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Learning Safe Control via On-the-Fly Bandit Exploration

ICML 2025 · Learning theory and algorithms › Prediction and decision losses · approach: Distributionally robust optimization · 0 citations (OpenAlex)

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Proposes an on-the-fly GP bandit exploration scheme that collects data whenever a robust CBF safety filter becomes infeasible, proving high-probability safety from a zero-mean prior without a backup controller.

Problem

Safe control with unknown dynamics where learned model uncertainty is so high that robust control barrier function safety filters become infeasible, and no backup controller or prior measurements are available.

Approach

When the GP-based robust CBF safety filter becomes infeasible, switch to exploring by maximizing the UCB of the CBF time derivative (bandit-style), with a sampling time chosen high enough that feasibility is recovered before the safe set boundary is reached, giving a high-probability safety guarantee.

Key results

• In simulations with zero-mean prior and no prior measurements, the safety filter becomes feasible after about 6 s (cruise control) and about 2 s (quadrotor) with CBF staying above zero.
• Across 100 runs at varying sampling frequencies, the proposed exploration has a lower failure rate than random exploratory inputs in both cruise control and quadrotor settings.
• Theorem gives a sampling-time condition Delta t > epsilon/(L_alpha L_h L_system N_max) and a bound on data needed, guaranteeing safety with probability at least 1-delta.

Measured effects reported in the paper

Surprising findings

• Higher sampling frequency improves data efficiency, since the model is more faithful right after each update.

Limitations

• Requires a sampling time high enough (Delta t bound), which may be impractical on real hardware with limited sampling frequency.
• Assumes a known CBF satisfying robust feasibility with margin epsilon and RKHS-bounded dynamics with known norm bounds.
• Only simulation experiments; closed-loop performance is not addressed.

Experimental setup

Datasets: simulated cruise control data simulated quadrotor data

Benchmarks: adaptive cruise control simulation quadrotor with ground dynamics simulation

Metrics: failure rate (CBF becomes positive) CBF value over time minimum LCB of CBF derivative

Baselines: random exploratory control inputs

Builds on: control barrier functions Gaussian process confidence bounds (RKHS) GP-UCB bandit

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