Constrained controlling of a computer-controlled system

1 . A computer-implemented control method of constrained controlling of a computer-controlled system, wherein the computer-controlled system is controlled according to a control input, and wherein the control input is safe when a constraint quantity resulting from the controlling of the computer-controlled system exceeds a constraint threshold, the method comprising:

accessing data representing previous control inputs and corresponding previous noisy measurements of a resulting constraint quantity;

determining a current control input based on the previous control inputs and the corresponding previous noisy measurements to maximize mutual information over a safety of a further control input, wherein the mutual information is defined between a first random variable representing the constraint quantity resulting from the current control input and a second random variable indicating whether a further control input is safe;

approximating the mutual information by approximating an entropy of the further control input being safe by a Taylor expansion of a Gaussian distribution; and

controlling the computer-controlled system according to the current control input, thereby obtaining a current noisy measurement of the resulting constraint quantity.

2 . The method of claim 1 , wherein the mutual information is defined according to a Gaussian Process model of the constraint quantity given the control input.

3 . The method of claim 2 , wherein the current control input and the further control input are determined to maximize the mutual information.

4 . The method of claim 3 , wherein the mutual information is maximized by a multi-start gradient descent.

5 . The method of claim 1 , wherein the mutual information is averaged over multiple further control inputs.

6 . The method of claim 1 , wherein the constraint quantity represents a safety constraint.

7 . The method of claim 1 , wherein the current control input is determined such that the current control input lies in a safe set of control inputs determined likely to be safe, wherein the safe set is defined based on the previous control inputs and the corresponding previous noisy measurements, and wherein the further control input does not lie in the safe set.

8 . The method of claim 1 , wherein the control input includes one or more continuous-valued control parameters.

9 . The method of claim 1 , further comprising:

training a control model for controlling the computer-controlled system by Bayesian optimization, wherein: a) the current control input is determined based on the Bayesian optimization, and/or b) the Bayesian optimization is performed subsequently to the mutual information-based controlling, using the obtained control inputs and corresponding noisy measurements.

10 . The method of claim 9 , wherein the current control input is determined based further on an upper confidence bound acquisition function.

11 . The method of claim 9 , wherein the control model is trained based on a model of the computer-controlled system as a Markov Decision process.

12 . A control system for constrained controlling of a computer-controlled system, wherein the computer-controlled system is controlled according to a control input, and wherein the control input is safe if a constraint quantity resulting from the controlling of the computer-controlled system exceeds a constraint threshold, wherein the control system comprises:

a data interface configured for accessing data representing previous control inputs and corresponding previous noisy measurements of the resulting constraint quantity;

a processor subsystem configured to:

determine a current control input based on the previous control inputs and corresponding previous noisy measurements to maximize mutual information over a safety of a further control input, wherein the mutual information is defined between a first random variable representing the constraint quantity resulting from the current control input and a second random variable indicating whether a further control input is safe;

approximate the mutual information by approximating an entropy of the further control input being safe by a Taylor expansion of a Gaussian distribution; and

control the computer-controlled system according to the current control input, thereby obtaining a current noisy measurement of the resulting constraint quantity,

wherein the current control input is determined based on a mutual information between a first random variable representing the constraint quantity resulting from the current control input and a second random variable indicating whether a further control input is safe.

13 . A system, comprising:

a control system; and

a computer-controlled system;

wherein the computer-controlled system is controlled according to a control input, and wherein the control input is safe if a constraint quantity resulting from the controlling of the computer-controlled system exceeds a constraint threshold, wherein the control system includes:

a data interface configured for accessing data representing previous control inputs and corresponding previous noisy measurements of the resulting constraint quantity;

a processor subsystem configured to:

determine a current control input based on the previous control inputs and corresponding previous noisy measurements to maximize mutual information over a safety of a further control input, wherein the mutual information is defined between a first random variable representing the constraint quantity resulting from the current control input and a second random variable indicating whether a further control input is safe;

approximate the mutual information by approximating an entropy of the further control input being safe by a Taylor expansion of a Gaussian distribution; and

control the computer-controlled system according to the current control input, thereby obtaining a current noisy measurement of the resulting constraint quantity,

wherein the current control input is determined based on a mutual information between a first random variable representing the constraint quantity resulting from the current control input and a second random variable indicating whether a further control input is safe.

14 . A non-transitory computer-readable medium on which are stored data representing instructions for constrained controlling of a computer-controlled system, wherein the computer-controlled system is controlled according to a control input, and wherein the control input is safe when a constraint quantity resulting from the controlling of the computer-controlled system exceeds a constraint threshold, the instructions, when executed by a processor system, causing the processor system to perform:

accessing data representing previous control inputs and corresponding previous noisy measurements of a resulting constraint quantity;

determining a current control input based on the previous control inputs and the corresponding previous noisy measurements to maximize mutual information over a safety of a further control input, wherein the mutual information is defined between a first random variable representing the constraint quantity resulting from the current control input and a second random variable indicating whether a further control input is safe;

approximating the mutual information by approximating an entropy of the further control input being safe by a Taylor expansion of a Gaussian distribution; and

controlling the computer-controlled system according to the current control input, thereby obtaining a current noisy measurement of the resulting constraint quantity;

wherein the current control input is determined based on a mutual information between a first random variable representing the constraint quantity resulting from the current control input and a second random variable indicating whether a further control input is safe.