Trust regions

With trust_region = true, each acquisition solve is restricted to a local hyperrectangle centered on the incumbent, with per-dimension edge length L (clamped to the variable bounds). This is the TuRBO approach — the state of the art for high-dimensional bound-constrained Bayesian optimization.

options = BayesOptOptions(
    sub_options = ...,
    trust_region = true,
    tr_length_init = 0.8,   # initial TR edge length (fraction of the box)
    tr_min_factor = 1/32,   # restart below this fraction of the initial TR
    tr_success_max = 3,     # grow after this many consecutive improvements
    tr_fail_max = nothing,  # shrink after this many failures (default
                            # max(1, n) where n is the number of variables)
)

The success/failure rule:

• L doubles (up to tr_length_init) after tr_success_max consecutive improvements,
• L halves after tr_fail_max consecutive non-improvements,
• when the region collapses below tr_min_factor * L_init, it restarts at full size around the incumbent.

The number of restarts is reported in the result's n_restarts field. Trust regions require finite variable bounds for all variables.

The acquisition multistart points (acq_multistart) are clamped into the current trust region. Batched Thompson sampling over multiple simultaneous trust regions remains a future refinement.