Solving a batch of trajectory optimization problems on a GPU about trajax HOT 9 OPEN

Hi, I can't answer any Trajax related questions, but I think we are looking for the same thing. I have yet to find a good way on how to solve "batched" TOs, however this publication looks promising, leveraging the a new CUDA enabled spare linear system solver: https://discourse.julialang.org/t/examodels-jl-and-madnlp-jl-on-gpus/111377.

In their work they use GPU to accellerate large scale sparse optimal control. One approach would be to calculate all objectives and constraints in parallell on a GPU and the "concatenating" everything into one large, and very sparse TO.

Let me know if you find anything interesting!

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Thanks for the feedback @larsrpe . However I think that concatenating everything into a large sparse TO would be suboptimal in terms of performance. Moreover, the performance gains reported at that link are not as good as I was hoping for, which makes sense because solving a single TO problem on GPU is much more challenging that solving a batch of TOs on GPU in my opinion. I'll let you know if I find anything.

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Yes, that indeed could be an option. Alternatively, one could modify their QP solver to become a nonlinear solver. Since it's based on a Primal-Dual Interior Point algorithm, I'd say it shouldn't be too difficult.

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I agree. Maybe I will find some time to look into it!

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Hello @andreadelprete. What kind of problems are you solving? If unconstrained (i.e., dynamics constraints only), the iLQR solve call can be wrapped with jax's vmap function. This will give you parallelization within a single device. As to how the matrix factorizations in the TV-LQR step are "parallelized," this will be largely abstracted away by the XLA code.

If your problem is more complex (has state-control constraints that you don't want to treat as cost penalties), you can use the SQP solver in experimental. However, the outer-most part of this solver needs a slight restructuring to enable wrapping with vmap (I have to remove some non-jittable parts like verbose printing, etc).

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I am interested in both unconstrained and constrained problems, so I could start experimenting with unconstrained ones using iLQR with vmap. Thanks for the feedback @ssingh19 ! Do you mind if we leave this issue open to discuss future developments for this use case?

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Cool! Can I ask what kind of OC problems you are solving @andreadelprete ?

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Cool! Can I ask what kind of OC problems you are solving @andreadelprete ?

Sure, you can find some examples of the unconstrained problems in our paper "CACTO: Continuous Actor-Critic with Trajectory Optimization -- Towards global optimality", https://arxiv.org/abs/2211.06625

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