The thing that eventually leapt out when comparing the two behaviours is that behaviour 2 is far more informative about what the restriction was, than behaviour 1 was.
It sounds to me like the agent overfit to the restriction R. I wonder if you can draw some parallels to the Vapnik-style classical problem of empirical risk minimization, where you are not merely fitting your behavior to the training set, but instead achieve the optimal trade-off between generalization ability and adherence to R.
In your example, an agent that inferred the boundaries of our restriction could generate a family of restrictions R_i that derive from slightly modifying its postulates. For example, if it knows you check in usually at midnight, it should consider the counterfactual scenario of you usually checking in at 11:59, 11:58, etc. and come up with the union of (R_i = play quietly only around time i), i.e., play quietly the whole time, since this achieves maximum generalization.
Unfortunately, things are complicated by the fact you said “I’ll be checking up on you!” instead of “I’ll be checking up on you at midnight!” The agent needs to go one step farther than the machine teaching problem and first know how many counterfactual training points it should generate to infer your intention (the R_i’s above), and then infer it.
A high-level conjecture is whether human CEV, if it can be modeled as a region within some natural high-dimensional real-valued space (e.g., R^n for high n where each dimension is a utility function?), admits minimal or near minimal curvature as a Riemannian manifold assuming we could populate the space with the maximum available set of training data as mined from all human literature.
A positive answer to the above question would be philosophically satisfying as it would imply a potential AI would not have to set up corner cases and thus have the appearance of overfitting to the restrictions.
EDIT: Framed in this way, could we use cross-validation on the above mentioned training set to test our CEV region?
It sounds to me like the agent overfit to the restriction R. I wonder if you can draw some parallels to the Vapnik-style classical problem of empirical risk minimization, where you are not merely fitting your behavior to the training set, but instead achieve the optimal trade-off between generalization ability and adherence to R.
In your example, an agent that inferred the boundaries of our restriction could generate a family of restrictions R_i that derive from slightly modifying its postulates. For example, if it knows you check in usually at midnight, it should consider the counterfactual scenario of you usually checking in at 11:59, 11:58, etc. and come up with the union of (R_i = play quietly only around time i), i.e., play quietly the whole time, since this achieves maximum generalization.
Unfortunately, things are complicated by the fact you said “I’ll be checking up on you!” instead of “I’ll be checking up on you at midnight!” The agent needs to go one step farther than the machine teaching problem and first know how many counterfactual training points it should generate to infer your intention (the R_i’s above), and then infer it.
A high-level conjecture is whether human CEV, if it can be modeled as a region within some natural high-dimensional real-valued space (e.g., R^n for high n where each dimension is a utility function?), admits minimal or near minimal curvature as a Riemannian manifold assuming we could populate the space with the maximum available set of training data as mined from all human literature.
A positive answer to the above question would be philosophically satisfying as it would imply a potential AI would not have to set up corner cases and thus have the appearance of overfitting to the restrictions.
EDIT: Framed in this way, could we use cross-validation on the above mentioned training set to test our CEV region?
Incidentally, for a community whose most important goal is solving a math problem, why is there no MathJax or other built-in Latex support?
Thanks, looking at the Vapnik stuff now.