Promises of Deep Kernel Learning for Control Synthesis
This work addresses control synthesis for complex stochastic systems with formal guarantees, which is incremental as it builds on existing DKL and abstraction methods.
The authors tackled control synthesis for stochastic dynamical systems with temporal logic specifications by developing a scalable abstraction-based framework using Deep Kernel Learning (DKL) to learn unknown systems and formally abstract them into Interval Markov Decision Processes (IMDPs) for guaranteed correctness, demonstrating substantial outperformance over state-of-the-art methods on benchmarks including a 5-D nonlinear stochastic system.
Deep Kernel Learning (DKL) combines the representational power of neural networks with the uncertainty quantification of Gaussian Processes. Hence, it is potentially a promising tool to learn and control complex dynamical systems. In this work, we develop a scalable abstraction-based framework that enables the use of DKL for control synthesis of stochastic dynamical systems against complex specifications. Specifically, we consider temporal logic specifications and create an end-to-end framework that uses DKL to learn an unknown system from data and formally abstracts the DKL model into an Interval Markov Decision Process (IMDP) to perform control synthesis with correctness guarantees. Furthermore, we identify a deep architecture that enables accurate learning and efficient abstraction computation. The effectiveness of our approach is illustrated on various benchmarks, including a 5-D nonlinear stochastic system, showing how control synthesis with DKL can substantially outperform state-of-the-art competitive methods.