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GUIDE-FBO: Guidance via Uncertainty Intervention and Distributional Exchange for Federated Bayesian Optimization

Jintao Wei, Chenxi Li, Songhao Wang

arXiv:2609.35038v1stat.MLcs.LG

TL;DR

Federated Bayesian Optimization must support knowledge transfer across heterogeneous tasks under communication constraints without sharing raw local observations. GUIDE-FBO exchanges compact distributions over likely optima to guide local decisions through uncertainty intervention, and it achieves the best average rank across three heterogeneity levels on 12 synthetic benchmarks while remaining effective on three real-world tasks.

  • Problem

    FBO must enable knowledge transfer across heterogeneous tasks under bandwidth constraints while keeping raw local observations private.

    Source: §1 · p. 2

  • Method

    GUIDE-FBO exchanges compact distributions over likely optima inferred from local GP posteriors, then uses them to spatially rescale local GP covariance while preserving its mean.

    Source: §1 · p. 2

  • Results

    GUIDE-FBO achieves the best average rank across all three heterogeneity levels on 12 synthetic benchmarks and remains effective on three real-world tasks.

    Source: §1 · p. 2

  • Takeaways & Limitations

    Ablation and communication analyses support spatially localized uncertainty intervention and the efficiency of exchanging compact distributional messages.

    Source: §1 · p. 2

    The formulation assumes agents optimize related, potentially heterogeneous objectives over a shared compact domain, with raw observations kept local.

    Source: §2.2 · p. 3

Abstract

from arXiv · show

Federated Bayesian Optimization (FBO) enables distributed agents to collaboratively optimize expensive black-box objectives without sharing raw local observations. However, effective knowledge transfer remains challenging under communication constraints and task heterogeneity. We propose GUIDE-FBO, in which agents exchange compact distributions over the locations of their respective optima inferred from local Gaussian process (GP) posteriors, rather than raw observations, query points, or surrogate parameters. The server merges and reweights these distributional components before returning a subset to each agent. Each agent then constructs a Federated Interventional GP (FI-GP), which preserves the local posterior mean and spatially rescales its covariance for local decision making. For the upper confidence bound (UCB) instantiation, GUIDE-UCB, we prove that any bounded FI-GP uncertainty intervention preserves the leading-order cumulative regret rate of standard GP-UCB. When the transferred distributions place greater support near an optimum than in a suboptimal region, selecting the latter requires greater local posterior uncertainty. Experiments on 12 synthetic benchmarks and three real-world optimization tasks show that GUIDE-FBO remains effective across settings ranging from homogeneous to severely heterogeneous. Ablation results highlight the importance of spatially localized uncertainty intervention, while the communication analysis shows that GUIDE-FBO exchanges only compact distributional messages.

1 INTRODUCTION

The paper addresses how federated agents can exchange useful guidance across heterogeneous tasks under communication constraints without sharing raw observations. GUIDE-FBO transfers compact distributions over likely optima and uses them to intervene on local GP uncertainty.

1 INTRODUCTION

  • Bayesian Optimization uses a probabilistic surrogate and acquisition function to balance exploration and exploitation for expensive black-box objectives.FBO extends BO to distributed settings where agents collaborate without revealing raw local observations.Source: §1 · p. 1
  • FBO must transfer knowledge without exposing raw observations while addressing heterogeneous objectives and limited bandwidth, which can make blind aggregation or point-level transfer fragile.The setting includes costly local optimization tasks such as dose optimization across clinical centers, where personalized decisions matter.Source: §1 · pp. 1–2
  • Agents exchange compact distributions over likely optima inferred from local GP posteriors; the server merges, reweights, and redistributes them as global guidance.Only compact distribution parameters are transmitted.Source: §1 · p. 2
  • FI-GP preserves the local posterior mean and spatially rescales its covariance; for GUIDE-UCB, bounded intervention preserves GP-UCB's leading-order cumulative regret rate.When transferred distributions provide greater support near an optimum than at a suboptimal point, selecting that point requires greater local posterior uncertainty.Source: §1 · p. 2
  • GUIDE-FBO achieves the best average rank across all three heterogeneity levels on 12 synthetic benchmarks and remains effective on three real-world tasks.Ablation and communication analyses further support the proposed mechanism and its communication efficiency.Source: §1 · p. 2

2 RELATED WORK AND PROBLEM SETUP

The related-work section distinguishes how federated BO methods share knowledge, while the problem setup specifies agents with related but potentially heterogeneous objectives and private local observations.

2.1 RELATED WORK

  • Existing methods either coordinate query selection or incorporate shared knowledge into predictive modeling; GUIDE-FBO instead preserves the local posterior mean and rescales covariance for each decision.Its FI-GP is an auxiliary decision posterior, while the fitted local GP remains based exclusively on private observations.Source: §2.1 · pp. 2–3

2.2 FEDERATED MULTI-TASK BAYESIAN OPTIMIZATION

  • The setup has N agents with related but potentially heterogeneous black-box objectives over a shared compact domain, and raw observations remain local.Each agent maintains a local GP posterior based on its private observation set.Source: §2.2 · p. 3

3 METHODOLOGY

GUIDE-FBO transfers compact distributions over likely optimum locations, which the server merges and reweights before returning guidance to agents. Agents use that guidance to spatially rescale local GP uncertainty while preserving the local posterior mean.

3.1 OPTIMUM DISTRIBUTION EXTRACTION

  • Agents approximate their optimum-location distributions by sampling local GP posterior paths and fitting a DPGMM to the sampled optimum locations.The resulting mixture represents promising regions through component weights, centers, and spatial spreads.Source: §3.1 · pp. 3–4
  • To reduce communication, agents upload only the DPGMM component with the largest mixture weight under the default uplink budget.The component mixture summarizes sampled optimum locations, and its dominant component serves as the compact message.Source: §3.1 · p. 4

3.2 SERVER-SIDE COMPONENT MERGING AND REWEIGHTING

  • The server merges nearby components by complete-linkage clustering, represents each cluster with a moment-matched Gaussian, and reweights merged components using value scores.It sends each agent a sampled subset to avoid directing parallel searches toward the same regions.Source: §3.2 · pp. 4–5

3.3 FEDERATED INTERVENTIONAL GAUSSIAN PROCESS

  • Each agent builds an FI-GP that preserves its local posterior mean and spatially rescales covariance using returned guidance for local decision making.The uncertainty intervention can be used with acquisition-based rules including UCB and noisy expected improvement, as well as Thompson sampling.Source: §3.3 · pp. 5–6

4 THEORETICAL ANALYSIS

The analysis examines GUIDE-UCB under arbitrary bounded guidance and under informative guidance. It shows that bounded intervention preserves the leading-order regret rate, while informative guidance raises the local uncertainty needed for selecting a suboptimal point.

Analysis assumptions

  • The analysis assumes the standard simultaneous GP confidence event and a uniformly bounded guidance field; Gmax = 1 is valid under GUIDE-FBO’s normalized weighting.The regret guarantee also relies on the standard cumulative posterior variance bound.Source: §4 · p. 6

Theorem 1

  • GUIDE-UCB preserves the leading-order cumulative regret rate of standard GP-UCB under arbitrary bounded guidance.The guidance-dependent terms grow as √T and log T, while a fixed intervention strength also preserves the rate up to a constant factor.Source: §4 · p. 6

Proposition 1

  • When guidance is stronger near an optimum than at a suboptimal candidate, selecting that candidate requires sufficiently large local posterior uncertainty.With negligible guidance at the candidate, the required uncertainty exceeds the standard GP-UCB counterpart by approximately λmaxc σn,t−1(x∗n).Source: §4 · pp. 6–7

5 EXPERIMENTS

Across synthetic and real-world tasks, GUIDE performs strongly across heterogeneity levels. Ablations and communication analyses examine its intervention mechanism and message-cost trade-offs.

5.1 EXPERIMENTAL SETUP

  • Experiments compare nine baselines and three GUIDE acquisition variants across 12 synthetic benchmarks and three real-world tasks, using 30 initial evaluations and 50 BO rounds over 10 runs.Synthetic tasks use 16 agents and three heterogeneity levels; real-world tasks are Landmine Detection, Activity Recognition, and FedHPO.Source: §5.1 · p. 7

5.2 MAIN RESULTS

  • Matched comparisons favor GUIDE over UCB, NEI, and TS across acquisition rules, while Level 3 advantages are smaller and more task dependent.At Level 3, ranking correlation falls to 0.081; intervention strength decays over time, but negative transfer can still occur on individual tasks.Source: §5.2 · pp. 7–8
  • GUIDE-UCB ranks first across 12 synthetic benchmarks at all heterogeneity levels, while a GUIDE variant leads each of three real-world tasks.GUIDE-UCB’s average ranks are 1.33, 1.58, and 2.58; differences among leading methods are small on Activity Recognition and FedHPO.Source: §5.2 · pp. 7–8, Table 1 · p. 8, Table 2 · p. 8

5.3 ABLATION AND COMMUNICATION EFFICIENCY

  • Under Level 2 heterogeneity, full GUIDE-UCB ranks first, and replacing spatially varying intervention with uniform scaling produces the largest degradation.Average rank rises from 1.50 for Full GUIDE-UCB to 6.25 for uniform scaling; at Level 3, full GUIDE-UCB ranks first and removing value-aware reweighting ranks worst.Source: §5.3 · pp. 8–9, Table 3 · p. 9
  • With d = 10 and P = 5, GUIDE-FBO communicates at most 127 scalars per agent per round, versus 212 for CGP, 1000 for FTS, and 4000 for FTS-DE.FMTBO uses 14 scalars per round but has weaker aggregate synthetic performance than GUIDE-UCB.Source: Table 4 · p. 9, §5.3 · p. 9

5.4 ADDITIONAL ANALYSES

  • On tested Level 3 benchmarks, GUIDE remains stable across moderate choices of M, P, and δmerge, while overly strong uncertainty intervention degrades performance.GUIDE adds computation relative to independent BO but is more efficient than corresponding CGP variants on most Level 2 synthetic benchmarks.Source: §5.4 · p. 9

6 CONCLUSION

GUIDE-FBO exchanges distributions over optimum locations and uses them to rescale local posterior uncertainty. The analysis establishes a regret-rate guarantee for GUIDE-UCB, while the current framework lacks a formal privacy guarantee for exchanged distributions.

6 CONCLUSION

  • GUIDE-FBO represents local search information as distributions over optimum locations, separating global knowledge exchange from local surrogate fitting and rescaling uncertainty for local decisions.The intervention can be combined with UCB, NEI, and TS without redesigning their local decision rules.Source: §6 · pp. 9–10
  • Under bounded federated guidance, GUIDE-UCB has the same leading-order regret rate as GP-UCB; informative guidance can require a suboptimal point to retain sufficient local uncertainty for selection.Source: §6 · p. 10
  • GUIDE-FBO avoids sharing raw observations but provides no formal privacy guarantee for exchanged distributional information.The authors identify differential privacy for local release or server aggregation as future work.Source: §6 · p. 10

AI USE STATEMENT

The appendix documents AI use, gives the GUIDE-FBO procedure, and develops theoretical conditions and results for the FI-GP and GUIDE-UCB analysis.

AI USE STATEMENT

  • Generative AI assisted with proofs, methodology, experiments, implementation, translation, information search, and manuscript readability; authors reviewed the work and take responsibility for the final content.The authors state that AI did not generate synthetic datasets, develop theoretical models, formulate claims, write proofs, or interpret results.Source: AI USE STATEMENT · p. 10

A COMPLETE GUIDE-FBO PSEUDOCODE

  • Algorithm 1 proceeds through optimum-distribution extraction, server-side component merging and reweighting, then FI-GP-based local decision making.Agents fit local GPs, sample posterior paths to estimate optima, upload components, receive a subset, and select local queries using the FI-GP.Source: A COMPLETE GUIDE-FBO PSEUDOCODE · p. 13

B THEORETICAL ASSUMPTIONS, LEMMAS, AND PROOFS

B.4 PROOF OF LEMMA B.1

  • The instantaneous-regret decomposition underlies both the cumulative regret bound and the analysis of how guidance changes suboptimal-point selection.The cumulative-bound argument discards a nonpositive term, while the informative-guidance argument retains it.Source: B THEORETICAL ASSUMPTIONS, LEMMAS, AND… · p. 14

B.2 MAXIMUM INFORMATION GAIN

  • Conditioning on initial observations cannot increase covariance, so standard information-gain complexity remains a valid upper bound for the sequential analysis.The appendix uses the initial-data-conditioned covariance and cumulative posterior variance to connect the query sequence to information gain.Source: §B.2 · pp. 15–16

B.3 VALIDITY AND VARIANCE SCALING OF FI-GP

  • The FI-GP covariance kernel remains positive semidefinite while the decision posterior preserves the local mean and scales its variance.The intervention is therefore applied to uncertainty without changing the local posterior mean.Source: §B.3 · p. 16

B.5 PROOF OF THEOREM 1

  • The cumulative-regret proof combines the one-step bound with Cauchy–Schwarz and cumulative posterior-variance control, treating T and log T terms as lower order.The proof applies the cumulative-variance lemma and derives the leading-order bound from the resulting inequality.Source: §B.5 · p. 18

B.6 CONSTANT INTERVENTION STRENGTH

  • For fixed intervention strength, guidance changes only the constant factor in the regret bound, which remains sublinear when βT γn,T = o(T).This conclusion applies to any fixed λ ≥ 0.Source: §B.6 · p. 19

B.7 PROOF OF PROPOSITION 1

The appendix specifies when guidance raises the selection threshold for suboptimal points, interprets that condition geometrically, and describes the synthetic benchmark suite.

B.7 PROOF OF PROPOSITION 1

  • GUIDE-UCB raises the threshold for selecting a suboptimal point when guidance near the optimum is sufficiently stronger than guidance at that point.The comparison is against standard GP-UCB, whose threshold is recovered at λt = 0.Source: §B.7 · p. 19

B.8 GEOMETRIC INTERPRETATION OF INFORMATIVE GUIDANCE

  • A received component near the optimum can provide substantial guidance there, while a suboptimal candidate far into component tails receives little guidance.The appendix gives Mahalanobis-radius conditions for these cases.Source: §B.8 · p. 19

C.1 SYNTHETIC BENCHMARKS

  • The synthetic benchmark suite contains 12 maximization objectives, with dimensions and search domains reported for each function.The appendix notes that minimization functions are negated where necessary to express every objective as maximization.Source: §C.1 · p. 20, Table 5 · p. 20

C.2 REAL-WORLD FEDERATED OPTIMIZATION TASKS

The appendix details three real-world optimization tasks, synthetic heterogeneity construction and measurement, evaluation metrics, shared settings, and the scope of the reported results.

C.2 REAL-WORLD FEDERATED OPTIMIZATION TASKS

  • The real-world tasks comprise Landmine Detection across 29 fields, Activity Recognition across 30 subjects, and FedHPO across Cora, CiteSeer, and PubMed.They optimize SVM, logistic-regression, and GCN hyperparameters, respectively, using AUC or validation accuracy as the objective.Source: §C.2 · pp. 20–21

C.3 SYNTHETIC TASK HETEROGENEITY AND EMPIRICAL SIMILARITY

  • Synthetic heterogeneity is generated with agent-specific translations and rotations, then characterized by mean pairwise Spearman rank correlation across common probe locations.The three regimes correspond to identical objectives, moderate ranking agreement, and weak average agreement across agents.Source: §C.3 · pp. 21–22

C.4 EVALUATION METRICS

  • Synthetic performance is reported as average simple regret, while real-world performance uses average AUC for Landmine and validation accuracy for Activity Recognition and FedHPO.Simple regret is lower-is-better; the real-world metrics are higher-is-better.Source: §C.4 · pp. 22–23

C.5 SHARED EXPERIMENTAL SETTINGS

  • Experiments use 30 initial evaluations per agent, 50 BO rounds, and 10 independent repetitions, with the natural agent counts for real-world tasks.GUIDE-FBO uses the same configuration across benchmarks unless otherwise stated; its principal tunable parameters include sample count, packet size, merge threshold, and maximum guidance strength.Source: §C.5 · p. 23

D COMPLETE EXPERIMENTAL RESULTS AND CONVERGENCE TRAJECTORIES

  • The appendix reports final average simple regret on all 12 synthetic functions and convergence trajectories across three heterogeneity levels, plus trajectories for the real-world tasks.Curves summarize 10 independent runs with shaded regions showing ±1 standard error of the mean.Source: D COMPLETE EXPERIMENTAL RESULTS AND… · p. 24

D.1 LEVEL 1: δshift = 0 AND δrot = 0

GUIDE performs strongly across homogeneous, mildly heterogeneous, and severely heterogeneous synthetic settings, though its advantage becomes less uniform as heterogeneity increases. On real-world tasks, GUIDE-NEI achieves the best average rank, with leading methods often close in final performance.

D.1 LEVEL 1: δshift = 0 AND δrot = 0

  • At Level 1, GUIDE-UCB ranks first at 1.33 and has the lowest final regret on 10 of 12 benchmarks; all three GUIDE variants beat matched independent methods on every function.The agents optimize the same latent objective, with mean pairwise Spearman correlation 1.000.Source: Table 8 · p. 24, §D.1 · p. 25
  • At Level 1, GUIDE-UCB and GUIDE-NEI separate early on most benchmarks, but point transfer beats GUIDE on Michalewicz and Styblinski–Tang, where narrow valleys or competing basins favor exact, shared designs.On Styblinski–Tang, CGP-NEI and CGP-UCB obtain final regrets of 56.2330 and 62.7248, versus 99.6545 and 102.8457 for GUIDE-UCB and GUIDE-NEI.Source: §D.1 · p. 25

D.2 LEVEL 2: δshift = 0.05 AND δrot = 0.1

  • At Level 2, GUIDE-UCB ranks first overall at 1.58, has the lowest final regret on 9 benchmarks, and is top two on 11 of 12.GUIDE-NEI ranks second at 2.17; both improve over matched independent baselines on 11 of 12 functions.Source: §D.2 · p. 25, Table 9 · p. 26
  • At Level 2, GUIDE’s regional representation suits mild spatial mismatch: it leads on Michalewicz despite a mean pairwise Spearman correlation of only 0.034.GUIDE-UCB and GUIDE-NEI obtain final regrets of 5.8629 and 5.8783, respectively.Source: §D.2 · p. 27

D.3 LEVEL 3: δshift = 0.3 AND δrot = 1.0

  • At Level 3, GUIDE-UCB has the best aggregate rank (2.58) despite overlapping, less uniformly leading trajectories; it is top two on 8 of 12 benchmarks.GUIDE-UCB has the lowest final regret on Levy, Griewank, Rastrigin, and Zakharov; GUIDE-NEI is best on Ackley, Weierstrass, and Powell.Source: Table 10 · p. 27, §D.3 · p. 28
  • At Level 3, spatial transfer can still fail on narrow, misaligned landscapes: GUIDE-UCB’s Rosenbrock regret is 321.9631 versus 257.8472 for independent UCB.The narrow curved valley is particularly sensitive to strong translations and rotations.Source: §D.3 · p. 29

D.4 REAL-WORLD CONVERGENCE TRAJECTORIES

  • Across the three real-world tasks, GUIDE-NEI has the best average rank (1.67), and both GUIDE-UCB and GUIDE-NEI outperform their matched independent baselines on all three.The strongest methods finish within a narrow range on Activity Recognition and FedHPO.Source: §D.4 · pp. 29–30

E ABLATION STUDY DETAILS

  • The ablation setup compares GUIDE-UCB with variants using the same local GPs, initialization, budget, decision rule, and seeds; uniform scaling preserves average intervention magnitude but removes spatial variation.The main study uses Level 2, with the same configurations also evaluated at Level 3.Source: E ABLATION STUDY DETAILS · p. 30

E.1 LEVEL 2 ABLATION RESULTS

Ablations show that spatially localized uncertainty intervention is central to GUIDE-UCB’s Level 2 performance, while the relative value of other components shifts under severe heterogeneity. Full GUIDE-UCB retains the best aggregate rank at both levels, though it does not lead on every benchmark.

E.1 LEVEL 2 ABLATION RESULTS

  • At Level 2, full GUIDE-UCB has the best average rank (1.50), while uniform uncertainty scaling and Vanilla UCB rank last at 6.25 and 6.75.On Ackley, full GUIDE-UCB’s final regret is 8.4785, versus 19.1366 for uniform scaling and 19.4350 for Vanilla UCB.Source: §E.1 · pp. 30–31, Figure 8 · p. 31
  • Removing spatial variation while retaining the exchange pipeline and average intervention magnitude loses much of GUIDE-UCB’s advantage, indicating that uniform uncertainty increases are insufficient.The full method increases uncertainty selectively in regions supported by transferred distributions.Source: §E.1 · p. 31
  • Under Level 2, a single Gaussian ranks 4.50, while removing component merging ranks 3.75; the former cannot retain multiple separated modes, and the latter leaves redundant components.Agent-specific sampling and value-aware reweighting have less uniform effects across individual benchmarks.Source: §E.1 · p. 31

E.2 LEVEL 3 ABLATION RESULTS

  • At Level 3, full GUIDE-UCB still has the best average rank (2.50), but the best variant varies by benchmark and trajectories overlap more than at Level 2.Uniform scaling is best on Rastrigin, Vanilla UCB on Michalewicz, and full GUIDE-UCB on Zakharov.Source: §E.2 · p. 31, Table 11 · p. 32, Figure 9 · p. 32
  • Value-aware reweighting becomes more important in aggregate under severe heterogeneity: removing it shifts from rank 2.75 at Level 2 to the weakest rank, 5.25, at Level 3.The score filters components using favorable local function values in addition to mixture mass, though its effect is not uniform across tasks.Source: §E.1 · p. 30, §E.2 · pp. 31–32

F SENSITIVITY ANALYSIS

The Level 3 sensitivity analysis varies posterior-optimum sample count, downlink packet size, maximum intervention strength, and component-merging threshold on Rastrigin and Michalewicz. No parameter setting is uniformly best, and excessive uncertainty intervention performs poorly under weak cross-agent agreement.

F SENSITIVITY ANALYSIS

  • The effect of sample count reverses across tasks: Rastrigin is lowest at M = 500 with regret 90.8849, while Michalewicz is lowest at M = 1000 with 7.3473.Increasing M to 750 or 1000 does not consistently benefit both benchmarks.Source: F SENSITIVITY ANALYSIS · p. 33
  • The best packet size differs by task: P = 5 gives Rastrigin regret 90.8849, while P = 3 gives Michalewicz regret 7.3586.Larger packets degrade both benchmarks at P = 8 and P = 10.Source: F SENSITIVITY ANALYSIS · p. 33
  • At λmax = 0.25, final regret is 90.7113 on Rastrigin and 7.3563 on Michalewicz; λmax = 2.0 gives 95.0430 and 7.4711, respectively.The strongest intervention gives the worst result on both benchmarks.Source: F SENSITIVITY ANALYSIS · pp. 33–34
  • At δmerge = 0.04, Rastrigin’s final regret is 89.5435; Michalewicz instead reaches its lowest value, 7.3613, at δmerge = 0.02.The threshold controls spatial resolution, so the preferred setting depends on objective geometry.Source: F SENSITIVITY ANALYSIS · p. 34
  • Across the tested settings, larger sample counts, packet sizes, or intervention strengths do not consistently reduce regret, and the preferred merging threshold depends on the task.The study tests one parameter at a time on Rastrigin and Michalewicz under Level 3 heterogeneity.Source: F SENSITIVITY ANALYSIS · pp. 32–34, Table 13 · p. 33

G COMMUNICATION COST ANALYSIS

GUIDE-FBO’s communication analysis counts scalar values transmitted per agent per BO round under a default synthetic setting. With diagonal covariance and packet size P = 5, its total exchange is bounded at 127 scalars per round.

G COMMUNICATION COST ANALYSIS

  • Under the same accounting, FTS uses 500 scalars in each direction, FTS-DE 2000 each way, FMTBO 12 uplink and 2 downlink, and CGP 12 uplink and 200 downlink.The comparisons use d = 10 and DRFF = 500.Source: G COMMUNICATION COST ANALYSIS · pp. 34–35
  • Under the stated default setting, GUIDE-FBO’s uplink components contain a mean, diagonal covariance vector, mixture weight, and value score; downlink components carry a mean, diagonal covariance, and guidance weight.The uplink component count depends on active mixture components; downlink is capped by packet size P.Source: G COMMUNICATION COST ANALYSIS · p. 35
  • GUIDE-FBO transmits at most 127 scalars per agent per round under the default setting, including a downlink of at most 105 scalars.The setting uses d = 10, diagonal covariance, and P = 5.Source: G COMMUNICATION COST ANALYSIS · pp. 34–35

H COMPUTATIONAL EFFICIENCY ANALYSIS

Across 12 Level 2 synthetic benchmarks, GUIDE adds computation over independent local BO but is faster than corresponding CGP variants on most benchmarks. Its posterior-optimum sampling uses local random-feature paths, with only the selected distributional component uploaded.

H COMPUTATIONAL EFFICIENCY ANALYSIS

  • 129.1, 240.7, and 289.4 seconds per run for UCB, GUIDE-UCB, and CGP-UCB, respectively; GUIDE-UCB is faster than CGP-UCB on 9 of 12 benchmarks.Times are averaged across the 12 Level 2 benchmarks.Source: Table 14 · p. 35, H COMPUTATIONAL EFFICIENCY ANALYSIS · p. 35
  • 534.1 and 905.3 seconds per run for GUIDE-NEI and CGP-NEI, respectively; GUIDE-NEI is faster on 9 of 12 benchmarks.GUIDE remains less expensive than corresponding CGP variants on most tested benchmarks.Source: H COMPUTATIONAL EFFICIENCY ANALYSIS · p. 35, Table 14 · p. 35
  • GUIDE adds computation over local BO through posterior-optimum sampling, distribution fitting, and server-side processing; its runtime impact depends on objective-evaluation cost.When simulation, model training, or physical experimentation dominates optimization time, optimizer-side computation may represent a smaller share of end-to-end cost.Source: H COMPUTATIONAL EFFICIENCY ANALYSIS · p. 35

I ORTHOGONAL RANDOM FEATURES FOR POSTERIOR-OPTIMUM SAMPLING

  • Orthogonal random Fourier features approximate the local Matérn-5/2 covariance, while sampled paths preserve the fitted local GP posterior mean.The local GP supplies the mean and the Bayesian linear feature model supplies the stochastic residual.Source: I ORTHOGONAL RANDOM FEATURES FOR… · p. 36
  • Independent posterior-weight draws yield optimum-location samples for fitting the local DPGMM; only the selected distributional component is uploaded.Acquisition evaluation uses the intervened local GP posterior, while the feature sampler extracts optimum distributions.Source: I ORTHOGONAL RANDOM FEATURES FOR… · p. 36
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