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Bayesian Optimization of Function Networks with Partial Evaluations
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Proposes p-KGFN, a cost-aware knowledge-gradient acquisition function for Bayesian optimization of function networks that lets the optimizer evaluate individual nodes (partial evaluations) rather than the full network each iteration.
Problem
Bayesian optimization of function networks (BOFN) typically evaluates the entire network at each iteration, ignoring that nodes can often be evaluated individually with heterogeneous costs, which wastes budget when upstream nodes are cheap.
Approach
A one-step knowledge-gradient acquisition function (p-KGFN) that jointly selects a node and its inputs (from previously observed parent outputs plus controllable parameters), normalized by node-specific evaluation cost, with SAA and discretized inner maximization for tractable optimization.
Key results
- p-KGFN outperforms all baselines (EIFN, KGFN, TSFN, EI, KG, Random) across all four experiments, averaged over 30 replications.
- Advantages of partial evaluation grow as the downstream node cost increases; when node costs are equal p-KGFN performs roughly full evaluations.
- Theorem shows the discretized/SAA estimator's maximizer converges almost surely to the true maximizer as the number of fantasy samples grows.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use p-KGFN to select partial node evaluations instead of full-network evaluations | Bayesian optimization of function networks · Ackley | ground-truth objective value | Helped |
| Use p-KGFN to select partial node evaluations instead of full-network evaluations | Bayesian optimization of function networks · Manu-GP | ground-truth objective value | Helped |
| Use p-KGFN to select partial node evaluations instead of full-network evaluations | Bayesian optimization of function networks · FreeSolv | ground-truth objective value | Helped |
| Use p-KGFN to select partial node evaluations instead of full-network evaluations | Bayesian optimization of function networks · Pharma | ground-truth objective value | Helped |
| Increase the second-node evaluation cost while using cost-aware partial evaluations | p-KGFN · Two-node network problems | optimization performance | Helped |
| Use partial evaluations when both node evaluation costs are equal | p-KGFN · Two-node network problems | optimization performance | No clear effect |
| Use p-KGFN when upstream nodes are more challenging to model than downstream nodes | Bayesian optimization of function networks · Additional robustness experiments | optimization performance | No clear effect |
Surprising findings
- When costs of the two nodes are equal, p-KGFN mostly performs full evaluations and gains little over baselines.
- Gains are limited when the expensive upstream node must be evaluated before each cheap downstream evaluation.
Limitations
- Optimizing p-KGFN requires considerable computation, which may be challenging for large networks.
- One-step lookahead only; multi-step lookahead not explored.
- Assumes pairs of nodes do not share common inputs and that upstream outputs must be available before downstream evaluation.
Experimental setup
Datasets: FreeSolv Ackley6D (synthetic) Manu-GP (synthetic GP samples) ODT pharma surrogate models
Benchmarks: Ackley6D Manu-GP FreeSolv Pharma ODT
Metrics: ground-truth objective value of inferred best solution vs co
Baselines: EIFN KGFN TSFN EI KG Random
Builds on: EIFN knowledge gradient BoTorch
Closest papers by meaning
- Bayesian Optimization of Functions over Node Subsets in Graphs (NeurIPS 2024 · similarity 0.89)
- FunBO: Discovering Acquisition Functions for Bayesian Optimization with FunSearch (ICML 2025 · similarity 0.87)
- BONSAI: Bayesian Optimization with Natural Simplicity and Interpretability (NeurIPS 2026 · similarity 0.87)
- A General Framework for User-Guided Bayesian Optimization (ICLR 2024 · similarity 0.87)
- A Study of Bayesian Neural Network Surrogates for Bayesian Optimization (ICLR 2024 · similarity 0.87)
- Bayesian Optimization for Unknown Cost-Varying Variable Subsets with No-Regret Costs (AAAI 2025 · similarity 0.86)
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