用dqn算法出一个matlab求最短路径的题并给出代码

以下是使用DQN算法求解最短路径问题的Matlab代码：

% DQN Algorithm for Shortest Path Problem

% Initialize graph and start/end nodes
graph = [0 1 1 inf; 1 0 inf 1; 1 inf 0 1; inf 1 1 0];
startNode = 1;
endNode = 4;

% Initialize replay memory D
D = [];

% Initialize Q-network with random weights
Q = randn(size(graph,1), size(graph,2));

% Initialize target Q-network with same weights as Q-network
QTarget = Q;

% Initialize action selection parameters
epsilon = 1; % exploration rate
minEpsilon = 0.1; % minimum exploration rate
epsilonDecayRate = 0.0001; % exploration rate decay rate

% Initialize other hyperparameters
batchSize = 32; % minibatch size
gamma = 0.99; % discount factor
maxSteps = 10000; % maximum number of steps per episode

% Start training
for episode = 1:numEpisodes
    % Initialize state
    state = startNode;
    
    % Initialize episode variables
    totalReward = 0;
    step = 0;
    
    % Loop over steps in episode
    while step < maxSteps
        % Choose action according to epsilon-greedy policy
        if rand() < epsilon
            action = randi(size(graph,2));
        else
            [~, action] = min(Q(state,:));
        end
        
        % Take action and observe next state and reward
        nextState = action;
        reward = -graph(state,action);
        
        % Store transition in replay memory
        D = [D; state, action, reward, nextState];
        
        % Update state and total reward
        state = nextState;
        totalReward = totalReward + reward;
        
        % Sample minibatch from replay memory
        minibatch = D(randi(size(D,1),batchSize,1),:);
        
        % Compute target Q-values
        targetQ = minibatch(:,3) + gamma*max(QTarget(minibatch(:,4),:),[],2);
        
        % Compute predicted Q-values
        predictedQ = Q(minibatch(:,1),minibatch(:,2));
        
        % Compute loss and update Q-network
        loss = mean((targetQ - predictedQ).^2);
        Q(minibatch(:,1),minibatch(:,2)) = Q(minibatch(:,1),minibatch(:,2)) + alpha*(targetQ - predictedQ);
        
        % Update target Q-network every C steps
        if mod(step,C) == 0
            QTarget = Q;
        end
        
        % Decay exploration rate
        epsilon = max(minEpsilon, epsilon - epsilonDecayRate);
        
        % Check if episode is done
        if state == endNode
            break;
        end
        
        % Increment step counter
        step = step + 1;
    end
    
    % Print episode statistics
    fprintf('Episode %d: total reward = %.2f, epsilon = %.2f\n', episode, totalReward, epsilon);
end

% Compute shortest path
currentNode = startNode;
shortestPath = [currentNode];
while currentNode ~= endNode
    [~, action] = min(Q(currentNode,:));
    currentNode = action;
    shortestPath = [shortestPath, currentNode];
end

% Print shortest path
fprintf('Shortest path: ');
fprintf('%d ', shortestPath);
fprintf('\n');

在这个示例中，我们使用了一个4个节点的简单图，其中每个节点之间的距离表示为权重。我们使用DQN算法来寻找从起点到终点的最短路径。在每个步骤中，我们选择一个动作（即下一个节点），并计算奖励（即该动作所代表的边的权重的负值）。我们将每个状态转换和相关信息存储在回放内存中，并使用它们来更新我们的Q网络。我们使用epsilon贪婪策略来选择动作，以便在探索和利用之间进行权衡。我们使用Q网络来计算最短路径，并打印输出。