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//! A hill-climbing optimizer that works by systematically testing nearby //! candidates. //! //! This optimizer works even when the objective function (for which a maximum //! or minimum value is sought) is not differentiable, so that a gradient //! magnitude cannot be calculated. Any function may be optimized, //! provided its parameters are (or can be converted from) a `&[f64]` and its //! output implments `PartialOrd`. //! //! Here's an example optimization, using the Rosenbrock function. //! //! ``` //! use proximal_optimize::ProximalOptimizer; //! //! let mut po = ProximalOptimizer::new(2); //! po.iterations(10000); //! let initial_position = vec![-1.2, 1.0]; //! let optimized = po.optimize(&initial_position, |x: &[f64]| { //! ((1.0 - x[0]) * (1.0 - x[0]) //! + 100.0 * (x[1] - x[0] * x[0]) * (x[1] - x[0] * x[0])) //! }).unwrap(); //! println!("Optimized values is: {:?}", &optimized); //! assert_eq!(optimized, vec![0.999208314861111, 0.998416214890118]); //! ``` #![no_std] #[cfg(test)] #[macro_use] extern crate std; extern crate alloc; use core::{ cmp::Ordering, fmt::Debug, }; use alloc::vec::Vec; pub const DEFAULT_EXPANSION_RATIO: f64 = 1.5; pub const DEFAULT_COMPRESSION_RATIO: f64 = 0.5; pub const DEFAULT_INITIAL_STEP_SIZE: f64 = 1.0; pub const DEFAULT_NUM_ITERATIONS: usize = 100; /// A hill-climbing optimizer that works by systematically testing nearby /// candidates. /// /// This optimizer works even when the objective function (for which a maximum /// or minimum value is sought) is not differentiable, so that a gradient /// magnitude cannot be calculated. Any function may be optimized, /// provided its parameters are (or can be converted from) a `&[f64]` and its /// output implments `PartialOrd`. /// /// Here's an example optimization, using the Rosenbrock function. /// /// ``` /// use proximal_optimize::ProximalOptimizer; /// /// let mut po = ProximalOptimizer::new(2); /// po.iterations(10000); /// let initial_position = vec![-1.2, 1.0]; /// let optimized = po.optimize(&initial_position, |x: &[f64]| { /// ((1.0 - x[0]) * (1.0 - x[0]) /// + 100.0 * (x[1] - x[0] * x[0]) * (x[1] - x[0] * x[0])) /// }).unwrap(); /// println!("Optimized values is: {:?}", &optimized); /// assert_eq!(optimized, vec![0.999208314861111, 0.998416214890118]); /// ``` pub struct ProximalOptimizer { parameters: Vec<Parameters>, iterations: usize, maximize: bool, } impl ProximalOptimizer { /// Creates a new proximal optimizer with default values for step sizing and /// the number of iterations. pub fn new(num_parameters: usize) -> ProximalOptimizer { let mut climb_parameters = Vec::with_capacity(num_parameters); for _ in 0..num_parameters { climb_parameters.push(Parameters::default()) } ProximalOptimizer { parameters: climb_parameters, iterations: DEFAULT_NUM_ITERATIONS, maximize: false, } } /// Returns the number of parameters expected by this optimizer. pub fn get_num_parameters(&self) -> usize { self.parameters.len() } /// Set the optimizer to find input parameters that _maximize_ the objective /// function, not minimize it. pub fn maximize(&mut self) { self.maximize = true; } /// Set the optimizer to find input parameters that _minimize_ the objective /// function. This is the default. pub fn minimize(&mut self) { self.maximize = false; } /// Sets the maximum number of iterations that the optimizer will perform /// before returning the optimized parameters. pub fn iterations(&mut self, iterations: usize) { self.iterations = iterations; } /// Returns the number of iterations the optimizer will perform before /// returning the optimized parameters. pub fn get_iterations(&self) -> usize { self.iterations } /// Sets the initial step distance for all parameters to `step_size`. pub fn initial_step_size(&mut self, step_size: f64) { for param in self.parameters.iter_mut() { param.step_size = step_size; } } /// Sets the initial step sizes for each parameter to the value specified /// by `step_sizes`. pub fn initial_step_sizes(&mut self, step_sizes: &[f64]) -> Result<(), ProximalOptimizerErr> { if step_sizes.len() != self.parameters.len() { return Err(ProximalOptimizerErr::ParameterLengthMismatch); } for (i, param) in self.parameters.iter_mut().enumerate() { param.step_size = step_sizes[i]; } Ok(()) } /// Sets the step growth ratio for all parameters to `step_expansion_ratio`. pub fn step_expansion_ratio(&mut self, step_expansion_ratio: f64) { for param in self.parameters.iter_mut() { param.compression_ratio = step_expansion_ratio; } } /// Sets the step growth ratio for each parameter to the value specified /// by `step_expansion_ratio`. pub fn step_expansion_ratios(&mut self, step_expansion_ratio: &[f64]) -> Result<(), ProximalOptimizerErr> { if step_expansion_ratio.len() != self.parameters.len() { return Err(ProximalOptimizerErr::ParameterLengthMismatch); } for (i, param) in self.parameters.iter_mut().enumerate() { param.expansion_ratio = step_expansion_ratio[i]; } Ok(()) } /// Sets the step compression ratio for all parameters to `step_compression_ratio`. pub fn step_compression_ratio(&mut self, step_compression_ratio: f64) { for param in self.parameters.iter_mut() { param.compression_ratio = step_compression_ratio; } } /// Sets the step compression ratio for each parameter to the value /// specified by `step_increase_ratios`. pub fn step_decrease_ratios(&mut self, step_compression_ratios: &[f64]) -> Result<(), ProximalOptimizerErr> { if step_compression_ratios.len() != self.parameters.len() { return Err(ProximalOptimizerErr::ParameterLengthMismatch); } for (i, param) in self.parameters.iter_mut().enumerate() { param.compression_ratio = step_compression_ratios[i]; } Ok(()) } pub fn optimize<F, T>(&self, start: &[f64], mut func: F) -> Result<Vec<f64>, ProximalOptimizerErr> where F: FnMut(&[f64]) -> T, T: PartialOrd + Debug { // === Let's check some assumptions === // The number of input variables must be equal to the length of our // parameters vector if start.len() != self.parameters.len() { return Err(ProximalOptimizerErr::ParameterLengthMismatch); } // The starting fitness should have an ordering when compared with itself let start_fit = func(start); let mut current_fit = func(start); let start_cmp = start_fit.partial_cmp(&start_fit); if start_cmp.is_none() { return Err(ProximalOptimizerErr::StartUnorderable); } // Temporary variables to keep track of the current estimate as we iterate. // We start at the position provided to this function in `start`. let mut parameters = self.parameters.clone(); let mut current_pos = Vec::<f64>::with_capacity(start.len()); current_pos.extend_from_slice(start); // A temporary variable for storing the candidate vector for which we want // to test the fitness (i.e., so we don't have to allocate a new one for // every test). In testing, this will contain our current position, // modified by the current step-size for one of our $X_n$ input variables. let mut candidate = current_pos.clone(); // Shorthand for the number of input parameters let x_n = start.len(); // The main training loop for _train_iteration in 0..self.iterations { current_fit = func(¤t_pos); // Reset the candidate position to discard tests from last round. candidate.clear(); candidate.extend_from_slice(¤t_pos[..]); // x_i is the index of the input parameter we're currently testing. // We'll be testing and stepping each parameter separately in turn. for x_i in 0..x_n { let old_val = candidate[x_i]; candidate[x_i] = current_pos[x_i] + parameters[x_i].step_size; let test_fit = func(&candidate); let cmp = match test_fit.partial_cmp(¤t_fit) { Some(ordering) => { if !self.maximize { Some(ordering.reverse()) } else { Some(ordering) } }, None => None, }; match cmp { Some(Ordering::Less) | None => { // Going the direction we were, we saw a drop in fitness. Stay where // we are this step, but head the other direction, and reduce the // step size. parameters[x_i].step_size = parameters[x_i].step_size * -1.0 * parameters[x_i].compression_ratio; }, Some(Ordering::Greater) => { // Fitness is greater a step over. Move to the new position, and // increase the step size. parameters[x_i].step_size = parameters[x_i].step_size * self.parameters[x_i].expansion_ratio; current_pos[x_i] = candidate[x_i]; }, Some(Ordering::Equal) => { // Fitness is somehow exactly flat over a step. Stay where we are, // but reduce the step size parameters[x_i].step_size = parameters[x_i].step_size * self.parameters[x_i].compression_ratio; }, } // Restore the old value for this candidate vector. This has the effect // that, from the perspective of the position update, the steps for each // parameters/dimension are updated simultaneously, rather than in turn. candidate[x_i] = old_val; } } // If the ending fitness isn't better than the one we started with, return // an error. let final_cmp = current_fit.partial_cmp(&start_fit); match (final_cmp, self.maximize) { (Some(Ordering::Greater), true) | (Some(Ordering::Less), false) => { Ok(current_pos) }, _ => Err(ProximalOptimizerErr::SolutionNoBetter), } } } #[derive(Copy, Clone, Debug)] struct Parameters { expansion_ratio: f64, compression_ratio: f64, step_size: f64, } impl Default for Parameters { fn default() -> Self { Parameters { expansion_ratio: DEFAULT_EXPANSION_RATIO, compression_ratio: DEFAULT_COMPRESSION_RATIO, step_size: DEFAULT_INITIAL_STEP_SIZE, } } } /// #[derive(Copy, Clone, Debug)] pub enum ProximalOptimizerErr { /// Caused when the length of parameter vectors does not match the number /// of parameters specified when the optimizer was created. ParameterLengthMismatch, /// The objective function's value at the start position could not be compared /// with itself (perhaps a `NaN` condition?) StartUnorderable, /// The candidate solution is no better than the starting position, and /// may actually be worse. SolutionNoBetter, } #[cfg(test)] mod tests { use super::*; /// The Rosenbrock function was chosen for testing because it is known to be /// a "pathological" function for gradient descent algorithms. This should /// zero in on the optimum, though this does take a large number of updates. #[test] pub fn test_rosenbrock() { let mut po = ProximalOptimizer::new(2); let glob_opt = vec![1.0, 1.0]; let tolerance = vec![0.01, 0.01]; po.iterations(10000); let mut pos = vec![-1.2, 1.0]; println!("Start Position: {:?}, value: {:?}", &pos, rosenbrock(&pos)); pos = po.optimize(&pos, rosenbrock).unwrap(); println!("End Position: {:?}, value: {:?}", &pos, rosenbrock(&pos)); confirm_dif(&glob_opt, &pos, &tolerance); po.iterations(40000); let mut pos = vec![2.0, 2.0]; println!("Start Position: {:?}, value: {:?}", &pos, rosenbrock(&pos)); pos = po.optimize(&pos, rosenbrock).unwrap(); println!("End Position: {:?}, value: {:?}", &pos, rosenbrock(&pos)); confirm_dif(&glob_opt, &pos, &tolerance); po.iterations(10000); let mut pos = vec![0.0, 0.0]; println!("Start Position: {:?}, value: {:?}", &pos, rosenbrock(&pos)); pos = po.optimize(&pos, rosenbrock).unwrap(); println!("End Position: {:?}, value: {:?}", &pos, rosenbrock(&pos)); confirm_dif(&glob_opt, &pos, &tolerance); po.iterations(400000); let mut pos = vec![100.0, 100.0]; println!("Start Position: {:?}, value: {:?}", &pos, rosenbrock(&pos)); pos = po.optimize(&pos, rosenbrock).unwrap(); println!("End Position: {:?}, value: {:?}", &pos, rosenbrock(&pos)); confirm_dif(&glob_opt, &pos, &tolerance); } #[test] pub fn test_simple_parabola() { let mut po = ProximalOptimizer::new(1); po.iterations(10); po.maximize(); let pos = po.optimize(&vec![0.0], simple_parabola).unwrap(); println!("pos {:?}", &pos); assert_eq!(pos, vec![49.2578125]) } fn simple_parabola(x: &[f64]) -> f64 { -0.5 * x[0] * x[0] + 50.0 * x[0] + 12.0 } fn rosenbrock(x: &[f64]) -> f64 { // This is actually the inverse, because our function maximizes fitness // rather than minimizes error. ((1.0 - x[0]) * (1.0 - x[0]) + 100.0 * (x[1] - x[0] * x[0]) * (x[1] - x[0] * x[0])) } fn confirm_dif(expected: &[f64], observed: &[f64], tolerance: &[f64]) { assert_eq!(expected.len(), observed.len()); assert_eq!(expected.len(), tolerance.len()); for i in 0..expected.len() { let diff = (expected[i] - observed[i]).abs(); if diff > tolerance[i] { panic!(); } } } }