LEARNING APPARATUS, LEARNING SYSTEM, LEARNING METHOD, AND PROGRAM

1 . A learning apparatus constituting a learning system including N learning apparatuses, the learning apparatus comprising:

processing circuitry configured to:

updates a model variable w i by using a dual variable z A and noise Rσ i including a random number R in a normal distribution and a standard deviation σ i of noise, obtains a parameter λ used when learning of an update difference y A and the standard deviation of noise is performed by using the updated model variable w i and the noise Rσ i , and exchanges the update difference y A when communication with another learning apparatus constituting the learning system is performed; and

updates the standard deviation σ i of noise by using a dual variable z B , a hyperparameter L, and noise Rλ including a random number R in a normal distribution and the parameter λ, obtains an update difference y B by using the updated standard deviation σ i , the hyperparameter L, and the noise Rλ, and exchanges the update difference y B when communication with the other learning apparatus is performed.

2 . The learning apparatus according to claim 1 , wherein

the hyperparameter L is any value of 0.02 or more and 0.03 or less.

3 . A learning system comprising: N learning apparatuses, wherein

each learning apparatus i includes

processing circuitry configured to:

updates a model variable w i by using a dual variable z A and noise Rσ i including a random number R in a normal distribution and a standard deviation σ i of noise, and obtains a parameter λ used when learning of an update difference y A and the standard deviation of noise is performed by using the updated model variable w i and the noise Rσ i ; and

updates the standard deviation σ i of noise by using a dual variable z B , a hyperparameter L, and noise Rλ including a random number R in a normal distribution and the parameter λ, and obtains an update difference y B by using the updated standard deviation σ i , the hyperparameter L, and the noise Rλ, and

the learning apparatus i and another learning apparatus j exchange the update differences y A and y B , when the learning apparatus i communicates with the other learning apparatus j.

4 . A learning method using N learning apparatuses, the learning method comprising:

a model learning step in which processing circuitry included in learning apparatus i updates a model variable w i by using a dual variable z A and noise Rσ i including a random number R in a normal distribution and a standard deviation σ i of noise, and obtains a parameter λ used when learning of an update difference y A and the standard deviation of noise is performed by using the updated model variable w i and the noise Rσ i ; and

a model parameter update difference exchange step in which the learning apparatus i and another learning apparatus j exchange the update differences y A , when the learning apparatus i and the other learning apparatus j communicate with each other;

a noise learning step in which the processing circuitry included in the learning apparatus i updates the standard deviation σ i of noise by using a dual variable z B , a hyperparameter L, and noise Rλ including a random number R in a normal distribution and the parameter λ, and obtains an update difference y B by using the updated standard deviation σ i , the hyperparameter L, and the noise Rλ; and

a noise standard deviation update difference exchange step in which the learning apparatus i and the other learning apparatus j exchange the update difference y B , when the learning apparatus i and the other learning apparatus j communicate with each other.

5 . A non-transitory computer-readable recording medium having recorded thereon a program for causing a computer to function as the learning apparatus according to claim 1 .