spsa 0.0.1

The purpose of this package is to provide multivariable optimizers using SPSA.

Simultaneous Perturbation Stochastic Optimization (SPSA)

The purpose of this package is to provide multivariable optimizers using SPSA. Although other optimizers exist, not many implement SPSA, which has various pros and cons. Additionally, SPSA has few requirements so that you don't have to install large packages like scipy just to optimize a function.

Usage

Synchronous Functions:

x = spsa.optimize(f, x)
x = spsa.optimize(spsa.maximize(f), x)  # For maximization.

for variables in spsa.optimize_iterator(f, x):
    print(variables)

Asynchronous Functions:

x = await spsa.aio.optimize(f, x)
x = await spsa.aio.optimize(spsa.aio.maximize(f), x)  # For maximization.

async for variables in spsa.aio.optimize(f, x):
    print(variables)

Example

import numpy as np
import spsa

# Sample function which has a minimum at 0.
def sphere(x: np.ndarray) -> float:
    return np.linalg.norm(x) ** 2

# Attempt to find the minimum.
print(spsa.optimize(sphere, [1, 2, 3]))
# Sample result:
#     [-5.50452777e-21 -9.48070248e-21  9.78726993e-21]

Pros & Cons

A comparison of SPSA, Gradient Descent, and Bayesian Optimization are shown below.

	SPSA	Gradient Descent	Bayesian Optimization
Calls per Iteration	Constant[1] f(x)	1 fprime(x)	Constant f(x)
Stochastic	Stochastic f	Stochastic fprime	Stochastic f
Convergence	Local	Local	Global
Dimensions	Any	Any	<20
Lines of Code	~100	10-100	>100
Integer Optimization	Applicable[2]	Inapplicable	Applicable[3]
Parallel Calls	Applicable[4]	Not Obvious	Applicable

[1]: Normally requires only 2 calls, but linear search and noise-adjusting perturbation sizes require a few extra calls per iteration.

[2]: Use f(round(x)), px=0.5, and px_decay=0.

[3]: Use a different Gaussian process.

[4]: See spsa.aio.