What is `lr_policy` in Caffe?

问题:

I just try to find out how I can use Caffe. To do so, I just took a look at the different .prototxt files in the examples folder. There is one option I don't understand:

# The learning rate policy
lr_policy: "inv"

Possible values seem to be:

• "fixed"
• "inv"
• "step"
• "multistep"
• "stepearly"
• "poly"

Could somebody please explain those options?

回答1:

If you look inside the /caffe-master/src/caffe/proto/caffe.proto file (you can find it online here) you will see the following descriptions:

// The learning rate decay policy. The currently implemented learning rate
// policies are as follows:
//    - fixed: always return base_lr.
//    - step: return base_lr * gamma ^ (floor(iter / step))
//    - exp: return base_lr * gamma ^ iter
//    - inv: return base_lr * (1 + gamma * iter) ^ (- power)
//    - multistep: similar to step but it allows non uniform steps defined by
//      stepvalue
//    - poly: the effective learning rate follows a polynomial decay, to be
//      zero by the max_iter. return base_lr (1 - iter/max_iter) ^ (power)
//    - sigmoid: the effective learning rate follows a sigmod decay
//      return base_lr ( 1/(1 + exp(-gamma * (iter - stepsize))))
//
// where base_lr, max_iter, gamma, step, stepvalue and power are defined
// in the solver parameter protocol buffer, and iter is the current iteration.

回答2:

It is a common practice to decrease the learning rate (lr) as the optimization/learning process progresses. However, it is not clear how exactly the learning rate should be decreased as a function of the iteration number.

If you use DIGITS as an interface to Caffe, you will be able to visually see how the different choices affect the learning rate.

fixed: the learning rate is kept fixed throughout the learning process.

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inv: the learning rate is decaying as ~1/T

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step: the learning rate is piecewise constant, dropping every X iterations

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multistep: piecewise constant at arbitrary intervals

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You can see exactly how the learning rate is computed in the function SGDSolver<Dtype>::GetLearningRate (solvers/sgd_solver.cpp line ~30).

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Recently, I came across an interesting and unconventional approach to learning-rate tuning: Leslie N. Smith's work "No More Pesky Learning Rate Guessing Games". In his report, Leslie suggests to use lr_policy that alternates between decreasing and increasing the learning rate. His work also suggests how to implement this policy in Caffe.