In this paper, we aim to develop a Bayesian optimization algorithm for the (probabilistic) safe optimization of control over high-dimensional embodied systems. One of our motivated applications is the control of human neuro-musculo-skeletal systems in both simulation and real world experiments.
Previous Safe optimization methods
Most existing safe optimization methods
• use the Gaussian process (GP) to model the underlying functions
• discriminate safe regions with estimated function lower confidence bound
These method can be
• inefficient for objective optimization
• infeasible in high-dimensional and large-scale parameter settings
High-dimensional Safe Bayesian Optimization with local optimistic exploration (HdSafeBO)
We reformulate the original safe optimization problem as a probabilistic safe optimization problem. So that we can improve the sample efficiency by slightly loosing the safety constraint that allow a small number of unsafe decisions.
We propose High-dimensional Safe Bayesian Optimization with local optimistic exploration (HdSafeBO), which has two main components:
• Local optimistic safe optimization
• optimistically identify the safe space within the local trust region using GP upper confidence bound
• theoretical probabilistic safety guarantee and cumulative safety violation bound
• Isometric mapping
• reduce the problem dimension while preserving the distance of the original space.
• maintain safety guarantee during latent optimization
Safe Optimization of High-dimensional Embodied Control with HdSafeBO
High-dimensional safe control in simulation
We demonstrate that HdSafeBO is capable of
• safely optimizing a linear policy to actuate the 55-muscle model in one arm to hold a bottle.
• significantly surpassing all constrained baselines in both efficiency and safety, demonstrating efficient safe optimization over high-dimensional space.
Real clinical neural stimulation
We applied HdSafeBO to improve the motor function of a paraplegic patient where an electrode array is implanted in the spinal cord of the patient. We observe that HdSafeBO is capable of
• safely optimizing 17d stimulation parameters (discrete + continuous) to improve the neural stimulation induced motion control.
• successfully improving motor function of 7 out of 8 target muscles compared to the baseline.
Conclusion
We propose a high-dimensional safe Bayesian optimization method, HdSafeBO, that
• achieves efficient safe optimization of control over high-dimensional embodied systems
• has theoretical probabilistic safety guarantee with dimension reduction
• demonstrates practicality in real experiments over high-dimensional human neuro-musculo-skeletal systems