memory size usually cannot have regret going to zero, since it cannot store probabilities with arbitrary precision. However, it seems plausible that we can usually get learning with memory of size O(log11−γ). This is because something like “counting pieces of evidence” should be sufficient. For example, if consider finite MDPs, then it is enough to remember how many transitions of each type occurred to encode the belief state. There question is, does assuming O(log11−γ) memory (or whatever is needed for learning) is enough to reach superrationality.
What do you mean by equivalent? The entire history doesn’t say what the opponent will do later or would do against other agents, and the source code may not allow you to prove what the agent does if it involves statements that are true but not provable.
For a fixed policy, the history is the only thing you need to know in order to simulate the agent on a given round. In this sense, seeing the history is equivalent to seeing the source code.
The claim is: In settings where the agent has unlimited memory and sees the entire history or source code, you can’t get good guarantees (as in the folk theorem for repeated games). On the other hand, in settings where the agent sees part of the history, or is constrained to have finite memory (possibly of size O(log11−γ)?), you can (maybe?) prove convergence to Pareto efficient outcomes or some other strong desideratum that deserves to be called “superrationality”.