exp_grad_mult.m

function [simObj] = exp_grad_mult(simObj, lambda)
    % https://hudsonthames.org/online-portfolio-selection-momentum/
    % Regularization algorithm: Multiplicative update
    % large eta -> aggressively chase best performer
    % small eta -> passively chase best performer
    if nargin < 2
        lambda = 0.5;
    end
    simObj.reset(); % reset simulation environment
    w_const = ones(simObj.d,1)/simObj.d; % equal weighted portfolio vector
    x_t = ones(simObj.d, simObj.T); % initialize price relative S_t / S_{t-1}    
    eta = exp(-lambda);
    for i=1:simObj.T
        if i==1
            simObj.step(w_const);
        else
            % relative price change
            x_t(:,i) = simObj.s_hist(:, i) ./ simObj.s_hist(:, i-1);
            w_const = w_const .* exp(eta * x_t(:,i) ./ dot(w_const, x_t(:,i)));

            % Rescale weights to sum to 1
            w_const = w_const .* (w_const > 0);
            w_const = w_const / sum(w_const);
            simObj.step(w_const);
        end
    end
end