Research map / Probabilistic and scientific modeling / Bayesian optimization
Monte Carlo Tree Search based Space Transfer for Black Box Optimization
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Proposes MCTS-transfer, a search-space transfer method for Bayesian optimization that builds an MCTS partition from source-task data and adaptively reweights sources and reconstructs the tree during optimization.
Problem
Expensive black-box optimization with slow convergence from scratch; existing search space transfer methods lack adaptive mechanisms to identify and use similar source tasks during optimization.
Approach
Uses Monte Carlo tree search to recursively partition the space into good/bad subspaces via clustering and classification, with node potentials computed as a decayed, similarity-weighted combination of source and target sample values, and tree reconstruction (Treeify) when the partition becomes inconsistent with the data.
Key results
- On the HPO-B benchmark (39 test problems), MCTS-transfer-GP reports the best mean ranks in both similar and mixed transfer settings, with baseline ranks reported as very close.
- On BBOB and real-world problems, MCTS-transfer-GP with a plain GP reaches or surpasses the PFN surrogate-transfer baseline throughout optimization.
- Runtime analysis shows backpropagation and reconstruction take a minor fraction of total runtime, especially on expensive real-world tasks.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use MCTS-transfer-GP instead of search-space transfer baselines | GP-EI on BBOB · BBOB, mixed transfer | optimization performance | Helped |
| Use MCTS-transfer-GP instead of search-space transfer baselines | GP-EI on LunarLander, RobotPush, and Rover · Real-world problems, similar and mixed transfer | overall ranking | Helped |
| Use MCTS-transfer-GP instead of existing search-space transfer algorithms | GP-EI on Design-Bench · Design-Bench, similar and mixed transfer | ranking after 40 iterations | Helped |
| Use MCTS-transfer instead of existing search-space transfer algorithms | GP-EI on HPOB · HPOB, similar and mixed transfer | mean rank | Helped |
| Train the GP on the full target dataset rather than only selected points in the chosen subspace (ablation) | MCTS-transfer-GP · LunarLander, RobotPush, and Rover, mixed transfer | search performance | Helped |
| Use distribution-based similarity measures rather than point-based measures (ablation) | MCTS-transfer · LunarLander, RobotPush, and Rover, mixed transfer | similarity measurement quality | Mixed |
| Use KL divergence as the task similarity measure (ablation) | MCTS-transfer · Real-world problems, mixed transfer | optimization performance | Helped |
| Use exponential-change weights instead of linear-change weights (ablation) | MCTS-transfer · Rover, mixed transfer | convergence speed | Helped |
| Use all-one weights instead of similarity-ranked weights (ablation) | MCTS-transfer · Real-world problems, mixed transfer | late-stage convergence value | Mixed |
| Set the decay factor to 0.1 rather than 0.99 or 1.0 (ablation) | MCTS-transfer · Real-world problems, mixed transfer | optimization performance | Hurt |
| Use a smaller important-source-task ratio α (ablation) | MCTS-transfer with linear-change weights · Real-world problems, mixed transfer | early-stage convergence | Hurt |
| Increase the exploration factor Cp too much (ablation) | MCTS-transfer · Real-world problems, mixed transfer | convergence speed | Hurt |
Surprising findings
- Baseline search-space transfer methods perform nearly identically on HPOB, with the gaps in final convergence tiny.
- MCTS-transfer-GP is initially surpassed by PFN in mixed transfer on real-world problems before finally finding better solutions.
Limitations
- Cannot handle search space transfer across problems with different domains or dimensions.
- Similarity measures are heuristic; more accurate similarity measures are left to future work.
- No theoretical analysis of effectiveness is provided.
Experimental setup
Datasets: BBOB LunarLander RobotPush Rover Design-Bench HPO-B
Benchmarks: Sphere2D BBOB LunarLander RobotPush Rover Design-Bench HPO-B
Metrics: mean rank over iterations convergence of best objective value
Baselines: GP-EI LA-MCTS Box-GP Ellipsoid-GP Supervised-GP PFN
Builds on: LA-MCTS Box-GP Ellipsoid-GP Supervised-GP PFN
Closest papers by meaning
- Learning search spaces for Bayesian optimization: Another view of hyperparameter transfer learning (NeurIPS 2019 · similarity 0.91)
- Minimizing UCB: a Better Local Search Strategy in Local Bayesian Optimization (NeurIPS 2024 · similarity 0.86)
- BONSAI: Bayesian Optimization with Natural Simplicity and Interpretability (NeurIPS 2026 · similarity 0.85)
- Monte Carlo Tree Search in the Presence of Transition Uncertainty (AAAI 2024 · similarity 0.85)
- Batched Energy-Entropy acquisition for Bayesian Optimization (NeurIPS 2024 · similarity 0.85)
- Sample-and-Bound for Non-convex Optimization (AAAI 2024 · similarity 0.85)
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