I am pretty new to RL and I am trying to code a simple RL task with pytorch.
The goal/task is the following: The initial state is toto and the agent takes an action Δt: t_0+Δt=t_0+Δt=t_1.
If t_1 equals 450 or 475 then it gets a reward, else he does not get a reward.
I am training the agent with DQN algorithm on a NN ( with: 2 Linear layes: fist layer n_in=1 n_out 128 and second layer n_in=128 and n_out=5):
observation space(t_i) is 700 --> t_i∈[0,700[ti∈[0,700[
action space (Δt) is 5 --> (Δt∈[−50,−25,0,25,50]Δt∈[−50,−25,0,25,50])
epsilon_start=0.9#e-greedy threshold start value
epsilon_end=0.01#e-greedy threshold end value
epsilon_decay=200#e-greedy threshold decay learning_rate=0.001# NN
optimizer learning rate batch_size=64#Q-learning batch size
Unfortunately it does not seem to converge to the values t_i =  450 or 475. I doesn’t seem to care about getting a reward. How can I improve my code so that the agent learns what I am trying to teach him? I put my code below in case the explanations were not clear enough:
from gym import spaces

class RL_env(gym.Env):
    metadata = {'render.modes': ['human']}

    
    def __init__(self):
        super(RL_env, self).__init__()
        
        n_actions_delta = 1 #delta_t
        self.action_space = spaces.Discrete(5)
        
        n_observations = 1 #time
    
        self.observation_space = spaces.Discrete(700)
       
        #initial time
        self.time = 0
        
        self.done = 0
        self.reward = 0

    def reset(self):
        self.reward = 0
        self.done = False
        return self.time
       
    def step(self,delta_t):
        print('self time',self.time)
        d_t = np.arange(-50,70,25)
        
        self.time = (self.time + d_t[delta_t])%700
        print('delta time',d_t[delta_t],'-->','self time',self.time)
        
       
        
        if self.time == 475 or self.time == 450:
            self.reward+=1
            
            
        else:
            self.reward += 0
        
            
        info = {}
        print('total reward',self.reward)
        print('\n')
        return self.time,self.reward, self.done, info
    

    
    
    def render(self, mode='human', close=False):
        print()

import numpy as np
import matplotlib.pyplot as plt
import torch
import torch.nn as nn
import torch.optim as optim
import torch.nn.functional as F
from torch.autograd import Variable
from torch.distributions import Categorical
dtype = torch.float
device = torch.device("cpu")
import random
import math
import sys
if not sys.warnoptions:#igrnore warnings
    import warnings
    warnings.simplefilter("ignore")

#hyper parameters
epsilon_start=0.9
#e-greedy threshold start value
epsilon_end=0.01#e-greedy threshold end value
epsilon_decay=200#e-greedy threshold decay
learning_rate=0.001# NN optimizer learning rate
batch_size=64#Q-learning batch size 

env = RL_env()


#use replay memory (-> to stabilize and improve our algorithm)for training: store transitions observed by agent,
#then reuse this data later
#sample from it randomly (batch built by transitions are decorrelated)
class ReplayMemory:#allowes the agent to learn from earlier memories (speed up learning and break undesirable temporal correlations)
    def __init__(self, capacity):
        self.capacity = capacity
        self.memory = []
    def push(self, transition):#saves transition
        self.memory.append(transition)
        if len(self.memory)>self.capacity:#if length of memory arra is larger than capacity (fixed)
            del self.memory[0]#remove 0th element

    def sample(self, batch_number):#samples randomly a transition to build batch
        return random.sample(self.memory, batch_number)

    def __len__(self):
        return len(self.memory)
    
#Dqn NN (we want to maximize the discounted, cumulative reward)
#idea of Q-learning: we want to approximate with NN maximal Q-function (gives max return of action in given state)
#training update rule: use the fact that every Q-function for some policy obeys the Bellman equation
#difference between the two sides of the equality is known as the temporal difference error (we want to min -> Huber loss)
#calculate over batch of transitions sampled from the replay memory
class DqnNet(nn.Module):
    def __init__(self):
        super(DqnNet, self).__init__()
        
        state_space = 1
        action_space = env.action_space.n
        num_hid = 128
        self.fc1 = nn.Linear(state_space, num_hid)
        self.fc2 = nn.Linear(num_hid, action_space)
        self.gamma=0.5 #Q-learning discount factor (ensures that reward sum converges, 
                        #makes actions from far future less important)
    def forward(self, x):
        x = F.relu(self.fc1(x))
        x = F.sigmoid(self.fc2(x))
        return x

#select action accordingly to epsilon greedy policy
#sometimes we use model for choosing action, other times sample uniformly 
#probability of choosing a random action will start at epsilon_start and will decay (epsilon_decay) exponentially
#towards epsilon_end
steps_done=0
def predict_action(state):
    global steps_done
    sample=random.random()#random number
    eps_threshold=epsilon_end+(epsilon_start-epsilon_end)*math.exp(-1.*steps_done/epsilon_decay)
    steps_done += 1
    if sample>eps_threshold:  
        x  = eps_threshold,model(Variable(state,).type(torch.FloatTensor)).data.max(0)[1].view(1, 1)
        return x#chose action from model
    
    else:
        x = eps_threshold,torch.tensor([[random.randrange(env.action_space.n)]])
        return x#choose random action uniformly

#wtih the update_policy function we perform a single step of the optimization
#first sample a batch, concatenate all the tensors into a single one, compute Q-value and max Q-value, 
#and combine them into loss
def update_policy():
    if len(memory)<batch_size:#we want to sample a batch of size 64
        return
    transitions = memory.sample(batch_size)#take random transition batch from experience replay memory
    batch_state, batch_action, batch_next_state, batch_reward = zip(*transitions)#convert batch-array of Transitions
                                                                              #to Transition of batch-arrays   
    #-->zip(*) takes iterables as arguments and return iterator
    
    batch_state = Variable(torch.cat(batch_state))#concatenate given sequence tensors in the given dimension
    batch_state = batch_state.resize(batch_size,1)
    batch_action = Variable(torch.cat(batch_action))
    batch_next_state = Variable(torch.cat(batch_next_state))
    batch_next_state = batch_next_state.reshape(batch_size,1)
    batch_reward = Variable(torch.cat(batch_reward))
    
    #print('model batch state',model(Variable(batch_state[0])))
    current_q_values = model(batch_state).gather(1, batch_action)#current Q-values estimated for all actions,
                                                                 #compute Q, then select the columns of actions taken,
                                                                 #these are the actions which would've been taken
                                                                 #for each batch state according to policy_net
    max_next_q_values = model(batch_next_state).detach().max(1)[0]#predicted Q-values for non-final-next-states
                                                                  #(-> gives max Q)
    expected_q_values = batch_reward + (model.gamma * max_next_q_values)

    #loss is measured from error between current and newly expected Q values (Huber Loss)
    loss = F.smooth_l1_loss(current_q_values, expected_q_values)

    # backpropagation of loss to NN --> optimize model
    optimizer.zero_grad()
    loss.backward()
    optimizer.step()
    return loss, np.sum(expected_q_values.numpy())
    

def train(episodes):
    scores = []
    Losses = []
    Bellman = []
    Epsilon = []
    Times = []
    Deltas = []
    
    
    
    for episode in range(episodes):  
        state=env.reset()#reset environment
        print('\n')
        print('episode',episode)
           
        epsilon_action = predict_action(torch.FloatTensor([state]))
        
        action = epsilon_action[1] #after each time step predict action

        next_state, reward, done,info = env.step(action.item())#step through environment using chosen action
        
        epsilon = epsilon_action[0]
        Epsilon.append(epsilon)
        print(reward,'reward')
              
        state=next_state
        Times.append(state)
        scores.append(reward)            

    
        memory.push((torch.FloatTensor([state]),action,torch.FloatTensor([next_state]),
                         torch.FloatTensor([reward])))#action is already a tensor
        up = update_policy()#update_policy()#update policy
            
        if up != None:
            Losses.append(Variable(up[0]))
            print('loss',Variable(up[0]))
            Bellman.append(up[1])

        #calculate score to determine when the environment has been solved
        mean_score=np.mean(scores[-50:])#mean of score of last 50 episodes
        #every 50th episode print score
        if episode%50 == 0:
            print('Episode {}\tScore: {}\tAverage score(last 50 episodes): {:.2f}'.format(episode,scores[-50:],mean_score))

    
    #print('Losses',Losses)
    Losses = torch.stack(Losses).numpy()
    #print('Losses',Losses)
    plt.plot(np.arange(len(Losses)),Losses)
    plt.xlabel('Training iterations')
    plt.ylabel('Loss')
    plt.show()
    
    Bellman = np.array(Bellman)
    #print('Bellman',Bellman,'\n')
    plt.plot(np.arange(len(Bellman)),Bellman)
    plt.xlabel('Training iterations')
    plt.ylabel('Bellman target')
    plt.show()
    
    #print('scores',scores)
    plt.plot(np.arange(len(scores)),scores)
    plt.xlabel('Training iterations')
    plt.ylabel('Reward')
    plt.show()
    
    #print('epsilon',Epsilon)
    plt.plot(np.arange(len(Epsilon)),Epsilon)
    plt.xlabel('Training iterations')
    plt.ylabel('Epsilon')
    plt.show()
    
    print('Times',Times[-25:])
    print('Deltas',Deltas[-25:])
    
    Times = np.array(Times)
    print('Times',Times)
    #plt.figure(figsize=(31,20))
    plt.figure(figsize=(9,7))
    plt.plot(np.arange(len(Times)),(np.array(Times)))
    plt.xlabel('Training iterations')
    plt.ylabel('t')
    plt.show()
     
    Times_1 = np.array(Times[-300:])
    print('t',Times)
    plt.figure(figsize=(9,7))
    plt.plot(np.arange(len(Times_1)),(np.array(Times_1)))
    plt.xlabel('Last 300 Training iterations')
    plt.ylabel('t')
    plt.ylim(0,1000)
    plt.show()
    
model = DqnNet()#policy         
memory = ReplayMemory(20000)
optimizer = optim.Adam(model.parameters(), lr=learning_rate)

train(10000)