Zeroth order pytorch optimizers and gradient approximators (SPSA, RDSA, FDSA, etc) with efficient foreach implementations; as well as few first order optimizers. Better docs later.

from torchzero.optim import SPSA
optimizer = SPSA(model.parameters(), lr = 1e-3, magn = 1e-5)
for inputs, targets in dataloader:
    @torch.no_grad
    def closure():
        preds = model(inputs)
        loss = criterion(preds, targets)
        return loss
    optimizer.step(closure)

from torchzero.optim import SPSA
grad_approximator = SPSA(model.parameters(), magn = 1e-5, set_grad = True)
optimizer = torch.optim.AdamW(model.parameters(), lr = 1e-3)
for inputs, targets in dataloader:
    optimizer.zero_grad()
    @torch.no_grad
    def closure():
        preds = model(inputs)
        loss = criterion(preds, targets)
        return loss
    grad_approximator.step(closure) # sets .grad attrubute
    optimizer.step() 

• Simultaneous perturbation stochastic approximation (SPSA), random direction stochastic approximation (RDSA), and two-step random search - all implemented by the SPSA optimizer, e.g. SPSA(..., variant = "RDSA");
• Finite Differences Stochastic Approximation (FDSA);
• Random optimization (RandomOptimizer);
• Random search, random annealing;
• Sign gradient descent
• Bit gradient descent (not thoroughly tested)
• Newton's root finding method
• Caputo fractional derivative optimizer

All of those are available in optim submodule and work like any other pytorch optimizer. For small problems (1-10 parameters, FDSA or SPSA may work well; for more parameters SPSA is much faster because it only needs 2 evaluations per step. For very large number of parameters, around >10000, I found that RandomOptimizer + AdamW works best. First order and root finding methods are to be tested (I made sure they work though). Most algorithms use foreach operations (optionally, controlled by foreach argument), which makes them a bit more efficient.