> what the OP was claiming about "rational agents"
Since prediction and compression are isomorphic, OP's point is that compression algorithms are relevant to these decision processes. This actually references the work of Marcus Hutter, who added an extra axiom to these established definitions: that agents and environments are (Turing) computable.
This lets us apply techniques from Algorithmic Information Theory, like Solomonoff Induction, and prove that the optimal policy is to:
- Compress all of the observations received so far, into the smallest program possible (for a predetermined Universal Turing Machine). Note that this is uncomputable, since it would tell us its Kolmogorov complexity!
- Predict the outcome of our possible actions, by simulating them against that program
- Choose the action whose simulation leads to the highest reward
Sure it's not an algebraic object; but it's still a well-defined mathematical notion.
Nah, it's just an informal concept. A game theoretic "rational agent" in general isn't assumed to have any limitations on it's computing ability, for example.
[Game theory is] trying to solve a partially-observable Markov decision problem
Not according to standard texts on game theory. In fact, this is just can't be true in any usual interpretation. POMDPs are "single agent" problems whereas game theory nearly always deals with two competing players/agents each assume attempting to optimize their returns - it's the difference between a single optimum and a saddle point, maximum and minimax.
This actually references the work of Marcus Hutter, who added an extra axiom to these established definitions: that agents and environments are (Turing) computable.
This is my point. You can't "add an extra axiom" and be referencing a standard mathematical object at the same time.
Sure it's not an algebraic object; but it's still a well-defined mathematical notion.
> You should notice that the definition of rational agent found in game theory doesn't imply any kind of prediction or computation
Of course it does! Game theory (and rational agents in general) is about optimisation ( https://en.wikipedia.org/wiki/Optimization_problem#Continuou... https://en.wikipedia.org/wiki/Optimal_decision#Formal_mathem... https://en.wikipedia.org/wiki/Rational_choice_theory#Formal_... ); it's trying to solve a partially-observable Markov decision problem ( https://en.wikipedia.org/wiki/Markov_decision_process#Defini... ). That requires prediction (of other agents, and/or the environment), and computation (to search through action-space, for Bayesian updating, for backwards-induction, etc.)
> what the OP was claiming about "rational agents"
Since prediction and compression are isomorphic, OP's point is that compression algorithms are relevant to these decision processes. This actually references the work of Marcus Hutter, who added an extra axiom to these established definitions: that agents and environments are (Turing) computable.
This lets us apply techniques from Algorithmic Information Theory, like Solomonoff Induction, and prove that the optimal policy is to:
- Compress all of the observations received so far, into the smallest program possible (for a predetermined Universal Turing Machine). Note that this is uncomputable, since it would tell us its Kolmogorov complexity!
- Predict the outcome of our possible actions, by simulating them against that program
- Choose the action whose simulation leads to the highest reward