Vector-valued objective functions #1556
Comments
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Hi @remypa , We haven't intended to support this, nor have we tested it before. However, we can put this on our roadmap for future versions. It's possible some of my changes in #1551 may make it work, but it's unlikely. What I don't understand exactly is why you'd need to do this, perhaps you can explain. My understanding is you have a set of objective function Typically you'd combine all of these in a single objective function, eg. by summing over Ultimately if you are able to combine everything you'd like to do in a single objective function, it should still be possible to use Note that you can always use |
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Hi, thanks a lot for your reply. I am working on a minimax-type of problem : which I reformulate as Which is why I don't really recombine the |
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I see. Yea we will have to work on improving the compatibility with tidy3d adjoint and nlopt for these sorts of problems. In the meantime, I might suggest you use a Some pseudo-code below but double check the specifics. def objective(x):
fs = jnp.array([f(x, i) for i in range(m)])
weights = jnp.nn.softmax(fs)
return jnp.sum(weights * fs)My intuition tells me that this should work reasonably well without needing to transform the problem to constraints. |
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EDIT: forgot to |
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The direct use of You don't need to use |
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Hey @remypa, to add to the above - since everything in nlopt needs to happen outside of JAX anyway, it is perfectly fine to construct the constraint vector as @ianwilliamson described. In the simplest case (single wavelength, only differentiating w.r.t. a single argument), that would look something like this: def nlopt_epigraph_constraint(result: np.ndarray, x: np.ndarray, gd: np.ndarray) -> None:
t, v = x[0], x[1:]
# evaluate all objectives and get their gradients, assuming obj_fun_vgs is a list
# of gradient functions defined somewhere else of the form:
# d_obj = jax.value_and_grad(objective)
obj_vec, grad_vec = [], []
for obj_fun_vg in obj_fun_vgs:
obj_val, grad_val = obj_fun_vg(v)
obj_vec.append(obj_val)
grad_vec.append(grad_val)
if gd.size > 0:
gd[:, 0] = -1
gd[:, 1:] = np.asarray(grad_vec)
result[:] = np.asarray(obj_vec) - tYou can also parallelize the evaluation of the objective functions in that loop with something like |
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Hi, thanks for all your inputs/suggestions. @ianwilliamson , @yaugenst : that is the way I am doing it at the moment. It does work, but the difficulty is that I think I can't use Tidy3D's batch infrastructure out of the box, hence my initial post. @tylerflex : I have started looking into softmax. My initial results are promising. Cheers. |
I am using tidy3D to perform multi-objectives inverse design. To speed things up, I'd like to run batches with web.run_async and return the different objectives as a vector value (I need the different individual values to define multiple constraints to y optimisation problem).
To do that, I can't use jax.value_and_grad (which is limited to scalar functions). Instead, I need to use jax.jacrev or jax.jacfwd.
But when I do that, I run into ConcretizationTypeError if I'm using a FieldMonitor, or a TracerArrayConversionError if I'm using a ModeMonitor.
A simple way to reproduce the problem is to extend the tutorial at https://www.flexcompute.com/tidy3d/examples/notebooks/AdjointPlugin1Intro/ , with
This is not a vector-valued objective function, but the problem is the same:
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