Module multi_fidelity 

Multi-Fidelity Bayesian Optimization.

Implements multi-fidelity BO using an auto-regressive (AR(1)) coregionalization model across fidelity levels. Cheap, low-fidelity evaluations are used to inform the surrogate of the expensive, high-fidelity objective, letting the optimizer spend its budget efficiently.

Approach

The AR(1) coregionalization model (Kennedy & O’Hagan 2000) assumes:

  f_{l}(x) = rho_l * f_{l-1}(x) + delta_l(x)

where delta_l is an independent GP correction at each fidelity level. Each level l is fitted as a GP whose training target is y_l - rho_l * mu_{l-1}(x).

The acquisition function is the cost-normalized Expected Improvement

  EI_cost(x, l) = EI(x, model_l) / cost_l

which automatically selects both the next evaluation point and the fidelity level to use.

Quick Start

use scirs2_optimize::bayesian::multi_fidelity::{
    MultiFidelityBo, FidelityLevel, MultiFidelityConfig,
};

// Two-level example: level 0 is cheap (cost 1), level 1 is expensive (cost 10)
let levels = vec![
    FidelityLevel { cost: 1.0, noise: 0.05, correlation: 1.0 },
    FidelityLevel { cost: 10.0, noise: 0.001, correlation: 0.95 },
];

let bounds = vec![(-2.0_f64, 2.0_f64), (-2.0, 2.0)];

let mut mfbo = MultiFidelityBo::new(levels, bounds, MultiFidelityConfig::default())
    .expect("build mfbo");

// Low-fidelity oracle (cheap)
let lf_fn = |x: &[f64]| x[0].powi(2) + x[1].powi(2) + 0.1 * (x[0] * x[1]);
// High-fidelity oracle (expensive)
let hf_fn = |x: &[f64]| x[0].powi(2) + x[1].powi(2);

let fns: Vec<Box<dyn Fn(&[f64]) -> f64>> = vec![
    Box::new(lf_fn),
    Box::new(hf_fn),
];

let result = mfbo.optimize(&fns, 30.0).expect("optimize");
println!("Best x: {:?}, f: {:.4}", result.x_best, result.f_best);

Structs

AutoRegressiveGp

AR(1) coregionalization multi-output GP.

FidelityLevel

Descriptor of a single fidelity level.

MultiFidelityBo

Multi-Fidelity Bayesian Optimizer.

MultiFidelityConfig

Configuration for multi-fidelity Bayesian optimization.

MultiFidelityResult

Result of multi-fidelity Bayesian optimization.

Functions

extended_ei

Compute the cost-normalized Expected Improvement at a candidate point.

mfbo_optimize

Run multi-fidelity Bayesian optimization.