Reinforcement Learning is an area of Artificial Intelligence and Machine Learning that involves simulating many scenarios in order to optimize the outcomes. One of the most used approaches in Reinforcement Learning is the Q-learning method. In Q-learning, a simulation environment is created and the algorithm involves a set of ‘S’ states for each simulating scenario, a set of ‘A’ actions, and an agent that takes these actions to permeate through the states.
Each time the agent takes an action ‘a’ within the set ‘A’ it transitions from one state to another into the environment. Performing an action in a specific state in the environment returns a reward for the agent, which can be good or bad. The model’s objective is always to find a set of actions that maximize the reward and evolve in the best possible way for the environment. There are several different techniques within a group of Reinforcement Learning algorithms, from mathematical models with defined policies to more complex models such as evolutionary models and deep learning models such as Deep Reinforcement Learning.
In the last article, that you find the link below, I wrote on how to Predict Real Soccer Game Results using Machine Learning, and now I will be writing about how to use a Reinforcement Learning model to place and optimize bets on real football games.
Q-learning is a Reinforcement Learning off policy model that aims to find the best action to take based on the current state, in this case without a defined action policy. This model is considered an off-policy model because the Q-learning function learns through actions that are outside the current policy, in other words, its learning follows in an exploratory way by taking random actions to create an action policy that maximizes the total reward of the episode.
Why Q? And what would this policy be?
The letter Q stands for Quality and the learning model is based on a Q table (Quality table) which is the policy of actions that the model can use in the environment for each state. Thus, we have a table [state, action] that represents a policy where each action has a quality value (Q value) for each state.
Actions are part of the environment, as in the example above we have actions of walking to the North, South, East, West, etc. The concept of state is a set of variables that represent the evolution of the model through the simulated environment.
With each action taken, the Q value is updated by the concept of Value Iteration following the decision-making process known as the Markov Decision Process (MDP) and the Bellman equation. The equation consists of the old Q value for the action taken along with the action’s reward and the maximum Q value for the new state, both discounted from the “learning rate” that weighs the quality between the current value and the new value. Therefore, the model depends only on the [state, action] and the reward observed in the action taken into the environment.
After going through the concept I will proceed with the code part and the results of the model. The complete code of the solution can be found on my GitHub through the link below:
The libraries used for development were, according to their imports:
import numpy as np
import matplotlib.pyplot as plt
from matplotlib import style
import pandas as pd
In the beginning, we have the definition of some values for the Bellman equation, the episodes, and the learning rate, in addition to initial values for the simulation environment of the bets with the investment value per game and the initial portfolio value.
HM_EPISODES = 45000
epsilon = 0.9
EPS_DECAY = 0.9998
LEARNING_RATE = 0.1
DISCOUNT = 0.95
- Learning rate defines the weight of the reward in the exploration with the update of the quality (Q) value.
- At first I used 45000 episodes which is the number of iterations that the model will follow.
- Epsilon and eps decay indicates the initial exploitation factor and its decay with iterations
- Discount represents the weight of the future value of Q after the action
After definition, the model loads a previous Q table if necessary or starts a new Q table to start the iterations.
Iterations are made with each episode that goes through each of the games previously selected.
Creating the Simulation Environment
The simulation environment has 3 different functions:
- action() that performs the action defined by the model by selecting a strategy and a bet
- strategy() that receives the action from action() function and effectively performs the previously defined strategy. We have 3 strategies in this model: “Min” who chooses the team with the lowest odd, “Max” who chooses the highest odd, and “ML” who chooses the team according to a machine learning model developed at another time.
- bet() that receives action() and strategy() values and applies the strategy in the dataset with the real values of the game, thus returning the result value of the bet, whether it is a hit or a miss.
Right after, we have within the loops of episodes and games the definition of the exploitation policy:
if np.random.random() > epsilon:
action_n = np.argmax(q_table[obs])
action_n = np.random.randint(0,high=2)
We have a section that performs the profit and reward calculation of each bet, updates the accumulated profit, and sets up a new observation state, a state that is represented by the value of the portfolio and the accumulated profit.
j = result
if j == -1:
erros += 1
l_tot = 0
elif j == 0:
l_tot = 0
elif j == 1:
l_tot = result
lucro = (l_tot*invest) - invest
reward = lucro
lucro0 += lucro
new_obs = (carteira,lucro0) # get new state
Finally, the application of the Bellman equation to update the Q-value for that state.
max_future_q = np.max(q_table[new_obs])
q_table[new_obs] = [0 for i in range(val)]
max_future_q = np.max(q_table[new_obs])
current_q = q_table[obs][action_n]
new_q = (1 - LEARNING_RATE) * current_q + LEARNING_RATE * (reward + DISCOUNT * max_future_q)
q_table[obs][action_n] = new_q #update actual q
The model was executed and through the Matplotlib library, some graphics were generated to follow the model’s performance and a log with the results of the matches.
The graph below shows at the top the average profit per 300 episodes and at the bottom, it shows the result of each bet in blue and the initial portfolio value in red.