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The Behavior and Convergence of Local Bayesian Optimization
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| increase batch size linearly as b_t = dt (ablation) | Local BO · Noisy GP sample paths, RBF or Matérn ν = 2.5 | minimum squared gradient norm: \Oc\bb{\sigma d} -> \Oc\bigl(\sigma d^{\frac54} n^{-\frac14} \log n\bigr) | Helped |
| increase batch size quadratically as b_t = dt^2 rather than linearly (ablation) | Local BO · Noisy GP sample paths, RBF or Matérn ν = 2.5 | minimum squared gradient norm: \Oc\bigl(\sigma d^{\frac54} n^{-\frac14} \log n\bigr) -> \Oc\bigl(\sigma d^{\frac43} n^{-\frac13} \log^2 n\bigr) | Helped |
| use batch size d + 1 instead of a smaller constant batch (ablation) | Local BO · Noiseless RKHS setting | minimum squared gradient norm: B^2 E_{d, k, 0}(b) -> 0; \Oc\bb{d / n} | Helped |
| use projected updates (ablation) | Local BO · Noisy GP sample paths | minimum squared gradient mapping norm: The paper says: “These rates are slower than [ref].” | Hurt |
| perform 10–20 random restarts instead of a single restart (ablation) | Local BO · GP sample paths, 100 dimensions | best objective value | Helped |
| increase random restarts beyond a handful (ablation) | Local BO · GP sample paths, 100 dimensions | best objective value | No clear effect |
| increase the number of observations from n = 5 to n = 10 (ablation) | Matérn GP gradient estimation · Two-dimensional ℓ1 norm at (0, 1) | gradient estimation error: n = 5 -> n = 10 | Helped |
| estimate the slope of a nondifferentiable ℓ1 objective rather than a differentiable quadratic with the same queries (ablation) | Matérn GP gradient estimation · Two-dimensional objective at (0, 1), n = 5 | gradient estimation error | Hurt |
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