Optuna killed 60% of the trials and gave back 28% of the time. The gap is in the config.

The author's explanation stops one step short of the arithmetic. Twenty trials in 13.0 seconds is 0.65 seconds per completed trial ^[1]. Had the 12 killed trials cost nothing, the eight survivors would have finished in about 5.2 seconds ^[2]. The pruned run took 9.4 ^[3], so the dead trials burned roughly 4.2 seconds between them, about 0.35 each, a bit over half the price of running one to the end ^[3]. Close to 45% of the faster run's wall clock went into trials whose results were discarded ^[4].

The settings explain where that floor sits. MedianPruner was built with n_startup_trials=5, so the first five trials could not be pruned at all ^[5], leaving 15 eligible. Twelve of those 15 died, which is 80% of everything the pruner was allowed to touch ^[5]. It killed nearly all of what it could reach and still returned 28% ^[3].

The other knob sets the rest. The model reports every 40 trees up to 200 ^[8], and n_warmup_steps=2 means two reports before a trial is eligible ^[5], so the earliest possible stop is at 80 trees, with 40% of the tree-fitting work already spent ^[6]. Assume per-tree cost is roughly flat, and the ceiling for this study is five full trials plus 15 partial ones at 40%, or 11 trial-equivalents out of 20: about 7.2 seconds, a 45% saving, and only if every eligible trial dies at its first legal opportunity ^[7]. The measured 28% is not far off what this configuration permits. You buy the difference back by lowering both knobs, and you pay for it in the risk the author prices at 0.0005 log loss ^[4], 0.26% of the baseline ^[9], on a search where he notes a trial that looks hopeless at 80 trees can be excellent at 200 ^[11].

The scaling argument in the post is that pruning is a wall-clock optimisation whose value tracks what a trial costs, so 13 seconds is noise and 13 hours is one overnight run instead of three ^[9]. The ratio, though, does not scale with the clock. Twenty-eight over sixty is 0.47 ^[8], and that fraction is fixed by the startup count, the warmup steps and where the bad configurations happen to fall, not by how long a single fit takes. A 13-hour study with this pruner and comparable luck saves 28%, and whoever sized the window from the kill rate is out by roughly half.

The production advice makes the floor heavier. The author says the pruning signal should come from cross-validation rather than the single validation split used here ^[10]. Cross-validation multiplies the cost of every report by the number of folds ^[10], and the reports you cannot avoid are precisely the warmup ones charged to every trial you later throw away, so a five-fold signal makes the unavoidable part of a pruned trial about five times more expensive in absolute terms. Pruning does not take the bad candidates off the bill. It issues a partial refund, and the size of the refund is something you set in the constructor ^[5].