Adaptive Rate Monte Carlo Optimizer

class ARMCOptimizer(_opt_id=None, _signal_pipe=None, _results_queue=None, _pause_flag=None, _is_log_detailed=False, _workers=1, _backend='threads', phi=1.0, gamma=2.0, a_target=0.25, super_iter_len=1000, sub_iter_len=100, move_range=array([0.9, 0.905, 0.91, 0.915, 0.92, 0.925, 0.93, 0.935, 0.94, 0.945, 0.95, 0.955, 0.96, 0.965, 0.97, 0.975, 0.98, 0.985, 0.99, 0.995, 1.005, 1.01, 1.015, 1.02, 1.025, 1.03, 1.035, 1.04, 1.045, 1.05, 1.055, 1.06, 1.065, 1.07, 1.075, 1.08, 1.085, 1.09, 1.095, 1.1  ]), move_func=<ufunc 'multiply'>)

Bases: scm.glompo.optimizers.baseoptimizer.BaseOptimizer

An optimizer using the Adaptive Rate Monte Carlo (ARMC) algorithm.

1. A trial state, \(S_{\omega}\), is generated by moving a random parameter retrieved from a user-specified parameter set (e.g. atomic charge). By default, parameters moves are applied in a multiplicative manner.

2. The move is accepted if the new set of parameters, \(S_{\omega}\), lowers the auxiliary error (\(\Delta \varepsilon_{QM-MM}\)) with respect to the previous set of accepted parameters \(S_{\omega-i}\) (\(i > 0\); see (1)). The auxiliary error is calculated with a user-specified cost function.

(1)\[p(\omega \leftarrow \omega-i) = \Biggl \lbrace { 1, \quad \Delta \varepsilon_{QM-MM} ( S_{\omega} ) \; \lt \; \Delta \varepsilon_{QM-MM} ( S_{\omega-i} ) \atop 0, \quad \Delta \varepsilon_{QM-MM} ( S_{\omega} ) \; \gt \; \Delta \varepsilon_{QM-MM} ( S_{\omega-i} ) }\]

3. The parameter history is updated. Either \(S_{\omega}\) or \(S_{\omega-i}\) is increased by the variable \(\phi\) (see (2)) if, respectively, the new parameters are accepted or rejected. In this manner the underlying PES is continuously modified, preventing the optimizer from getting permanently stuck in a (local) parameter space minima.

(2)\[\Delta \varepsilon_{QM-MM} ( S_{\omega} ) + \phi \quad \text{if} \quad \Delta \varepsilon_{QM-MM} ( S_{\omega} ) \; \lt \; \Delta \varepsilon_{QM-MM} ( S_{\omega-i} ) \atop \Delta \varepsilon_{QM-MM} ( S_{\omega-i} ) + \phi \quad \text{if} \quad \Delta \varepsilon_{QM-MM} ( S_{\omega} ) \; \gt \; \Delta \varepsilon_{QM-MM} ( S_{\omega-i} )\]

4. The parameter \(\phi\) is updated at regular intervals in order to maintain a constant acceptance rate \(\alpha_{t}\). This is illustrated in (3), where \(\phi\) is updated the beginning of every super-iteration \(\kappa\). In this example the total number of iterations, \(\kappa \omega\), is divided into \(\kappa\) super- and \(\omega\) sub-iterations.

(3)\[\phi_{\kappa \omega} = \phi_{ ( \kappa - 1 ) \omega} * \gamma^{ \text{sgn} ( \alpha_{t} - \overline{\alpha}_{ ( \kappa - 1 ) }) } \quad \kappa = 1, 2, 3, ..., N\]

Parameters

_opt_id, _signal_pipe, _results_queue, _pause_flag, _is_log_detailed, _workers, _backend

See BaseOptimizer.

phi

The variable \(\phi\).

gamma

The constant \(\gamma\).

a_target

The target acceptance rate \(\alpha_{t}\).

super_iter_len

The total number of each super-iterations \(\kappa\). Total number of iterations: \(\kappa \omega\).

sub_iter_len

The length of each ARMC sub-iteration \(\omega\). Total number of iterations: \(\kappa \omega\).

move_range

An array-like object containing all allowed move sizes.

move_func

A callable for performing the moves. The callable should take 2 floats (i.e. a single value from the parameter set S_{omega-i} and the move size) and return 1 float (i.e. an updated value for the parameter set S_{omega}).

Attributes

phifloat

The variable \(\phi\).

gammafloat

The constant \(\gamma\).

a_targetfloat

The target acceptance rate \(\alpha_{t}\).

super_iterrange

A range object with the total number of each super-iterations \(\kappa\). Total number of iterations: \(\kappa \omega\).

sub_iterrange

A range object with the length of each ARMC sub-iteration \(\omega\). Total number of iterations: \(\kappa \omega\).

move_rangenumpy.ndarray[float]

An array-like object containing all allowed move sizes.

move_funcCallable[[float, float], float]

A callable for performing the moves. The callable should take 2 floats (i.e. a single value from the parameter set S_{omega-i} and the move size) and return 1 float (i.e. an updated value for the parameter set S_{omega}).

runCallable

See the function parameter in ARMCOptimizer.minimize().

boundsnumpy.ndarray or (None, None)

An 2D array (or 2-tuple filled with None) denoting minimum and maximum values for each to-be moved parameter. See the bounds parameter in ARMCOptimizer.minimize().

x_bestnumpy.ndarray[float]

The parameter set which minimizes the user-specified error function.

fx_bestfloat

The error associated with x_best.

fx_oldfloat

The error of the last set of accepted parameters.

See Also:

The paper describing the original ARMC implementation: Salvatore Cosseddu et al., J. Chem. Theory Comput., 2017, 13, 297–308 10.1021/acs.jctc.6b01089.

The Python-based implementation of ARMC this class is based on: Automated Forcefield Optimization Extension github.com/nlesc-nano/auto-FOX.

property bounds

Get or set the bounds parameter of ARMCOptimizer.minimize().

checkpoint_save(path, force=None, block=None)

Save current state, suitable for restarting.

Parameters

path

Path to file into which the object will be dumped. Typically supplied by the manager.

force

Set of variable names which will be forced into the dumped file. Convenient shortcut for overwriting if fails for a particular optimizer because a certain variable is filtered out of the data dump.

block

Set of variable names which are typically caught in the construction of the checkpoint but should be excluded. Useful for excluding some properties.

Notes

1. Only the absolutely critical aspects of the state of the optimizer need to be saved. The manager will resupply multiprocessing parameters when the optimizer is reconstructed.

2. This method will almost never be called directly by the user. Rather it will be called (via signals) by the manager.

3. This is a basic implementation which should suit most optimizers; may need to be overwritten. Typically it is sufficient to call the super method and use the force and block parameters to get a working implementation.

minimize(function, x0, bounds=None)

Start the minimization process.

Parameters:

functionCallable

The function to be minimized.

x0array-like[float]

A 1D array-like object representing the set of to-be optimized parameters \(S\).

boundsarray-like[float], optional

An (optional) 2D array-like object denoting minimum and maximum values for each to-be moved parameter. The sequence should be of the same length as x0.

move(x0, x0_min=None, x0_max=None)

Create a copy of x0 and apply a random move to it.

The move will be applied with move_func (multiplication by default) using a random value from move_range.

Parameters:

x0numpy.ndarray[float]

A 1D array of parameters \(S_{\omega-i}\).

value_minnumpy.ndarray[float], optional

A 1D array minimum values for each to-be moved parameter. The array should be of the same length as x0.

value_maxnumpy.ndarray[float], optional

A 1D array maximum values for each to-be moved parameter. The array should be of the same length as x0.

Returns:

numpy.ndarray[float]

A copy of x0 \(S_{\omega}\). A single value is moved within this parameter set.

phi_apply(aux_err)

Apply phi to the supplied auxiliary error: \(\Delta \varepsilon_{QM-MM} + \phi\).

phi_update()

Update the variable \(\phi\) (phi).

\(\phi\) is updated based on the target acceptance rate, \(\alpha_{t}\) (a_target), and the acceptance rate, acceptance, of the current super-iteration:

\[\phi_{\kappa \omega} = \phi_{ ( \kappa - 1 ) \omega} * \gamma^{ \text{sgn} ( \alpha_{t} - \overline{\alpha}_{ ( \kappa - 1 ) }) }\]

Parameters:

acceptancenumpy.ndarray[bool]

A boolean array for keeping track of accepted moves over the course of the current sub-iteration of \(\kappa\).