Asymmetrical robustness for classification in adversarial environments

1. A computational method for training a classifier, the method comprising:

receiving a training data set comprised of pairs of training input signals and corresponding output signals, the classifier parameterized by parameters and configured to classify input signals obtained from a sensor into at least two different classes including first and second classes, a class-dependent allowed perturbation for each of the at least two different classes and including a first class-dependent allowed perturbation for the first class and a second class-dependent allowed perturbation for the second class, and a loss function;

initializing a total loss and a stopping condition;

partitioning the training data set into a first subset labelled with a first label corresponding to the first class and a second subset labelled with a second label corresponding to the second class;

calculating a first loss in response to the first subset and the first class-dependent allowed perturbation and a second loss calculated in response to the second subset and the second class-dependent allowed perturbation;

updating the total loss in response to the first and second losses to obtain an updated total loss;

updating the stopping condition in response to the updated total loss to obtain an updated stopping condition;

iteratively performing the partitioning, calculating, updating the total loss, and updating the stopping condition steps within a class loop until the updated stopping condition is a stopping value different than a pre-determined value; and

updating the parameters in response to the first and second losses to obtain updated parameters after the iteratively performing steps.

2. The computational method of claim 1 , further comprising:

sending the input signals obtained from the sensor into the classifier parameterized by the updated parameters to obtain output signals configured to characterize a classification of the input signals; and

transmitting an actuator control command to an actuator of a computer-controlled machine in response to the output signals.

3. The computational method of claim 1 , wherein the updating step is carried out by a machine learning (ML) algorithm.

4. The computational method of claim 1 , wherein the pre-determined value is one of first and second binary values.

5. The computational method of claim 4 , wherein the pre-determined value is the first binary value and the stopping value is the second binary value.

6. The computational method of claim 1 , wherein the first and second class-dependent allowed perturbations are in a set on which a discriminator is unable to distinguish perturbed data from unperturbed data.

7. The computational method of claim 1 , wherein the first label is different than the second label.

8. A non-transitory computer-readable medium comprising computer-executable instructions and a memory for maintaining the computer-executable instructions, the computer-executable instructions when executed by a processor of a computer perform the following functions:

receiving a training data set comprised of pairs of training input signals and corresponding output signals, the classifier parameterized by parameters and configured to classify input signals obtained from a sensor into at least two different classes including first and second classes, a class-dependent allowed perturbation for each of the at least two different classes and including a first class-dependent allowed perturbation for the first class and a second class-dependent allowed perturbation for the second class, and a loss function;

initializing a total loss and a stopping condition;

partitioning the training data set into a first subset labelled with a first label corresponding to the first class and a second subset labelled with a second label corresponding to the second class;

calculating a first loss in response to the first subset and the first class-dependent allowed perturbation and a second loss calculated in response to the second subset and the second class-dependent allowed perturbation;

updating the total loss in response to the first and second losses to obtain an updated total loss;

updating the stooping condition in response to the updated total loss to obtain an updated stopping condition;

iteratively performing the partitioning, calculating, updating the total loss, and updating the stopping condition steps within a class loop until the updated stopping condition is a stopping value different than a pre-determined value; and

updating the parameters in response to the first and second losses to obtain updated parameters after the iteratively performing steps.

9. The non-transitory computer-readable medium of claim 8 , wherein the computer-executable instructions when executed by the processor of the computer perform the following functions:

sending the input signals obtained from the sensor into the classifier parameterized by the updated parameters to obtain output signals configured to characterize a classification of the input signals; and

transmitting an actuator control command to an actuator of a computer-controlled machine in response to the output signals.

10. The non-transitory computer-readable medium of claim 8 , wherein the updating function is carried out by a machine learning (ML) algorithm.

11. The non-transitory computer-readable medium of claim 8 , wherein the pre-determined value is one of first and second binary values.

12. The non-transitory computer-readable medium of claim 11 , wherein the pre-determined value is the first binary value and the stopping value is the second binary value.

13. The non-transitory computer-readable medium of claim 8 , wherein the first and second class-dependent allowed perturbations are dependent on a discriminator that is unable to distinguish perturbed data from unperturbed data.

14. The non-transitory computer-readable medium of claim 8 , wherein the first label is different than the second label.

15. A computer system comprising:

a computer having a processor for executing computer-executable instructions and a memory for maintaining the computer-executable instructions, the computer-executable instructions when executed by the processor of the computer perform the following functions:

receiving a training data set comprised of pairs of training input signals and corresponding output signals, the classifier parameterized by parameters and configured to classify input signals obtained from a sensor into at least two different classes including first and second classes, a class-dependent allowed perturbation for each of the at least two different classes and including a first class-dependent allowed perturbation for the first class and a second class-dependent allowed perturbation for the second class, and a loss function;

initializing a total loss and a stopping condition;

partitioning the training data set into a first subset labelled with a first label corresponding to the first class and a second subset labelled with a second label corresponding to the second class;

calculating a first loss in response to the first subset and the first class-dependent allowed perturbation and a second loss calculated in response to the second subset and the second class-dependent allowed perturbation;

updating the total loss in response to the first and second losses to obtain an updated total loss;

updating the stopping condition in response to the updated total loss to obtain an updated stopping condition;

iteratively performing the partitioning, calculating, updating the total loss, and updating the stopping condition steps within a class loop until the updated stopping condition is a stopping value different than a pre-determined value; and

updating the parameters in response to the first and second losses to obtain updated parameters after the iteratively performing steps.

16. The computer system of claim 15 , wherein the computer-executable instructions when executed by the processor of the computer perform the following further functions:

sending the input signals obtained from the sensor into the classifier parameterized by the updated parameters to obtain output signals configured to characterize a classification of the input signals; and

transmitting an actuator control command to an actuator of a computer-controlled machine in response to the output signals.

17. The computer system of claim 15 , wherein the updating function is carried out by a machine learning (ML) algorithm.

18. The computer system of claim 15 , wherein the pre-determined value is one of first and second binary values.

19. The computer system of claim 18 , wherein the pre-determined value is the first binary value and the stopping value is the second binary value.

20. The computer system of claim 15 , wherein the first and second class-dependent allowed perturbations are dependent on a discriminator that is unable to distinguish perturbed data from unperturbed data.