Compiling version of backtracking line search, needs debugging

src/gradient_descent/line_search.rs

@@ -1,12 +1,49 @@
+use crate::{objective_function::ObjectiveFun, traits::XVar};
+
 pub enum LineSearch {
-    ConstAlpha { learning_rate: f64 },
+    ConstAlpha {
+        learning_rate: f64,
+    },
+    BackTrack {
+        max_iterations: usize,
+        gamma: f64,
+        c: f64,
+    },
 }
 
 impl LineSearch {
-    pub fn get_learning_rate(&self) -> f64 {
+    pub fn get_learning_rate<T, E>(
+        &self,
+        fun: &dyn ObjectiveFun<T, E>,
+        xs: &T,
+        direction: &E,
+    ) -> f64
+    where
+        T: XVar<E> + Clone,
+        E:,
+    {
         match self {
             LineSearch::ConstAlpha { learning_rate } => *learning_rate,
+            LineSearch::BackTrack {
+                max_iterations,
+                gamma,
+                c,
+            } => {
+                let prime = fun.prime(xs);
+                let mut del_f = T::scale_prime(&prime, *c);
+                let mut new_f = fun.eval(&xs.update(-1.0, &prime));
+                let mut t = 1.0;
+                for i in 0..*max_iterations {
+                    if new_f > T::prime_inner_product(&T::scale_prime(&del_f, t), direction) {
+                        break;
+                    }
+                    t *= gamma;
+                    let new_x = xs.update(-t, &prime);
+                    new_f = fun.eval(&new_x);
+                    del_f = fun.prime(&new_x);
+                }
+                t
+            }
         }
     }
 }
-

src/gradient_descent/steepest_descent.rs

@@ -23,7 +23,7 @@ pub fn steepest_descent<T: XVar<E> + Clone, E>(
     let mut i = 0;
     for _ in 0..max_iters {
         let primes = fun.prime(&xs);
-        let learning_rate = line_search.get_learning_rate(fun, &xs);
+        let learning_rate = line_search.get_learning_rate(fun, &xs, &T::scale_prime(&primes, -1.0));
         xs = xs.update(direction * learning_rate, &primes);
         f = fun.eval(&xs);
 
@@ -60,9 +60,17 @@ mod test {
         let prime = Box::new(|xs: &Vec<f64>| xs.iter().map(|x| 2.0 * x).collect());
 
         let obj = Fun::new(fun, prime);
-        let line_search = LineSearch::ConstAlpha {
+        let line_searches = vec![
+            LineSearch::ConstAlpha {
                 learning_rate: 0.25,
-        };
+            },
+            LineSearch::BackTrack {
+                max_iterations: 100,
+                gamma: 0.5,
+                c: 0.1,
+            },
+        ];
+        for line_search in line_searches {
             let res = steepest_descent(&obj, &vec![20.0], 1000, 1e-12, &line_search, -1.0);
 
             if let ExitCondition::MaxIter = res.exit_con {
@@ -75,3 +83,4 @@ mod test {
             assert!(res.best_fun_val < 1e-8);
         }
     }
+}

src/traits.rs

@@ -1,9 +1,18 @@
 /// Trait defining the data structure that must be implemented for the independent variables used
 /// in the objective function. The generic type denotes the type of the prime of that variable
-///
+/// NOTE: This trait also defines some functions that are required to operate on the prime data
+/// type. It should be noted that we are unable to just require T to implement Mul<f64> or Add<f64>
+/// Bbecause then we wouldn't be able to implement XVar for plain Vec types which seems
+/// inconvenient
 pub trait XVar<T>: Clone {
     /// Update the current Xvariable based on the prime
     fn update(&self, alpha: f64, prime: &T) -> Self;
+    /// Multiply the prime by a float
+    fn scale_prime(prime: &T, rhs: f64) -> T;
+    /// Add a float to the prime
+    fn add_prime(prime: &T, rhs: f64) -> T;
+    /// Inner Produce
+    fn prime_inner_product(prime: &T, rhs: &T) -> f64;
 }
 
 /// Implementation of XVar for an f64 type
@@ -11,6 +20,18 @@ impl XVar<f64> for f64 {
     fn update(&self, alpha: f64, prime: &f64) -> Self {
         self + alpha * prime
     }
+
+    fn scale_prime(prime: &f64, rhs: f64) -> f64 {
+        prime * rhs
+    }
+
+    fn add_prime(prime: &f64, rhs: f64) -> f64 {
+        prime + rhs
+    }
+
+    fn prime_inner_product(prime: &f64, rhs: &f64) -> f64 {
+        prime * rhs
+    }
 }
 
 /// Implementation of XVar for a Vec<f64> type
@@ -21,4 +42,19 @@ impl XVar<Vec<f64>> for Vec<f64> {
             .map(|(x, xprime)| x + alpha * xprime)
             .collect()
     }
+
+    fn scale_prime(prime: &Vec<f64>, rhs: f64) -> Vec<f64> {
+        prime.iter().map(|val| val * rhs).collect()
+    }
+
+    fn add_prime(prime: &Vec<f64>, rhs: f64) -> Vec<f64> {
+        prime.iter().map(|val| val + rhs).collect()
+    }
+
+    fn prime_inner_product(prime: &Vec<f64>, rhs: &Vec<f64>) -> f64 {
+        prime
+            .iter()
+            .zip(rhs.iter())
+            .fold(0.0, |acc, a| acc + a.0 * a.1)
+    }
 }