DQN Pytorch Loss keeps increasing
I am implementing simple DQN algorithm using pytorch, to solve the CartPole environment from gym. I have been debugging for a while now, and I cant figure out why the model is not learning.
Observations:

using SmoothL1Loss performs worse than MSEloss, but loss increases for both
smaller LR in Adam does not work, I have tested using 0.0001, 0.00025, 0.0005 and default

Notes:

I have debugged various parts of the algorithm individually, and can say with good confidence that the issue is in the learn function. I am wondering if this bug is due to me misunderstanding detach in pytorch or some other framework mistake im making.
I am trying to stick as close to the original paper as possible (linked above)

References:

example: GitHub gist
example: pytroch official

import torch as T
import torch.nn as nn
import torch.nn.functional as F

import gym
import numpy as np


class ReplayBuffer:
    def __init__(self, mem_size, input_shape, output_shape):
        self.mem_counter = 0
        self.mem_size = mem_size
        self.input_shape = input_shape

        self.actions = np.zeros(mem_size)
        self.states = np.zeros((mem_size, *input_shape))
        self.states_ = np.zeros((mem_size, *input_shape))
        self.rewards = np.zeros(mem_size)
        self.terminals = np.zeros(mem_size)

    def sample(self, batch_size):
        indices = np.random.choice(self.mem_size, batch_size)
        return self.actions[indices], self.states[indices], \
            self.states_[indices], self.rewards[indices], \
            self.terminals[indices]

    def store(self, action, state, state_, reward, terminal):
        index = self.mem_counter % self.mem_size

        self.actions[index] = action
        self.states[index] = state
        self.states_[index] = state_
        self.rewards[index] = reward
        self.terminals[index] = terminal
        self.mem_counter += 1


class DeepQN(nn.Module):
    def __init__(self, input_shape, output_shape, hidden_layer_dims):
        super(DeepQN, self).__init__()

        self.input_shape = input_shape
        self.output_shape = output_shape

        layers = []
        layers.append(nn.Linear(*input_shape, hidden_layer_dims[0]))
        for index, dim in enumerate(hidden_layer_dims[1:]):
            layers.append(nn.Linear(hidden_layer_dims[index], dim))
        layers.append(nn.Linear(hidden_layer_dims[-1], *output_shape))

        self.layers = nn.ModuleList(layers)

        self.loss = nn.MSELoss()
        self.optimizer = T.optim.Adam(self.parameters())

    def forward(self, states):
        for layer in self.layers[:-1]:
            states = F.relu(layer(states))
        return self.layers[-1](states)

    def learn(self, predictions, targets):
        self.optimizer.zero_grad()
        loss = self.loss(input=predictions, target=targets)
        loss.backward()
        self.optimizer.step()

        return loss


class Agent:
    def __init__(self, epsilon, gamma, input_shape, output_shape):
        self.input_shape = input_shape
        self.output_shape = output_shape
        self.epsilon = epsilon
        self.gamma = gamma

        self.q_eval = DeepQN(input_shape, output_shape, [64])
        self.memory = ReplayBuffer(10000, input_shape, output_shape)

        self.batch_size = 32
        self.learn_step = 0

    def move(self, state):
        if np.random.random() &lt; self.epsilon:
            return np.random.choice(*self.output_shape)
        else:
            self.q_eval.eval()
            state = T.tensor([state]).float()
            action = self.q_eval(state).max(axis=1)[1]
            return action.item()

    def sample(self):
        actions, states, states_, rewards, terminals = \
            self.memory.sample(self.batch_size)

        actions = T.tensor(actions).long()
        states = T.tensor(states).float()
        states_ = T.tensor(states_).float()
        rewards = T.tensor(rewards).view(self.batch_size).float()
        terminals = T.tensor(terminals).view(self.batch_size).long()

        return actions, states, states_, rewards, terminals

    def learn(self, state, action, state_, reward, done):
        self.memory.store(action, state, state_, reward, done)

        if self.memory.mem_counter &lt; self.batch_size:
            return

        self.q_eval.train()
        self.learn_step += 1
        actions, states, states_, rewards, terminals = self.sample()
        indices = np.arange(self.batch_size)
        q_eval = self.q_eval(states)[indices, actions]
        q_next = self.q_eval(states_).detach()
        q_target = rewards + self.gamma * q_next.max(axis=1)[0] * (1 - terminals)

        loss = self.q_eval.learn(q_eval, q_target)
        self.epsilon *= 0.9 if self.epsilon &gt; 0.1 else 1.0

        return loss.item()


def learn(env, agent, episodes=500):
    print('Episode: Mean Reward: Last Loss: Mean Step')

    rewards = []
    losses = [0]
    steps = []
    num_episodes = episodes
    for episode in range(num_episodes):
        done = False
        state = env.reset()
        total_reward = 0
        n_steps = 0

        while not done:
            action = agent.move(state)
            state_, reward, done, _ = env.step(action)
            loss = agent.learn(state, action, state_, reward, done)

            state = state_
            total_reward += reward
            n_steps += 1

            if loss:
                losses.append(loss)

        rewards.append(total_reward)
        steps.append(n_steps)

        if episode % (episodes // 10) == 0 and episode != 0:
            print(f'{episode:5d} : {np.mean(rewards):5.2f} '
                  f': {np.mean(losses):5.2f}: {np.mean(steps):5.2f}')
            rewards = []
            losses = [0]
            steps = []

    print(f'{episode:5d} : {np.mean(rewards):5.2f} '
          f': {np.mean(losses):5.2f}: {np.mean(steps):5.2f}')
    return losses, rewards


if __name__ == '__main__':
    env = gym.make('CartPole-v1')
    agent = Agent(1.0, 1.0,
                  env.observation_space.shape,
                  [env.action_space.n])

    learn(env, agent, 500)


The main problem I think is the discount factor, gamma. You are setting it to 1.0, which mean that you are giving the same weight to the future rewards as the current one. Usually in reinforcement learning we care more about the immediate reward than the future, so gamma should always be less than 1.
Just to give it a try I set gamma = 0.99 and run your code:
Episode: Mean Reward: Last Loss: Mean Step
  100 : 34.80 :  0.34: 34.80
  200 : 40.42 :  0.63: 40.42
  300 : 65.58 :  1.78: 65.58
  400 : 212.06 :  9.84: 212.06
  500 : 407.79 : 19.49: 407.79

As you can see the loss still increases (even if not as much as before), but so does the reward. You should consider that loss here is not a good metric for the performance, because you have a moving target. You can reduce the instability of the target by using a target network. With additional parameter tuning and a target network one could probably make the loss even more stable.
Also generally note that in reinforcement learning the loss value is not as important as it is in supervised; a decrease in loss does not always imply an improvement in performance, and vice versa.
The problem is that the Q target is moving while the training steps happen; as the agent plays, predicting the correct sum of rewards gets extremely hard (e.g. more states and rewards explored means higher reward variance), so the loss increases. This is even clearer in more complex the environments (more states, variated rewards, etc).
At the same time the Q network is getting better at approximating the Q values for each action, so the rewards (could) increase.
