Derivatives of optimal solutions w.r.t parameters

User Questions
1

Hi all,

I’m wonder if there is anyway to get the derivate of the optimal solution w.r.t the parameters (preferably from Python interface, C interface is also ok). The eval_param_sens function seems to be able to calculate the sensitivity w.r.t the initial condition, but I’m wondering if more general settings exists, e.g., when parameters appears in the cost function or system dynamics.

Thanks a lot!

2

Hi :wave:

we just merged a pull request implementing solution sensitivities with respect to parameters! Note that this feature is currently limited to external costs and discrete dynamics and does not cover parametric constraints.

I recommend you check the example here. Note that the solution sensitivities are only correct if an exact Hessian is used. Whenever you use any form of Hessian approximation or regularization (e.g. Gauss-Newton Hessian) for solving your OCP, we recommend to create two solvers: one for solving using an approximate Hessian, and one using an exact Hessian that is used to compute solution sensitivities. This approach is also taken in the example.

Best, Katrin

2 Likes
3

Hi Katrin,

Glad to see this feature! I believe this would be super useful for applications combining MPC and learning, e.g. differentiable MPC.

Thanks for your work. I will have a look into that.

Best,
Fenglong

1 Like
4

Hi Katrin,

I’ve looked into the example and I’d like to thank you for adding this great feature. Now I’m wondering what would be the best manner if I want to have a differentiable OCP layer in neural network, for example, if I want to implement an AcadosOcpLayer which can be integrated into PyTorch and trained on GPU.

I think it’s possible to extend a PyTorch layer by subclassing torch.autograd.Function and customize forward() and backward() function with acados (forward just solves the OCP and return optimal inputs, backward evaluates the sensitivity of optimal inputs w.r.t OCP parameters). But I’m wondering if this is a good solution for training on GPU. As far as I know, acados is optimized for CPU operations. So I’m not sure how efficient it would be on GPU. Another approach might be to run the AcadosOcpLayer on CPU and keep transporting the data between CPU and GPU, which could be slow as I can imagine.

I don’t have an answer to this question, so I’d like to ask about your thoughts. I would appreciate your opinions.

Thanks and best,
Fenglong