feat: add the beginning of backtracking line search

Author: NunoSempere

index.js

@@ -44,29 +44,50 @@ const find_beta_from_ci = ({ci_lower, ci_upper}) => {
 		let result = (f_h - f)/h
 		return result
 	}
+	
+	// backtracking line search
+	// <https://en.wikipedia.org/wiki/Backtracking_line_search>
+	// Once we know the direction, how far to go along it?
+	const get_optimal_step_size_a = ({a,b, d, is_a}) => {
+		let dir = d_a > 0 ? 1 : -1 
+		
+		let step_size_min = 0
+		let loss_s_min = is_a ? loss(a + step_size_min * dir, b) : loss(a, b + step_size_min * dir)
+		
+		let step_size_max = 0.1
+		let loss_s_max = is_a ? loss(a + step_size_max * dir, b) : loss(a, b + step_size_max * dir)
+
+
+		for(let i=0; i<20; i++){
+			if(loss_s_min < loss_s_max){
+				step_size_max = (step_size_max + step_size_min) / 2
+				loss_s_max = is_a ? loss(a + step_size_max * dir, b) : loss(a, b + step_size_max * dir)
+			}else{
+				step_size_min = (step_size_max + step_size_min) / 2
+				loss_s_min = is_a ? loss(a + step_size_min * dir, b) : loss(a, b + step_size_min * dir)
+			}
+		}
+		return (step_size_min + step_size_max)/2
+	}
 
 	// gradient descent step
 	const gradient_descent = (a_init,b_init) => {
-		let epsilon = 2**(-14) // 1/16384
-		let n_a = 2
-		let n_b = 2
 		let a = a_init 
 		let b = b_init
 		let max_steps =  2000
 		for(let i = 0; i<max_steps; i++){
 			// gradient step for a
 			let dir_a = - df_da(a,b)
+			// console.log(dir_a)
 			let stepsize_a = 0.0005 // 1/n_a 
-			let step_a = stepsize_a * dir_a 
+			let step_a = stepsize_a // * dir_a 
 			a = Math.max(a + step_a, 0)
-			n_a = n_a + 1
 
 			// gradient step for b
 			let dir_b = - df_db(a,b)
 			let stepsize_b = 0.0005 // 1/n_b
-			let step_b = stepsize_b * dir_b
+			let step_b = stepsize_b // * dir_b
 			b = Math.max(b + step_b,0)
-			n_b = n_b + 1
 			// console.log(`a: ${a}, b: ${b}`)
 		}
 		return [a, b]