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Safe Time-Varying Optimization based on Gaussian Processes with Spatio-Temporal Kernel
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Proposes TVSafeOpt, a safe Bayesian optimization algorithm with a spatio-temporal GP kernel and time-Lipschitz constants that safely propagates the safe set over time for unknown time-varying reward and constraints, with safety and near-optimality (stationary case) guarantees.
Problem
Optimizing an unknown time-varying reward subject to unknown, time-varying safety constraints, where safe sets from previous time steps may become unsafe.
Approach
Extends SafeOpt with a spatio-temporal kernel and time-Lipschitz constants so the safe set is robustly propagated to the next time step by subtracting a safety margin, allowing the safe set to shrink or track the safe region without explicit change detection.
Key results
- On the synthetic example, TVSafeOpt's cumulative regret is 77.3% below SafeOpt's.
- On the gas compressor case study, TVSafeOpt keeps unsafe decisions in its safe sets 73.9% lower than SafeOpt and 97.6% lower than approximate optimization, at the cost of covering 40.0% less of the ground truth safe region than SafeOpt.
- In the compressor case study, TVSafeOpt's cumulative regret is 74.9% above SafeOpt's, reflecting a safety-optimality trade-off.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use TVSAFEOPT instead of SafeOpt | Safe Bayesian optimization on the synthetic example · Synthetic example | cumulative regret: 77.3% | Helped |
| Account for time-varying safety functions and shrink safe sets robustly | SafeOpt on the gas compressor case study · Gas compressor case study | unsafe decisions in safe sets: 73.9% | Helped |
| Account for time-varying safety functions and shrink safe sets robustly | Approximate optimization on the gas compressor case study · Gas compressor case study | unsafe decisions in safe sets: 97.6% | Helped |
| Account for time-varying safety functions and shrink safe sets robustly | SafeOpt on the gas compressor case study · Gas compressor case study | ground-truth safe-region coverage: 40.0% | Hurt |
| Account for time-varying safety functions and shrink safe sets robustly | Approximate optimization on the gas compressor case study · Gas compressor case study | ground-truth safe-region coverage: 61.4% | Hurt |
| Account for time-varying safety functions and shrink safe sets robustly | SafeOpt on the gas compressor case study · Gas compressor case study | cumulative regret: 74.9% | Hurt |
| Account for time-varying safety functions and shrink safe sets robustly | Approximate optimization on the gas compressor case study · Gas compressor case study | cumulative regret: 208.1% | Hurt |
| Use TVSAFEOPT instead of SafeOpt | Safe optimization on the synthetic example · Synthetic example | safety of computed safe sets | Helped |
| Use TVSAFEOPT instead of SafeOpt | Safe optimization on the gas compressor case study · Gas compressor case study | reward value | Hurt |
Surprising findings
- On the compressor case study, the safety-focused TVSafeOpt finds lower reward than SafeOpt, showing a clear safety-optimality trade-off under strong non-stationarity.
Limitations
- Near-optimality guarantee only holds when the problem is locally stationary; non-stationary optimality is not guaranteed.
- Requires Lipschitz constants with respect to both decisions and time, which are hard to estimate in practice.
- Safe set may become empty and the algorithm terminates, and it can be overly conservative, covering less of the ground truth safe region.
Experimental setup
Datasets: gas compressor data (demand, compressor head, degradation) from an existing open dataset
Benchmarks: synthetic 2D time-varying optimization problem gas compressor station case study
Metrics: cumulative regret ratio of unsafe decisions in safe sets ratio of ground truth safe region covered
Baselines: SafeOpt approximate optimization
Builds on: SafeOpt GOOSE contextual GP-UCB
Closest papers by meaning
- Stagewise Safe Bayesian Optimization with Gaussian Processes (ICML 2018 · similarity 0.86)
- Gaussian Process-Based Real-Time Learning for Safety Critical Applications (ICML 2021 · similarity 0.86)
- Safely Learning Controlled Stochastic Dynamics (NeurIPS 2025 · similarity 0.84)
- Learning Safe Control via On-the-Fly Bandit Exploration (ICML 2025 · similarity 0.83)
- Stochastic Bayesian Optimization with Unknown Continuous Context Distribution via Kernel Density Estimation (AAAI 2024 · similarity 0.83)
- Adaptive Kernel Design for Bayesian Optimization Is a Piece of CAKE with LLMs (NeurIPS 2025 · similarity 0.83)
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