Bisection then TPE Refine
Fast deterministic narrow, then a Bayesian polish, in one run.
- Quality
- Highest
- Speed
- Moderate
- Budget
- O(N log N + K log K)
How it works
This is the best of both methods in a single run. Phase one is the complete 3-phase Bisection search: coarse sweep, golden-section narrow, then top-value polish, exactly as the standalone method runs it.
Phase two takes whatever cycle budget is left and hands it to TPE. TPE starts already knowing everything Bisection found, so instead of warming up from scratch it immediately refines around the discovered peak.
You get Bisection's deterministic speed on the broad search plus TPE's Bayesian polish near the optimum, with no manual chaining of two separate runs.
Under the hood
The budget split is adaptive. Bisection runs to its natural plan length (capped by your target), and TPE receives the remainder. If you under-budget the run so Bisection alone exceeds your target, the method degrades cleanly to plain Bisection and TPE simply gets zero cycles.
TPE does not re-seed manually: the rows Bisection produced are already in the history, so TPE's kernel density estimates treat them as prior observations and the refinement is local from the first cycle.
Complexity is roughly Bisection's narrowing cost plus TPE's refinement over the leftover budget K, which is why it lands a notch slower than either part alone but with the highest effectiveness of the seven.
- Phase 1
- Full Bisection
- Phase 2
- TPE on remainder
- Budget split
- Adaptive
- Bisection plan, then the rest
When to use it
Reach for it when
- Most strategies where you want maximum quality from one run
- When you would otherwise run Bisection and then TPE by hand
- Medium parameter spaces with a real peak worth polishing
Reach for something else when
- Very small budgets that Bisection alone would consume
- Tiny spaces where Brute Force already guarantees the answer
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Related methods
-
Bisection (Smart Search)
Brackets the best region of each parameter and zooms in, deterministically and resumably.
Quality 4 of 5Speed 5 of 5O(N) How it works -
Recommended
TPE (Bayesian)
Builds a probabilistic model of what works and spends your cycles where the payoff is most likely.
Quality 5 of 5Speed 5 of 5O(N) How it works