[tune] Fix Hyperband to terminate Trial when max_i is reached

[richardliaw]

Describe the problem

Hyperband should terminate all trials in bracket when bracket is finished.

[haoyangz]

I tried running hyperband_example.py with #1586 merged and no longer saw trials that hung forever, but when visualizing using tensorboard, I do find two trials with iterations > 100. Shouldn't all trials finish at 100 iteration as per the specification of hyperband instance used in hyperband_example.py? Did I miss something?

[richardliaw]

The point of confusion actually is inherited from the original paper: https://people.eecs.berkeley.edu/~kjamieson/hyperband.html

I'll rename the parameter to a more intuitive value.

[haoyangz]

Hmm so what does the max_t here mean exactly? Taking the example in https://people.eecs.berkeley.edu/~kjamieson/hyperband.html, is max_t=81+27+9+3+1 instead of 81?

[richardliaw]

For what I interpreted from the paper and the post,

the number of iterations they are run for r_i within each round of the Successive Halving innerloop

would end up giving total_iterations = 81 + 27 + 9 + 3 + 1. Originally, max_t was intended to be equivalent to max_iter.