GradientDescent¶

class hoomd.tune.GradientDescent(alpha: float = 0.1, kappa: ndarray | None = None, tol: float = 1e-05, maximize: bool = True, max_delta: float | None = None)¶

Bases: Optimizer

Solves equations of \(min_x f(x)\) using gradient descent.

Derivatives are computed using the forward difference.

The solver updates x each step via,

\[x_n = x_{n-1} - \alpha {\left (1 - \kappa) \nabla f + \kappa \Delta_{n-1} \right)}\]

where \(\Delta\) is the last step size. This gives the optimizer a sense of momentum which for noisy (stochastic) optimization can lead to smoother optimization. Due to the need for two values to compute a derivative, then first time this is called it makes a slight jump higher or lower to start the method.

The solver will stop updating when a maximum is detected (i.e. the step size is smaller than tol).

Parameters:

alpha (hoomd.variant.variant_like, optional) – Either a number between 0 and 1 used to dampen the rate of change in x or a variant that varies not by timestep but by the number of times solve has been called (i.e. the number of steps taken) (defaults to 0.1). alpha scales the corrections to x each iteration. Larger values of alpha lead to larger changes while a alpha of 0 leads to no change in x at all.
kappa (numpy.ndarray, optional) – Real number array that determines how much of the previous steps’ directions to use (defaults to None which does no averaging over past step directions). The array values correspond to weight that the \(N\) last steps are weighted when combined with the current step. The current step is weighted by \(1 - \sum_{i=1}^{N} \kappa_i\).
tol (float, optional) – The absolute tolerance for convergence of y, (defaults to 1e-5).
maximize (bool, optional) – Whether or not to maximize function (defaults to True).
max_delta (float, optional) – The maximum step size to allow (defaults to None which allows a step size of any length).

kappa¶

Real number array that determines how much of the previous steps’ directions to use. The array values correspond to weight that the \(N\) last steps are weighted when combined with the current step. The current step is weighted by \(1 - \sum_{i=1}^{N} \kappa_i\).

Type:: numpy.ndarray

tol¶

The absolute tolerance for convergence of y.

Type:: float

maximize¶

Whether or not to maximize function.

Type:: bool

max_delta¶

The maximum step size to allow.

Type:: float

__eq__(other)¶: Test for equality.

property alpha¶

Number between 0 and 1 that dampens of change in x.

Larger values of alpha lead to larger changes while a alpha of 0 leads to no change in x at all. The property returns the current alpha given the current number of steps.

The property can be set as in the constructor.

Type:: float

reset()¶: Reset all solving internals.

solve(tunables)¶

Iterates towards a solution for a list of tunables.

If a y for one of the tunables is None then we skip that tunable. Skipping implies that the quantity is not tuned and solve will return False.

Parameters:: tunables (list[hoomd.tune.ManualTuneDefinition]) – A list of tunable objects that represent a relationship f(x) = y.
Returns:: Returns whether or not all tunables were considered tuned by the object.
Return type:: bool

solve_one(tunable)¶: Solve one step.