Struct argmin::solver::quasinewton::LBFGS

pub struct LBFGS<L, P, G, F> { /* private fields */ }

Limited-memory BFGS (L-BFGS) method

L-BFGS is an approximation to BFGS which requires a limited amount of memory. Instead of storing the inverse, only a few vectors which implicitly represent the inverse matrix are stored.

It requires a line search and the number of vectors to be stored (history size m) must be set. Additionally an initial guess for the parameter vector is required, which is to be provided via the configure method of the Executor (See IterState, in particular IterState::param). In the same way the initial gradient and cost function corresponding to the initial parameter vector can be provided. If these are not provided, they will be computed during initialization of the algorithm.

Two tolerances can be configured, which are both needed in the stopping criteria. One is a tolerance on the gradient (set with with_tolerance_grad): If the norm of the gradient is below said tolerance, the algorithm stops. It defaults to sqrt(EPSILON). The other one is a tolerance on the change of the cost function from one iteration to the other. If the change is below this tolerance (default: EPSILON), the algorithm stops. This parameter can be set via with_tolerance_cost.

Orthant-Wise Limited-memory Quasi-Newton (OWL-QN) method

OWL-QN is a method that adapts L-BFGS to L1-regularization. The original L-BFGS requires a loss function to be differentiable and does not support L1-regularization. Therefore, this library switches to OWL-QN when L1-regularization is specified. L1-regularization can be performed via with_l1_regularization.

TODO: Implement compact representation of BFGS updating (Nocedal/Wright p.230)

Requirements on the optimization problem

The optimization problem is required to implement CostFunction and Gradient.

Reference

Jorge Nocedal and Stephen J. Wright (2006). Numerical Optimization. Springer. ISBN 0-387-30303-0.

Galen Andrew and Jianfeng Gao (2007). Scalable Training of L1-Regularized Log-Linear Models, International Conference on Machine Learning.

Implementations

impl<L, P, G, F> LBFGS<L, P, G, F>

where F: ArgminFloat,

pub fn new(linesearch: L, m: usize) -> Self

Construct a new instance of LBFGS

Example

let lbfgs: LBFGS<_, Vec<f64>, Vec<f64>,  f64> = LBFGS::new(linesearch, 5);

pub fn with_tolerance_grad(self, tol_grad: F) -> Result<Self, Error>

The algorithm stops if the norm of the gradient is below tol_grad.

The provided value must be non-negative. Defaults to sqrt(EPSILON).

Example

let lbfgs: LBFGS<_, Vec<f64>, Vec<f64>,  f64> = LBFGS::new(linesearch, 3).with_tolerance_grad(1e-6)?;

pub fn with_tolerance_cost(self, tol_cost: F) -> Result<Self, Error>

Sets tolerance for the stopping criterion based on the change of the cost stopping criterion

The provided value must be non-negative. Defaults to EPSILON.

Example

let lbfgs: LBFGS<_, Vec<f64>, Vec<f64>, f64> = LBFGS::new(linesearch, 3).with_tolerance_cost(1e-6)?;

pub fn with_l1_regularization(self, l1_coeff: F) -> Result<Self, Error>

Activates L1-regularization with coefficient l1_coeff.

Parameter l1_coeff must be > 0.0.

Example

let lbfgs: LBFGS<_, Vec<f64>, Vec<f64>, f64> = LBFGS::new(linesearch, 3).with_l1_regularization(1.0)?;

Trait Implementations

impl<L: Clone, P: Clone, G: Clone, F: Clone> Clone for LBFGS<L, P, G, F>

fn clone(&self) -> LBFGS<L, P, G, F>

Returns a copy of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl<'de, L, P, G, F> Deserialize<'de> for LBFGS<L, P, G, F>

where L: Deserialize<'de>, P: Deserialize<'de>, G: Deserialize<'de>, F: Deserialize<'de>,

fn deserialize<__D>(__deserializer: __D) -> Result<Self, __D::Error>

where __D: Deserializer<'de>,

Deserialize this value from the given Serde deserializer.

impl<L, P, G, F> Serialize for LBFGS<L, P, G, F>

where L: Serialize, P: Serialize, G: Serialize, F: Serialize,

fn serialize<__S>(&self, __serializer: __S) -> Result<__S::Ok, __S::Error>

where __S: Serializer,

Serialize this value into the given Serde serializer.

impl<O, L, P, G, F> Solver<O, IterState<P, G, (), (), (), F>> for LBFGS<L, P, G, F>

where O: CostFunction<Param = P, Output = F> + Gradient<Param = P, Gradient = G>, P: Clone + ArgminSub<P, P> + ArgminSub<F, P> + ArgminAdd<P, P> + ArgminAdd<F, P> + ArgminDot<G, F> + ArgminMul<F, P> + ArgminMul<P, P> + ArgminMul<G, P> + ArgminL1Norm<F> + ArgminSignum + ArgminZeroLike + ArgminMinMax, G: Clone + ArgminL2Norm<F> + ArgminSub<G, G> + ArgminAdd<G, G> + ArgminAdd<P, G> + ArgminDot<G, F> + ArgminDot<P, F> + ArgminMul<F, G> + ArgminMul<F, P> + ArgminZeroLike + ArgminMinMax, L: Clone + LineSearch<P, F> + Solver<LineSearchProblem<O, P, G, F>, IterState<P, G, (), (), (), F>>, F: ArgminFloat,

fn name(&self) -> &str

Name of the solver. Mainly used in Observers.

fn init( &mut self, problem: &mut Problem<O>, state: IterState<P, G, (), (), (), F>, ) -> Result<(IterState<P, G, (), (), (), F>, Option<KV>), Error>

Initializes the algorithm.

fn next_iter( &mut self, problem: &mut Problem<O>, state: IterState<P, G, (), (), (), F>, ) -> Result<(IterState<P, G, (), (), (), F>, Option<KV>), Error>

Computes a single iteration of the algorithm and has access to the optimization problem definition and the internal state of the solver. Returns an updated state and optionally a KV which holds key-value pairs used in Observers.

fn terminate( &mut self, state: &IterState<P, G, (), (), (), F>, ) -> TerminationStatus

Used to implement stopping criteria, in particular criteria which are not covered by (terminate_internal.

fn terminate_internal(&mut self, state: &I) -> TerminationStatus

Checks whether basic termination reasons apply.