  This paper studies the problem of online performance optimization of
constrained closed-loop control systems, where both the objective and the
constraints are unknown black-box functions affected by exogenous time-varying
contextual disturbances. A primal-dual contextual Bayesian optimization
algorithm is proposed that achieves sublinear cumulative regret with respect to
the dynamic optimal solution under certain regularity conditions. Furthermore,
the algorithm achieves zero time-average constraint violation, ensuring that
the average value of the constraint function satisfies the desired constraint.
The method is applied to both sampled instances from Gaussian processes and a
continuous stirred tank reactor parameter tuning problem; simulation results
show that the method simultaneously provides close-to-optimal performance and
maintains constraint feasibility on average. This contrasts current
state-of-the-art methods, which either suffer from large cumulative regret or
severe constraint violations for the case studies presented.
