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This Too Shall Pass: Removing Stale Observations in Dynamic Bayesian Optimization
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Proposes W-DBO, which scores each dataset observation's relevance via a normalized 2-Wasserstein distance between GP posteriors (with and without the observation) on future predictions, and greedily removes stale observations under an exponential removal budget.
Problem
Dynamic Bayesian optimization of time-varying black-box functions must discard stale observations to keep GP inference (O(n^3)) fast enough for high sampling frequency, but no online criterion existed for measuring observation relevance.
Approach
Measure an observation's relevance by the relative 2-Wasserstein drift its removal causes in GP posteriors over future space-time domain S x [t0, inf), normalized by the distance from the prior, with closed-form upper bounds via self-convolutions of spatial and temporal kernels, and remove observations under a budget (1+alpha)^t.
Key results
- W-DBO obtains the lowest average regret on most benchmarks, e.g., Rosenbrock 3.81 vs 17.55 for TV-GP-UCB (best baseline) and Powell 428.1 vs 534.2 for ET-GP-UCB.
- Normalized average performance over 12 experiments: W-DBO 0.01 vs 0.29 for TV-GP-UCB (next best) and 0.62 for ABO.
- Sensitivity analysis identifies alpha = 1/4 as the sweet spot balancing dataset size and sampling frequency.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use W-DBO instead of GP-UCB | Dynamic Bayesian optimization · Rastrigin | average regret: 17.81 -> 18.54 | Hurt |
| use W-DBO instead of ET-GP-UCB | Dynamic Bayesian optimization · Schwefel | average regret: 428.97 -> 290.34 | Helped |
| use W-DBO instead of TV-GP-UCB | Dynamic Bayesian optimization · StyblinskiTang | average regret: 15.74 -> 13.04 | Helped |
| use W-DBO instead of ABO | Dynamic Bayesian optimization · Eggholder | average regret: 256.92 -> 225.68 | Helped |
| use W-DBO instead of TV-GP-UCB | Dynamic Bayesian optimization · Ackley | average regret: 3.27 -> 2.24 | Helped |
| use W-DBO instead of TV-GP-UCB | Dynamic Bayesian optimization · Rosenbrock | average regret: 17.55 -> 3.81 | Helped |
| use W-DBO instead of TV-GP-UCB | Dynamic Bayesian optimization · Shekel | average regret: 2.03 -> 1.72 | Helped |
| use W-DBO instead of R-GP-UCB | Dynamic Bayesian optimization · Hartmann3 | average regret: 0.26 -> 0.35 | Hurt |
| use W-DBO instead of TV-GP-UCB | Dynamic Bayesian optimization · Hartmann6 | average regret: 0.44 -> 0.32 | Helped |
| use W-DBO instead of ET-GP-UCB | Dynamic Bayesian optimization · Powell | average regret: 534.2 -> 428.1 | Helped |
| use W-DBO instead of R-GP-UCB | Dynamic Bayesian optimization · Temperature | average regret: 0.69 -> 0.68 | Helped |
| use W-DBO instead of TV-GP-UCB | Dynamic Bayesian optimization · WLAN | average regret: 1.33 -> 1.19 | Helped |
Surprising findings
- Standard DBO baselines such as ABO and ET-GP-UCB perform roughly on par with vanilla GP-UCB in the authors' experiments.
Limitations
- Greedy removal policy may overestimate the impact of removing multiple observations jointly.
- No regret bound in continuous time is provided; left as future work.
- Approximation of the Wasserstein integrals via self-convolution introduces error, only partly compensated between numerator and denominator.
Experimental setup
Datasets: Rastrigin Schwefel StyblinskiTang Eggholder Ackley Rosenbrock Shekel Hartmann3 Hartmann6 Powell Temperature WLAN
Benchmarks: Rastrigin Schwefel StyblinskiTang Eggholder Ackley Rosenbrock Shekel Hartmann3 Hartmann6 Powell Temperature WLAN
Metrics: average regret
Baselines: GP-UCB R-GP-UCB TV-GP-UCB ET-GP-UCB ABO
Builds on: GP-UCB TV-GP-UCB R-GP-UCB ABO
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