This is the post with some needed concepts and discussion that didn't cleanly fit into any other section, so it might be a bit of a rambly mess.

Specifically, this post splits into two parts. One is assorted musings about when to defer to past-you vs current-you when making decisions, if we're permitting unplannable observations. The other is looking at Vanessa's dynamically consistent update rule, and combining that with our earlier reasoning on affineness to reduce the complexity of the finite-time-horizon version of UDT down from exponential to a smaller exponential.

Why Defer To Past-You?

So, one of the major features of the standard model (environmental observation space $O$ , action space $A$ , finite sequences of environmental observations are our plannables, there is a function $e : O^{< n} \times (Δ A)^{O^{< n}} \to Δ O$ that's affine in the second variable), which makes things a lot easier than they'd be in practice, is that there's an objective answer to what $e$ is. All the versions of you agree on which tree they're in and how their actions affect how probability-mass flows through it. There's an objective answer to "how much does playing a bit more of this action over here affect what observation happens over there?"

But, if our information about how actions influence results doesn't descend from heaven at the start at the time, things get more complicated. If "my beliefs about how actions affect other places" are unplanned observations that you receive after thinking for a while, you can't just go "have me-at-the-start-of-time say what to do"

If you're having to learn which tree/environment you're in, and that learning consists of unplanned observations, and your actions affect how probability-mass flows through that tree, then this raises the problem that the yous which have made different observations can disagree on how their actions affect how probability-mass flows through the tree, and act at cross-purposes.

Is there any principled way of figuring out which sorts of things you should defer to past-you's wishes on, or which sorts of things you should delegate to future-you, when you allow unplanned observations to be something that happens sometimes? Well, to be honest, I'm still sorta confused about this, but I feel more confident than I used to be.

One of the standard arguments trotted out in UDT discussions, is that if you're not behaving in an updateless way, the early v...