`blackjax.optimizers.dual_averaging`#

Module Contents#

State carried through the dual averaging procedure.

dual_averaging(→ tuple[Callable, Callable, Callable])

Find the state that minimizes an objective function using a primal-dual

class DualAveragingState[source]#

State carried through the dual averaging procedure.

log_x: The logarithm of the current state
log_x_avg: The time-weighted average of the values that the logarithm of the state has taken so far.
step: The current iteration step.
avg_err: The time average of the value of the quantity \(H_t\), the difference between the target acceptance rate and the current acceptance rate.
mu: Arbitrary point the values of log_step_size are shrunk towards. Chose to be \(\log(10 \epsilon_0)\) where \(\epsilon_0\) is chosen in this context to be the step size given by the find_reasonable_step_size procedure.

dual_averaging(t0: int = 10, gamma: float = 0.05, kappa: float = 0.75) → tuple[Callable, Callable, Callable][source]#

Find the state that minimizes an objective function using a primal-dual subgradient method.

See [Nes09] for a detailed explanation of the algorithm and its mathematical properties.

Parameters:

t0 (float >= 0) – Free parameter that stabilizes the initial iterations of the algorithm. Large values may slow down convergence. Introduced in [HG+14] with a default value of 10.
gamma – Controls the speed of convergence of the scheme. The authors of [HG+14] recommend a value of 0.05.
kappa (float in ]0.5, 1]) – Controls the weights of past steps in the current update. The scheme will quickly forget earlier step for a small value of kappa. Introduced in [HG+14], with a recommended value of .75

Returns:

init – A function that initializes the state of the dual averaging scheme.
update – a function that updates the state of the dual averaging scheme.
final – a function that returns the state that minimizes the objective function.