BayMOTH: Bayesian optiMizatiOn with meTa-lookahead -- a simple approacH
Authors: Rahman Ejaz, Varchas Gopalaswamy, Ricardo Luna, Aarne Lees, Vineet Gundecha, Christopher Kanan, Soumyendu Sarkar, Riccardo Betti
Organizations: Laboratory for Laser Energetics, Rochester, NY, USA · Department of Mechanical Engineering, University of Rochester, Rochester, NY, USA · Hewlett Packard Labs, Santa Clara, CA, USA · Department of Computer Science, University of Rochester, Rochester, NY, USA · Department of Physics, University of Rochester, Rochester, NY, USA
Bayesian optimization (BO) has for sequential optimization of expensive black-box functions demonstrated practicality and effectiveness in many real-world settings. Meta-Bayesian optimization (meta-BO) focuses on improving the sample efficiency of BO by making use of information from related tasks. Although meta-BO is sample-efficient when task structure transfers, poor alignment between meta-training and test tasks can cause suboptimal queries to be suggested during online optimization. To this end, we propose a simple meta-BO algorithm that utilizes related-task information when determined useful, falling back to lookahead otherwise, within a unified framework. We demonstrate competitiveness of our method with existing approaches on function optimization tasks, while retaining strong performance in low task-relatedness regimes where test tasks share limited structure with the meta-training set.
Figures & tables
Figure 1: An overview of BayMOTH
Figure 2: Optimization trajectories across relatedness settings (Sets 1–4) for synthetic ICF experiments. Sample budget is restricted to 10, reflecting the realistic sample budget for ICF.
Figure 3: Simple regret trajectories on HPO tasks. The combined plot includes HPO-B tasks such as glmnet (ID:5860) and rpart.preproc (ID:4796), along with the HPOBench XGBoost results. Curves show performance versus sample steps, with mean trajectories and variability over randomly initialized starting locations.
Appendix figures & tables16 assets
Supplementary material from the paper’s appendix.
Appendix
Sχ,t←NCC(μt,μ~χ,t)
Appendix
Algorithm 1 BayMOTH
Figure 4: Set 1 (highest NCC in set ≈ 0.85) trajectory and source-task usage across γ values.
Figure 5: Set 2 (highest NCC in set ≈ 0.60) trajectory and source-task usage across γ values.
Figure 6: Set 3 (highest NCC in set ≈ 0.82) trajectory and source-task usage across γ values.
Figure 7: Set 4 (highest NCC in set ≈ 0.10) trajectory and source-task usage across γ values.
Figure 8: Scan on the number of samples for the Monte Carlo estimator, using set 1 of the synthetic ICF dataset. Shown is <> line and ±σ shaded region over 30 randomly initialized starting locations.
Figure 9: Ablation on the greedy balancing parameter α . Shown is <> line and ±σ shaded region over 30 randomly initialized starting locations.
Method
Cost profile
BayMOTH
Offline source task GP meta-training (cheap ≈ 40s); primary computational cost is paid online during proposal generation.
MetaBO
Main cost is offline PPO training; approximately 4 hours for 2000 PPO iterations.
NAP
Main cost is offline PPO training; approximately 11 hours for 2000 PPO iterations.
Appendix
Table 1: High-level computational cost profile of BayMOTH and offline-trained baselines.
BayMOTH stage
Frequency
Share of proposal time
Avg per call
Meaning
Source-task GP training
once
N/A
40.00 s
One-time offline training.
Comparison GP update
once after observation
N/A
0.234 s
Online overhead outside the proposer.
Proposal optimization
once per suggestion
100.00%
44.84 s
Full online proposal cost.
BayMOTH acquisition evaluation
inside L-BFGS-B
98.66%
145.85 ms
Nearly all proposal-time computation is spent here.
Horizon-step simulation
once per acquisition evaluation
97.99%
144.85 ms
Main bottleneck.
Future EI (inside horizon)
M times per acquisition evaluation
72.17%
21.34 ms
Repeated future-EI computation dominates the inner loop.
Appendix
Table 2: Profiling-based breakdown of BayMOTH proposal-time cost on ranger9 ( d=10 ).
(a) Set 1: High relatedness
(c) Set 3: Moderate relatedness
Figure 12: Source task pool sensitivity studies on test task performance (Set 1 test task). Shown is <> line and ±σ shaded region over 100 randomly initialized starting locations.
Figure 13: Source task pool sensitivity studies on test task performance (Set 4 test task). Shown is <> line and ±σ shaded region over 100 randomly initialized starting locations.
Figure 14: Convergence study over PPO iterations using Set 2 of the ICF dataset.
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Colin Doumont, Henry Moss, Philipp Hennig
University of Tübingen, Tübingen AI Center · Lancaster University
Bayesian optimization (BO) of expensive black-box functions is traditionally addressed with Gaussian processes (GPs), which scale cubically with observations, or Bayesian neural networks (BNNs), which incur costly posterior sampling and inner-loop acquisition optimization. We propose VBO-MI (Variational Bayesian Optimization with Mutual Information), a fully gradient-based BO framework that requires no explicit GP prior or fixed parametric posterior family over objective function and treats it as a strict black box. An actor-critic architecture pairs an action-net with a variational critic that estimates information gain, eliminating the acquisition optimization bottleneck and achieving up to 102× fewer FLOPs than BNN-BO baselines. A lightweight surrogate network further reduces real function queries to one batch per iteration. We establish consistency guarantees and evaluate VBO-MI on synthetic benchmarks (Ackley, Levy, Griewank) and real-world tasks (Rover Trajectory, Lunar Lander, Pest Control), demonstrating competitive or superior performance over the baselines.
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Masaki Adachi, Yuta Suzuki, Juliusz Ziomek
Lattice Lab · Toyota Motor Corporation · Machine Learning Research Group +1