An example Hyperband schedule is given in @tbl-hyperband where $s = 3$ is the
most exploratory bracket and $s = 0$ essentially performs a random search using
the full budget. @tbl-hyperband-eg demonstrates how this schedule may look if we
were to tune 20 different hyperparameter configurations; note that each entry in
the table is a unique ID referring to a possible configuration of multiple
hyperparameters to tune.

  +-----+---------+---------+
  |     | $s = 3$ | $s = 2$ |
  +-----+---------+---------+
  | $i$ | $m_{i}$ | $r_{i}$ |
  +=====+=========+=========+
  | 0   | 8       | 1       |
  +-----+---------+---------+
  | 1   | 4       | 2       |
  +-----+---------+---------+

  : Hyperband schedule with the number of configurations, $m_{i}$, and
    resources, $r_{i}$, for each bracket, $s$, and stage, $i$, when $\eta = 2$,
    $r{_{min}} = 1$ and $r{_{max}} = 8$. {#tbl-hyperband}

  |         | $s = 3$          | $s = 2$             |
  | ------- | ---------------- | ------------------- |
  | $i = 0$ | $\{1, 2, 3, 4\}$ | $\{9, 10, 11, 12\}$ |
  | $i = 1$ | $\{1, 2\}$       | $\{9, 14\}$         |

  : Hyperparameter configurations in each stage and bracket from the schedule in
    @tbl-hyperband. Entries are unique identifiers for tested hyperparameter
    configurations (HPCs). $HPC^*_s$ is the optimal hyperparameter configuration
    in bracket $s$ and $HPC^*$ is the optimal hyperparameter configuration
    across all brackets. {#tbl-hyperband-eg}
