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lbfgs.rs
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lbfgs.rs
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// Copyright 2018-2020 argmin developers
//
// Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or
// http://apache.org/licenses/LICENSE-2.0> or the MIT license <LICENSE-MIT or
// http://opensource.org/licenses/MIT>, at your option. This file may not be
// copied, modified, or distributed except according to those terms.
//! # References:
//!
//! [0] Jorge Nocedal and Stephen J. Wright (2006). Numerical Optimization.
//! Springer. ISBN 0-387-30303-0.
use crate::prelude::*;
use serde::de::DeserializeOwned;
use serde::{Deserialize, Serialize};
use std::collections::VecDeque;
use std::fmt::Debug;
/// L-BFGS method
///
/// [Example](https://github.com/argmin-rs/argmin/blob/master/examples/lbfgs.rs)
///
/// TODO: Implement compact representation of BFGS updating (Nocedal/Wright p.230)
///
/// # References:
///
/// [0] Jorge Nocedal and Stephen J. Wright (2006). Numerical Optimization.
/// Springer. ISBN 0-387-30303-0.
#[derive(Clone, Serialize, Deserialize)]
pub struct LBFGS<L, P> {
/// line search
linesearch: L,
/// m
m: usize,
/// s_{k-1}
s: VecDeque<P>,
/// y_{k-1}
y: VecDeque<P>,
}
impl<L, P> LBFGS<L, P> {
/// Constructor
pub fn new(linesearch: L, m: usize) -> Self {
LBFGS {
linesearch,
m,
s: VecDeque::with_capacity(m),
y: VecDeque::with_capacity(m),
}
}
}
impl<O, L, P> Solver<O> for LBFGS<L, P>
where
O: ArgminOp<Param = P, Output = f64>,
O::Param: Clone
+ Serialize
+ DeserializeOwned
+ Debug
+ Default
+ ArgminSub<O::Param, O::Param>
+ ArgminAdd<O::Param, O::Param>
+ ArgminDot<O::Param, f64>
+ ArgminScaledAdd<O::Param, f64, O::Param>
+ ArgminNorm<f64>
+ ArgminMul<f64, O::Param>,
O::Hessian: Clone + Default + Serialize + DeserializeOwned,
L: Clone + ArgminLineSearch<O::Param> + Solver<OpWrapper<O>>,
{
const NAME: &'static str = "L-BFGS";
fn init(
&mut self,
op: &mut OpWrapper<O>,
state: &IterState<O>,
) -> Result<Option<ArgminIterData<O>>, Error> {
let param = state.get_param();
let cost = op.apply(¶m)?;
let grad = op.gradient(¶m)?;
Ok(Some(
ArgminIterData::new().param(param).cost(cost).grad(grad),
))
}
fn next_iter(
&mut self,
op: &mut OpWrapper<O>,
state: &IterState<O>,
) -> Result<ArgminIterData<O>, Error> {
let param = state.get_param();
let cur_cost = state.get_cost();
let prev_grad = state.get_grad().unwrap();
// .unwrap_or_else(|| op.gradient(¶m).unwrap());
let gamma: f64 = if let (Some(ref sk), Some(ref yk)) = (self.s.back(), self.y.back()) {
sk.dot(*yk) / yk.dot(*yk)
} else {
1.0
};
// L-BFGS two-loop recursion
let mut q = prev_grad.clone();
let cur_m = self.s.len();
let mut alpha: Vec<f64> = vec![0.0; cur_m];
let mut rho: Vec<f64> = vec![0.0; cur_m];
for (i, (ref sk, ref yk)) in self.s.iter().rev().zip(self.y.iter().rev()).enumerate() {
let sk = *sk;
let yk = *yk;
let yksk: f64 = yk.dot(sk);
let rho_t = 1.0 / yksk;
let skq: f64 = sk.dot(&q);
let alpha_t = skq.mul(&rho_t);
q = q.sub(&yk.mul(&alpha_t));
rho[cur_m - i - 1] = rho_t;
alpha[cur_m - i - 1] = alpha_t;
}
let mut r = q.mul(&gamma);
for (i, (ref sk, ref yk)) in self.s.iter().zip(self.y.iter()).enumerate() {
let sk = *sk;
let yk = *yk;
let beta = yk.dot(&r).mul(&rho[i]);
r = r.add(&sk.mul(&(alpha[i] - beta)));
}
self.linesearch.set_search_direction(r.mul(&-1.0));
// Run solver
let ArgminResult {
operator: line_op,
state:
IterState {
param: xk1,
cost: next_cost,
..
},
} = Executor::new(
OpWrapper::new_from_op(&op),
self.linesearch.clone(),
param.clone(),
)
.grad(prev_grad.clone())
.cost(cur_cost)
.ctrlc(false)
.run()?;
// take care of function eval counts
op.consume_op(line_op);
if state.get_iter() >= self.m as u64 {
self.s.pop_front();
self.y.pop_front();
}
let grad = op.gradient(&xk1)?;
self.s.push_back(xk1.sub(¶m));
self.y.push_back(grad.sub(&prev_grad));
Ok(ArgminIterData::new()
.param(xk1)
.cost(next_cost)
.grad(grad)
.kv(make_kv!("gamma" => gamma;)))
}
fn terminate(&mut self, state: &IterState<O>) -> TerminationReason {
if state.get_grad().unwrap().norm() < std::f64::EPSILON.sqrt() {
return TerminationReason::TargetPrecisionReached;
}
if (state.get_prev_cost() - state.get_cost()).abs() < std::f64::EPSILON {
return TerminationReason::NoChangeInCost;
}
TerminationReason::NotTerminated
}
}
#[cfg(test)]
mod tests {
use super::*;
use crate::solver::linesearch::MoreThuenteLineSearch;
use crate::test_trait_impl;
type Operator = MinimalNoOperator;
test_trait_impl!(lbfgs, LBFGS<Operator, MoreThuenteLineSearch<Operator>>);
}