Combining Policy and Value Estimation

Value-based methods, such as DQN, excel at learning the value of actions but can face challenges, particularly in environments with continuous action spaces. On the other hand, policy gradient methods like REINFORCE directly learn a policy, making them suitable for continuous actions, but their learning process can be hampered by high variance in the gradient estimates. This variance arises because the learning signal is often based on the entire return of an episode, which can fluctuate significantly depending on the actions taken.

Wouldn't it be effective if we could somehow combine the strengths of both approaches? Imagine using the direct policy learning capability of policy gradients but improving the learning signal with the evaluative insights from value-based methods. This is precisely the motivation behind Actor-Critic architectures.

The core idea is to maintain two distinct components, often implemented as separate neural networks (or sometimes sharing lower layers):

1. The Actor: This component learns and implements the policy, $\pi_\theta(a|s)$. Given a state $s$, the actor decides which action $a$ to take. Its goal is to optimize the policy parameters $\theta$ to achieve higher rewards.
2. The Critic: This component learns a value function to evaluate the states or state-action pairs encountered by the actor. It typically estimates either the state-value function $V_\phi(s)$ or the action-value function $Q_\phi(s, a)$, parameterized by $\phi$. Its role is not to select actions, but to critique the actions chosen by the actor by providing a measure of how good those actions or resulting states are.

How Interaction Improves Learning

The main interaction happens during the update step. Instead of the actor updating its policy based on the noisy, high-variance Monte Carlo return used in simple REINFORCE ($G_t$), it uses feedback derived from the critic. The critic, having learned a value function, can provide a more stable, lower-variance estimate of the quality of the actor's actions.

For example, the critic might estimate the state-value function $V_\phi(s)$. When the actor takes action $a$ in state $s$, receives reward $R$, and transitions to state $s'$, the critic can calculate the Temporal Difference (TD) error:

$$\delta_t = R_t + \gamma V_\phi(s_{t+1}) - V_\phi(s_t)$$

This TD error represents how much better or worse the outcome was compared to the critic's prior expectation for being in state $s_t$. A positive $\delta_t$ suggests the action taken led to a better-than-expected result, while a negative $\delta_t$ suggests the opposite.

The actor then uses this TD error $\delta_t$ (or a related measure like the Advantage, which we'll discuss soon) as the signal to update its policy parameters $\theta$. The update rule looks like:

$$\theta \leftarrow \theta + \alpha \nabla_\theta \log \pi_\theta(a_t|s_t) \delta_t$$

Simultaneously, the critic updates its own parameters $\phi$ to improve its value estimates, typically using the same TD error to minimize prediction inaccuracies, for instance, by minimizing $\delta_t^2$.

Diagram illustrating the interaction between the Actor, Critic, and Environment. The Actor selects actions based on the state, the Environment provides feedback, and the Critic evaluates the outcome, providing a learning signal back to the Actor. Both components update their internal parameters.

The Advantages of Collaboration

This collaborative structure offers significant benefits:

• Reduced Variance: The critic's estimate (like the TD error) is generally much less noisy than the full Monte Carlo return used in REINFORCE. This leads to more stable gradients and potentially faster convergence for the actor's policy.
• Faster Learning: Updates can happen at each step (like in TD learning) rather than waiting until the end of an episode (like in basic REINFORCE).
• Flexibility: Actor-Critic methods naturally handle continuous action spaces (via the actor's policy) while benefiting from the bootstrapping estimates provided by the critic.

By combining policy search with learned value functions, Actor-Critic methods provide a powerful framework that addresses limitations inherent in using either approach in isolation. The following sections will examine specific algorithms like Advantage Actor-Critic (A2C) and Asynchronous Advantage Actor-Critic (A3C), which refine this fundamental structure for improved performance and efficiency.