Overview of SARSA
SARSA (State-Action-Reward-State-Action) is a kind of control algorithm in reinforcement learning, which is mainly classified as a model-free method like Q learning. After observing the reward (r), the agent learns a series of transitions until it chooses the next action \(a’\) in a new state \(s’\).
The following is an overview of the SARSA algorithm.
1. initialization:
Initialize the Q function and other necessary variables.
2. start of episode:
The agent starts from the initial state\(s\) of the environment.
3. action selection:
The agent selects its next action \(a\) using the Q function, e.g., the epsilon-Greedy method.
4. Execution of the action and observation of the reward:
The selected action \(a\) is executed, and the reward \(r\) and the new state \(s’\) are observed from the environment.
5 Selection of next action:
The agent chooses its next action \(a’\) in the new state \(s’\).
6. Updating the Q value:
Based on the update formula, the value of the Q function is updated as follows.
\[ Q(s, a) \leftarrow Q(s, a) + \alpha \cdot [r + \gamma \cdot Q(s’, a’) – Q(s, a)] \]
where \(\alpha\) is the learning rate and \(\gamma\) is the discount rate.
7. termination decision:
Determine if the episode meets the termination condition. If not, it returns to the beginning of the episode and continues action selection in a new state\(s’\).
8. fulfillment of learning end condition:
Continue iterating through the episode until the learning termination condition is met.
SARSA is unique in that it updates the action value function (Q function) based on the actual action selected by the agent \(a\) and the next action to be selected \(a’\). This differs from Q learning, where SARSA is suited for online learning and uses actual behavioral data to update Q values sequentially.
Examples of SARSA Applications
SARSA has been used in a variety of reinforcement learning applications. They are described below.
1. Gameplay:
SARSA is well suited for learning optimal behaviors as agents move between states in game play, for example, in board games, video games, and robot control.
2. robot control:
SARSA has also been applied to robot control. A robot may learn as it moves through its environment and acquire optimal policies for goal-directed behavior.
3. trading agents:
Reinforcement learning is also used in finance, where SARSA has been applied to train trading agents for stock trading and other trading activities. Agents use time series data to learn optimal trading strategies.
4. automated vehicles:
SARSA has also been applied to the control of self-driving cars. Self-driving cars need to adapt to various situations and traffic patterns, and can learn using SARSA to obtain effective driving policies.
5. real-time decision problem:
SARSA is also suitable for real-time decision problems. For example, it is used for problems that require immediate adaptation in situations where the control object is fluctuating.
SARSA is useful in situations where agents need to learn optimal action policies while interacting with their environment. However, specific applications require comparisons with other methods and adjustments to the characteristics of the problem.
Examples of SARSA implementations
An example implementation of SARSA is shown using Python and NumPy. The following is an example of SARSA implementation in a simple grid world environment.
import numpy as np
# Grid World Definition
GRID_SIZE = 4
NUM_ACTIONS = 4 # Up, down, left, right
# Initialization of Q function
Q = np.zeros((GRID_SIZE, GRID_SIZE, NUM_ACTIONS))
# Parameter Setting
alpha = 0.1 # Learning rate
gamma = 0.9 # discount rate
epsilon = 0.1 # epsilon in the epsilon-Greedy method
# Action selection based on the epsilon-Greedy method
def epsilon_greedy_policy(state):
if np.random.rand() < epsilon:
return np.random.randint(NUM_ACTIONS)
else:
return np.argmax(Q[state[0], state[1]])
# SARSA Update
def update_sarsa(state, action, reward, next_state, next_action):
current_q = Q[state[0], state[1], action]
next_q = Q[next_state[0], next_state[1], next_action]
td_error = reward + gamma * next_q - current_q
Q[state[0], state[1], action] += alpha * td_error
# Execution of SARSA
def run_sarsa(num_episodes):
for episode in range(num_episodes):
state = [0, 0] # initial state
action = epsilon_greedy_policy(state)
while True:
# Update environment (e.g., calculate destination)
next_state = [new_state[0], new_state[1]] # hypothetical next state
reward = 0 # provisional remuneration
# Selection of next action based on the epsilon-Greedy method
next_action = epsilon_greedy_policy(next_state)
# SARSA Update
update_sarsa(state, action, reward, next_state, next_action)
state = next_state
action = next_action
# at end condition
if state == [GRID_SIZE - 1, GRID_SIZE - 1]:
break
# Execution of SARSA
run_sarsa(num_episodes=1000)
# Display of learned Q values
print("Learning result (Q function):")
print(Q)
The code considers a 4×4 grid world environment and implements a simple SARSA algorithm in which the agent learns as it moves up, down, left, and right.
Challenges for SARSA
The State-Action-Reward-State-Action (SARSA) algorithm also has several challenges. They are described below.
1. slow convergence:
SARSA may require many episodes before convergence, especially for problems with large and complex state spaces.
2. setting appropriate hyperparameters:
SARSA has hyperparameters such as learning rate ((alpha)), discount rate ((gamma)), and ε in the ε-Greedy method, and setting these parameters appropriately is a challenge. These parameters need to be adjusted for each problem.
3 Problem of the ε-Greedy Method:
The ε-Greedy method adjusts the trade-off between search and utilization, but the choice of appropriate ε is important: too large ε may lead to over-exploration, while too small ε may lead to inadequate search.
4. dealing with very large state spaces:
SARSA can be difficult to apply when the state space is very large, and the dimensionality of the Q-function explodes, making efficient learning difficult.
5. comparison with off-policy methods:
SARSA is an on-policy method and learns based on the actual actions chosen by the agent. In contrast, off-policy methods (e.g., Q-learning) learn based on the most valuable action rather than the optimal action. Depending on the nature of the problem, which is more appropriate.
To address these issues, modifications to the algorithm to improve convergence speed, search for appropriate hyperparameters, and introduction of function approximation methods will be considered. In addition, depending on the nature of the problem, there may be methods more suitable than SARSA.
Addressing to the SARSA’s Challenges
There are several approaches to addressing SARSA challenges, which are discussed below.
1. addressing slow convergence:
Slow convergence depends on appropriate settings of hyperparameters such as learning rate, discount rate, and parameters of the ε-Greedy method. Adjusting these parameters can speed up learning convergence, and function approximation methods (e.g., deep reinforcement learning with gradient methods) can also be introduced.
2. addressing appropriate hyperparameter settings:
The setting of hyperparameters is problem-dependent, and effective search using methods such as grid search and Bayesian optimization can be helpful. There are also methods to attenuate the learning rate or ε from episode to episode.
3. addressing the problem of the ε-Greedy method:
By dynamically adjusting the ε of the ε-Greedy method or a method called ε-decay, it is possible to emphasize exploration in the early stages of learning and gradually increase the emphasis on utilization.
4. dealing with very large state spaces:
To deal with large state spaces, it is common to introduce function approximation methods (e.g., linear function approximation, neural networks). This reduces the dimensionality of the state space and allows for efficient learning.
5. addressing comparisons with off-policy methods:
If SARSA does not perform well compared to off-policy methods, consider off-policy methods such as Q-learning as described in “Overview of Q-Learning and Examples of Algorithms and Implementations. Depending on the nature of the problem, off-policy methods may be more appropriate.
References and Reference Books
Details of reinforcement learning are described in “Theories and Algorithms of Various Reinforcement Learning Techniques and Their Python Implementations. Please also refer to this page.
A reference book is “Reinforcement Learning: An Introduction, Second Edition.
“Deep Reinforcement Learning with Python: With PyTorch, TensorFlow and OpenAI Gym“
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