(Not all of your knowledge about possible future reference signals and possible future delayed effects of past disturbances is represented, only your knowledge about possible future differences between them.)
So this isn’t a sufficient statistic, it’s only a sufficient-for-policy-implications statistic. Is there a name for that?
All “sufficient” statistics are only “sufficient” for some particular set of policy or epistemic implications. You could always care about the number of 1 bits, if you’re allowed to care about anything.
Then every “sufficient-for-policy-implications” statistic can become a “sufficient-for-implications-for-beliefs-about-the-future” statistic, under a coarsening of the sample space by some future-action-preserving and conditional-ratios-of-expected-payoff-differences-preserving equivalence relation?
(Would we expect deliberative thinking and memory to physically approximate such coarsenings, as linear controllers do?)
So this isn’t a sufficient statistic, it’s only a sufficient-for-policy-implications statistic. Is there a name for that?
All “sufficient” statistics are only “sufficient” for some particular set of policy or epistemic implications. You could always care about the number of 1 bits, if you’re allowed to care about anything.
Then every “sufficient-for-policy-implications” statistic can become a “sufficient-for-implications-for-beliefs-about-the-future” statistic, under a coarsening of the sample space by some future-action-preserving and conditional-ratios-of-expected-payoff-differences-preserving equivalence relation?
(Would we expect deliberative thinking and memory to physically approximate such coarsenings, as linear controllers do?)