by Vadim Kosoy 260 days ago | link | parent No, it doesn’t rule out any particular environment. A class that consists only of one environment is tautologically learnable, by the optimal policy for this environment. You might be thinking of learnability by anytime algorithms whereas I’m thinking of learnability by non-anytime algorithms (what I called “metapolicies”), the way I defined it here (see Definition 1).

 by Jessica Taylor 259 days ago | link Ok, I am confused by what you mean by “trap”. I thought “trap” meant a set of states you can’t get out of. And if the second law of thermodynamics is true, you can’t get from a high-entropy state to a low-entropy state. What do you mean by “trap”? reply
 by Vadim Kosoy 259 days ago | link To first approximation, a “trap” is a an action s.t. taking it loses long-term value in expectation, i.e an action which is outside the set $$\mathcal{A}_M^0$$ that I defined here (see the end of Definition 1). This set is always non-empty, since it at least has to contain the optimal action. However, this definition is not very useful when, for example, your environment contains a state that you cannot escape and you also cannot avoid (for example, the heat death of the universe might be such a state), since, in this case, nothing is a trap. To be more precise we need to go from an analysis which is asymptotic in the time discount parameter to an analysis with a fixed, finite time discount parameter (similarly to how with time complexity, we usually start from analyzing the asymptotic complexity of an algorithm, but ultimately we are interested in particular inputs of finite size). For a fixed time time discount parameter, the concept of a trap becomes “fuzzy”: a trap is an action which loses a substantial fraction of the value. reply

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