matlab adam优化器代码

Adam（Adaptive Moment Estimation）优化器是一种自适应学习率优化算法，它结合了动量梯度下降和RMSprop优化器的优点。下面是MATLAB中Adam优化器的代码示例：

function [xopt, fopt, iter] = adam(fun, x0, opts)
% Adam optimizer for unconstrained optimization
% fun: function handle
% x0: initial guess
% opts: struct containing parameters for Adam optimizer

% Set default options
if ~exist('opts', 'var')
    opts = struct();
end
alpha = getOpt(opts, 'alpha', 0.001); % learning rate
beta1 = getOpt(opts, 'beta1', 0.9); % decay rate for 1st moment estimate
beta2 = getOpt(opts, 'beta2', 0.999); % decay rate for 2nd moment estimate
eps = getOpt(opts, 'eps', 1e-8); % small constant to avoid division by zero
maxiter = getOpt(opts, 'maxiter', 1000); % maximum number of iterations
tol = getOpt(opts, 'tol', 1e-6); % stopping criterion

% Initialize variables
f = @(x) feval(fun, x);
n = length(x0);
m = zeros(n,1);
v = zeros(n,1);
x = x0;
fopt = f(x);
iter = 0;

% Main loop
while iter < maxiter
    iter = iter + 1;
    
    % Evaluate gradient
    grad = gradient(f, x);
    
    % Update biased first and second moment estimates
    m = beta1*m + (1-beta1)*grad;
    v = beta2*v + (1-beta2)*grad.^2;
    
    % Compute bias-corrected first and second moment estimates
    mhat = m / (1 - beta1^iter);
    vhat = v / (1 - beta2^iter);
    
    % Update parameters
    x = x - alpha * mhat ./ (sqrt(vhat) + eps);
    
    % Check for convergence
    fnew = f(x);
    if abs(fnew-fopt) < tol
        break;
    else
        fopt = fnew;
    end
end

xopt = x;
end

function optval = getOpt(opts, name, default)
% Helper function to get options from struct with default values
if isfield(opts, name)
    optval = opts.(name);
else
    optval = default;
end
end

这里的`fun`是代表要最小化的目标函数，`x0`是优化变量的初始值，`opts`是一个包含了Adam优化器的参数的结构体，其中包括了学习率、衰减率、小常数等参数。该代码实现了Adam算法的主要步骤，包括计算梯度、更新一阶和二阶矩、计算偏置校正后的一阶和二阶矩以及更新参数等过程。