[hauntsaninja]

Yay, I had fun with it too!

IIUC the way you'd do that right now is just repeatedly recording the individual observations on a single commit, which effectively gives it a probability + the number of trials to do the Beta update. I don't yet have a CLI entrypoint to record a batch observation of (probability, num_trials), but it would be easy to add one

But ofc part of the magic is that git_bayesect's commit selection tells you how to be maximally sample efficient, so you'd only want to do a batch record if your test has high constant overhead

[__s]

recompiling can be high constant overhead

[ajb]

In theory, the algorithm could deal with that by choosing the commit at each step, which gives the best expected information gain; divided by expected test time. In most cases it would be more efficient just to cache the compiled output though.

[sfink]

This doesn't sound quite right, but I'm not sure why.

Perhaps: a reasonable objective would be to say that for N bits of information, I would like to pick the test schedule that requires the least total elapsed time. If you have two candidate commits and a slow recompile time, it seems like your algorithm would do many repeats of commit A until the gain in information per run drops below the expected gain from B divided by the recompile time, then it would do many repeats of B, then go back to A, etc. So there are long runs, but you're still switching back and forth. You would get the same number of bits by doing the same number of test runs for each commit, but batching all of the A runs before all of the B runs.

Then again: you wouldn't know how many times to run each in advance, and "run A an infinite number of times, then run B an infinite number of times" is clearly not a winning strategy. Even with a fixed N, I don't think you could figure it out without knowing the results of the runs in advance. So perhaps your algorithm is optimal?

It still feels off. You're normalizing everything to bits/sec and choosing the maximum. But comparing an initial test run divided by the rebuild time vs a subsequent test run divided by a much faster time seems like you're pretending a discrete thing is continuous.

I wish I could math good.

[ajb]

The general requirement for this approach to be optimal, is called "dynamical consistency". A good description is in [1]. It is the situation where, suppose you have a budget B , and you search until your budget is exhausted. Then you are informed that there is an additional budget, B2, and you can continue searching until that is exhausted. A situation is dynamically consistent if, for any B,B2, the optimal strategy is such that you would make the same choices whether you know that you will get B2 or not.

So you are correct that discreteness is a problem, because if you are nearing the end of the budget you may optimally prefer to get more dice rolls than take bigger bets. But the optimal solution is then often analytically intractable (or at least it was - I last read about this a while back), and the entropy approach is often reasonable anyway. (For cases where search effort is significant, a good search plan can be found by simulation).

[1] https://bayes.wustl.edu/etj/articles/search.pdf

[hauntsaninja]

Note that "pick the commit with best expected information gain" in git_bayesect isn't optimal even in the no overhead regime. I provide a counterexample in the writeup, which implies ajb's heuristic is also not optimal. I don't see a tractable way to compute the optimal policy.

One idea: if you always spend time testing equal to your constant overhead, I think you're guaranteed to be not more than 2x off optimal.

(and agreed with ajb on "just use ccache" in practice!)