Merge LPGD into diffcp #67
Conversation
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This is great! I'm not sure what the failing builds are about. |
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The CI issues are a symptom of the master branch CI being broken. Fixing it is on my goals for the long weekend. I'd love a chance to review this PR carefully before merging, but on a quick pass it looks great Anselm! Is there any timeline you need this merged by? |
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Glad to hear you like it! There is no rush to merge it from my side, please take your time to carefully review it. |
| raise ValueError("Unsupported mode {}; the supported modes are " | ||
| "'dense', 'lsqr' and 'lsmr'".format(mode)) | ||
| "'dense', 'lsqr', 'lsmr', 'lpgd', 'lpgd_right' and 'lpgd_left'".format(mode)) | ||
| if np.isnan(A.data).any(): |
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Shouldn't we check here if P is None for the dense, lsqr, lsmr cases? They don't support quadratic objectives in my understanding.
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Yes that makes sense, I will add this.
diffcp/cone_program.py
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| return dA, db, dc | ||
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| def derivative_lpgd(dA, db, dc, tau, rho): |
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Do you have quadratic objective support? I noticed you weren't banning them in construction above.
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Yes this is probably good to discuss. The LPGD method supports derivatives and adjoint derivatives for all parameters, including the quadratic P term here. The reason I didn't include it was to not break some compatibility by changing the arguments/outputs of the exposed derivative and adjoint_derivative methods (and their batched versions). I guess the derivative would be simple to resolve by just adding an optional dP=None argument, but for the adjoint derivative one would need to change the number of outputs. I was thinking about adding a request_dP flag? If you think this makes sense I can come up with some proposal changes.
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I added the differentiation w.r.t. P now, see the latest commits. I added two examples but have not tested this extensively
| if solve_method == "ECOS": | ||
| warm_start = None | ||
| else: | ||
| warm_start = (np.hstack([x, s]), np.hstack([y, y]), np.hstack([s, s])) |
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It does not seem like they support it, currently in diffcp the warm_start is also not passed to the Clarabel solver so it definitely is not used at the moment. Probably better to make this explicit, I will add a check to throw an error when trying to use warmstarteing with Clarabel.
| xs, ys, ss, D_batch, DT_batch = diffcp.solve_and_derivative_batch(As, bs, cs, Ks, | ||
| n_jobs_forward=1, n_jobs_backward=n_jobs, solver="ECOS", verbose=False) | ||
| n_jobs_forward=1, n_jobs_backward=n_jobs, solve_method="ECOS", verbose=False) |
examples/dual_example.py
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| # defined as a product of a 3-d fixed cone, 3-d positive orthant cone, | |||
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| # defined as a product of a 3-d fixed cone, 3-d positive orthant cone, | |
| # defined as a product of a 3-d zero cone, 3-d positive orthant cone, |
examples/ecos_example.py
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| # defined as a product of a 3-d fixed cone, 3-d positive orthant cone, | |||
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| # defined as a product of a 3-d fixed cone, 3-d positive orthant cone, | |
| # defined as a product of a 3-d zero cone, 3-d positive orthant cone, |
examples/ecos_example_lpgd.py
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| # We generate a random cone program with a cone | ||
| # defined as a product of a 3-d fixed cone, 3-d positive orthant cone, |
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| # defined as a product of a 3-d fixed cone, 3-d positive orthant cone, | |
| # defined as a product of a 3-d zero cone, 3-d positive orthant cone, |
Pull request for enabling LPGD differentiation of the conic program in diffcp.
LPGD info
LPGD computes informative replacements for the true derivatives in degenerate cases as efficient finite differences.
For the forward derivatives this implementation just computes standard finite differences (with an additional optional regularization term).
For adjoint derivatives we compute finite differences between gradients of the conic program Lagrangian, evaluated at the original solution and a perturbed solution, requiring only one (two if double-sided) additional solver evaluations. See the paper for a detailed derivation of the LPGD adjoint derivatives as the gradient of an envelope function to the linearized loss.
Note that in the limit of small perturbations
tau, LPGD computes the true derivatives (if they exist). For largertauthe computed derivatives do not match the true derivatives but can provide more informative signal.Code
LPGD can be enabled with the
mode=LPGDargument ofsolve_and_derivative. It also requires passing the perturbation strengthtau(and optionally the regularization strengthrho) withderivative_kwargs=dict(tau=0.1, rho=0.1). Alternatively the derivative kwargs can be passed directly, e.g.adjoint_derivative(dx, dy, ds, tau=0.1, rho=0.1)In the code the main addition are the methods
derivative_lpgd/adjoint_derivative_lpgdincone_program.py. These methods internally callcompute_perturbed_solution/compute_adjoint_perturbed_solutionto get the solution to a perturbed optimization problem, and then return the derivatives as finite differences.For testing, the existing diffcp examples are included as modified versions using LPGD differentiation.
Note on implementation: If activated, the optional regularization requires solving a quadratic cone problem, i.e. setting
P!=0. For this reason we added an optionalP=Nonekwarg tosolve_internalwhich is passed to the solver if quadratic objectives are supported.