What is get_kl() doing in main.py?

[jtoyama4]

Hi. Thanks for publishing implementation of trpo.

I have question about get_kl().

I thought what get_kl() is supposed to do is to calculate the kl divergence of old policy and new policy, but this get_kl() seems always returning 0.

Also,I do not see kl constraining part in the parameters updating process.

Is this code the modification of trpo or do I have some misunderstanding?

Thanks,

[ikostrikov]

KL is used to compute the hessian (as in the original code).

[pxlong]

Hi, I've tested the get_kl() function in various environments, but the return is always 0. The following is an example of get_kl() outputs in BipedalWalker-v2:

*** kl: Variable containing: 0 0 0 0 0 0 0 0 0 0 0 0 ⋮
0 0 0 0 0 0 0 0 0 0 0 0 [torch.DoubleTensor of size 15160x4]

*** kl sum: Variable containing: 0 0 0 ⋮ 0 0 0 [torch.DoubleTensor of size 15160]

*** kl mean: Variable containing: 0 [torch.DoubleTensor of size 1]

** kl grad: Variable containing: 1.00000e-34 2.4390 [torch.DoubleTensor of size 1]

** kl grad grad: Variable containing: 1.00000e-34 2.4390 [torch.DoubleTensor of size 1]

('lagrange multiplier:', 2.509155592601353e-17, 'grad_norm:', 4.4529719813727475e-18) fval before 2.0545072021432404e-13 a/e/r 2.1300610441917076e-13 5.018311185202932e-19 424457.7439662247 fval after -7.555384204846721e-15

Does this make sense?

[pxlong]

@jtoyama4 Hi, have you figure out how does get_kl() work? I have the same question with you.

[jtoyama4]

@pxlong I think what get_kl() does is to get the gradient of kl (for hessian computing) , and kl-constraining part is somehow working with ratio in def linesearch but I really do not understand it theoretically.

[pxlong]

@jtoyama4, thanks for a quick reply. but what get_kl() return is always 0 how can you get a valid/useful gradient of it? I am a little confused.

[ikostrikov]

@pxlong a simple example:

In this case we have something like this f(x)=(x_0^2 - x^2), f(x_0) = 0 but f'(x_0)=-2x_0.

The function is not f(x) == 0 but it has a value at one specific point == 0.

[pxlong]

@ikostrikov, thanks for your explanation. But I've tested this implementation in various envs, such as BipedalWalker-v2, MountainCarContinuous-v0, Pendulum-v0 (except Reacher-v1), none of them gives reasonable results (i.e. the agent learns nothing during training).

To debug it, I added some print as you can see belowing:

def Fvp(v):
        kl = get_kl()
        kl = kl.mean()
        print('*** kl mean: ', kl)

        grads = torch.autograd.grad(kl, model.parameters(), create_graph=True)
        flat_grad_kl = torch.cat([grad.view(-1) for grad in grads])

        kl_v = (flat_grad_kl * Variable(v)).sum()
        print('*** kl_v: ', kl_v)
        grads = torch.autograd.grad(kl_v, model.parameters())
        flat_grad_grad_kl = torch.cat([grad.view(-1) for grad in grads]).data
        print('*** flat grad grad kl: ', flat_grad_grad_kl)

but all the tensors are zero (showed in the second message of this issue).

I am wondering what the problem of the bad performance on these environments?

[ikostrikov]

Check hyperparams from the original implementation (modular rl). And also estimates of how long does convergence take. Default hyperparams of this code are tuned specifically for reacher-v1

[pxlong]

ok, thanks.

[ikostrikov]

This part is used to compute the hessian of KL. KL itself == 0, the derivative of the KL == 0 but the hessian is not.

This is the reason why we have to compute a second order approximation of the KL terms. Because its first order approximation is equal to zero.

[ikostrikov]

@pxlong Sorry, that it took me so long to fix the bug.

It didn't work because they've changed default argument values for some functions in PyTorch recently.

[josiahls]

@pxlong And anyone else, I found the get_kl is related to the statement from (Schulman et al., 2015) [TRPO] Trust Region Policy Optimization:

computing the Hessian of DKL with respect to θ

It still feels non-intuitive to me, but I guess the goal is auto diff / hessian calc vs getting an actual value out of get_kl.

Also For two univariate normal distributions p and q the above simplifies t has the math that looks directly related to the code.

The paper cites Numerical Optimization so I guess I have some reading to do :)

*edit: So I if I understand correctly get_kl simply structures the kl for auto grad. The actual 2nd hessian is built in Fvp