The data scientist should obtain a correlated equilibrium policy by formulating this problem as a multi-agent reinforcement learning problem. This is because:
Multi-agent reinforcement learning (MARL) is a subfield of reinforcement learning that deals with learning and coordination of multiple agents that interact with each other and the environment 1. MARL can be applied to problems that involve distributed decision making, such as traffic signal control, where each traffic light can be modeled as an agent that observes the traffic state and chooses an action (e.g., changing the signal phase) to optimize a reward function (e.g., minimizing the delay or congestion) 2.
A correlated equilibrium is a solution concept in game theory that generalizes the notion of Nash equilibrium. It is a probability distribution over the joint actions of the agents that satisfies the following condition: no agent can improve its expected payoff by deviating from the distribution, given that it knows the distribution and the actions of the other agents 3. A correlated equilibrium can capture the correlation among the agents’ actions, which is useful for modeling the traffic behavior at each light that is subject to a small stochastic error term.
A correlated equilibrium policy is a policy that induces a correlated equilibrium in a MARL setting. It can be obtained by using various methods, such as policy gradient, actor-critic, or Q-learning algorithms, that can learn from the feedback of the environment and the communication among the agents 4. A correlated equilibrium policy can achieve a better performance than a Nash equilibrium policy, which assumes that the agents act independently and ignore the correlation among their actions 5.
Therefore, by obtaining a correlated equilibrium policy by formulating this problem as a MARL problem, the data scientist can most effectively model the traffic behavior and reduce congestion.
Multi-Agent Reinforcement Learning
Multi-Agent Reinforcement Learning for Traffic Signal Control: A Survey
Correlated Equilibrium
Multi-Agent Actor-Critic for Mixed Cooperative-Competitive Environments
Correlated Q-Learning
