Decay Schedules¶

Classes for defining decay schedules for simulated annealing.

class GeomDecay(init_temp=1.0, decay=0.99, min_temp=0.001)[source]¶

Schedule for geometrically decaying the simulated annealing temperature parameter T according to the formula:

$T(t) = \max(T_{0} \times r^{t}, T_{min})$

where:

$T_{0}$ is the initial temperature (at time t = 0);
$r$ is the rate of geometric decay; and
$T_{min}$ is the minimum temperature value.

Parameters:	init_temp (float, default: 1.0) – Initial value of temperature parameter T. Must be greater than 0. decay (float, default: 0.99) – Temperature decay parameter, r. Must be between 0 and 1. min_temp (float, default: 0.001) – Minimum value of temperature parameter. Must be greater than 0.

Example

>>> import mlrose
>>> schedule = mlrose.GeomDecay(init_temp=10, decay=0.95, min_temp=1)
>>> schedule.evaluate(5)
7.73780...

evaluate(t)[source]¶

Evaluate the temperature parameter at time t.

Parameters:	t (int) – Time at which the temperature paramter T is evaluated.
Returns:	temp (float) – Temperature parameter at time t.

class ArithDecay(init_temp=1.0, decay=0.0001, min_temp=0.001)[source]¶

Schedule for arithmetically decaying the simulated annealing temperature parameter T according to the formula:

$T(t) = \max(T_{0} - rt, T_{min})$

where:

$T_{0}$ is the initial temperature (at time t = 0);
$r$ is the rate of arithmetic decay; and
$T_{min}$ is the minimum temperature value.

Parameters:	init_temp (float, default: 1.0) – Initial value of temperature parameter T. Must be greater than 0. decay (float, default: 0.0001) – Temperature decay parameter, r. Must be greater than 0. min_temp (float, default: 0.001) – Minimum value of temperature parameter. Must be greater than 0.

Example

>>> import mlrose
>>> schedule = mlrose.ArithDecay(init_temp=10, decay=0.95, min_temp=1)
>>> schedule.evaluate(5)
5.25

evaluate(t)[source]¶

Evaluate the temperature parameter at time t.

Parameters:	t (int) – Time at which the temperature paramter T is evaluated.
Returns:	temp (float) – Temperature parameter at time t.

class ExpDecay(init_temp=1.0, exp_const=0.005, min_temp=0.001)[source]¶

Schedule for exponentially decaying the simulated annealing temperature parameter T according to the formula:

$T(t) = \max(T_{0} e^{-rt}, T_{min})$

where:

$T_{0}$ is the initial temperature (at time t = 0);
$r$ is the rate of exponential decay; and
$T_{min}$ is the minimum temperature value.

Parameters:	init_temp (float, default: 1.0) – Initial value of temperature parameter T. Must be greater than 0. exp_const (float, default: 0.005) – Exponential constant parameter, r. Must be greater than 0. min_temp (float, default: 0.001) – Minimum value of temperature parameter. Must be greater than 0.

Example

>>> import mlrose
>>> schedule = mlrose.ExpDecay(init_temp=10, exp_const=0.05, min_temp=1)
>>> schedule.evaluate(5)
7.78800...

evaluate(t)[source]¶

Evaluate the temperature parameter at time t.

Parameters:	t (int) – Time at which the temperature paramter T is evaluated.
Returns:	temp (float) – Temperature parameter at time t.

class CustomSchedule(schedule, **kwargs)[source]¶

Class for generating your own temperature schedule.

Parameters:	schedule (callable) – Function for calculating the temperature at time t with the signature `schedule(t, kwargs)`. kwargs** (additional arguments) – Additional parameters to be passed to schedule.

Example

>>> import mlrose
>>> def custom(t, c): return t + c
>>> kwargs = {'c': 10}
>>> schedule = mlrose.CustomSchedule(custom, **kwargs)
>>> schedule.evaluate(5)
15

evaluate(t)[source]¶

Evaluate the temperature parameter at time t.

Parameters:	t (int) – Time at which the temperature paramter T is evaluated.
Returns:	temp (float) – Temperature parameter at time t.