Comparison: REINFORCE vs A2C/A3C

A direct comparison of the REINFORCE algorithm and the fundamental architecture of Actor-Critic methods like A2C and A3C is useful. Both aim to optimize a parameterized policy $\pi_\theta(a|s)$, but they achieve this through different mechanisms, leading to distinct performance characteristics.

REINFORCE, as a pure Monte Carlo policy gradient method, updates the policy parameters $\theta$ based on the complete return $G_t$ experienced from a state-action pair $(s_t, a_t)$ onwards until the end of an episode. The update rule is proportional to $\nabla_\theta \log \pi_\theta(a_t|s_t) G_t$.

Actor-Critic methods, represented here by A2C and A3C, maintain two distinct components (or two heads of a single network):

• Actor: Updates the policy parameters $\theta$ based on feedback from the Critic.
• Critic: Learns a value function (typically $V_\phi(s)$ or sometimes $Q_\phi(s, a)$) using methods related to Temporal Difference (TD) learning.

This fundamental difference in how the learning signal for the policy update is generated leads to several important distinctions:

Variance and Stability

• REINFORCE: Relies on Monte Carlo returns ($G_t$). Since $G_t$ is the sum of potentially many stochastic rewards and transitions over the rest of the episode, its value can vary significantly from one trajectory to another, even starting from the same state-action pair. This high variance in the learning signal ($\nabla_\theta \log \pi_\theta(a_t|s_t) G_t$) can make the training process unstable and slow to converge. Introducing a baseline can mitigate this, but the core reliance on full returns remains.
• A2C/A3C: Uses the Critic's value estimate to compute a lower-variance signal, typically the Advantage Function $A(s_t, a_t)$. A common form is the TD advantage: $A(s_t, a_t) \approx r_{t+1} + \gamma V_\phi(s_{t+1}) - V_\phi(s_t)$. This signal depends only on the immediate reward and the estimated value of the next state, rather than the entire trajectory's return. Using this TD-based estimate dramatically reduces the variance of the policy gradient updates compared to $G_t$. The policy update becomes proportional to $\nabla_\theta \log \pi_\theta(a_t|s_t) A(s_t, a_t)$. This lower variance generally leads to more stable and faster learning.

Bias

• REINFORCE: The Monte Carlo return $G_t$ is an unbiased estimate of the true expected return $Q^{\pi_\theta}(s_t, a_t)$. While individual samples are noisy (high variance), the expectation is correct.
• A2C/A3C: The Critic's value function $V_\phi(s)$ is an estimate. If the Critic's estimate is inaccurate (which it will be, especially early in training), the resulting advantage $A(s_t, a_t)$ is a biased estimate of the true advantage. This introduces bias into the policy update. However, this bias is often acceptable in exchange for the significant reduction in variance. As the Critic improves, the bias tends to decrease. This reflects the classic bias-variance trade-off in machine learning.

Sample Efficiency

• REINFORCE: Updates occur only at the end of an episode, once the full return $G_t$ is known for all steps $t$ in that episode. This can be inefficient, as learning only happens after collecting potentially long trajectories.
• A2C/A3C: Can update the Actor and Critic after each step (or small batch of steps) using the TD error for the Critic and the advantage estimate for the Actor. This allows for learning from incomplete episodes and generally leads to better sample efficiency compared to Monte Carlo REINFORCE. Information propagates faster through the value estimates.

Implementation Complexity

• REINFORCE: Requires implementing a single policy network and calculating Monte Carlo returns. Adding a baseline (like a state-value function) increases complexity, moving it closer to an Actor-Critic structure but often still using Monte Carlo updates for the baseline itself.
• A2C/A3C: Requires managing both an Actor and a Critic network (which might share some layers). The update process involves coordinating updates for both components using potentially different loss functions (policy gradient loss for the Actor, typically MSE loss for the Critic). A3C adds complexity through asynchronous execution and parallel workers.

Summary Comparison

Feature	REINFORCE	A2C / A3C
Algorithm Type	Policy Gradient (Monte Carlo)	Actor-Critic (Policy Gradient + Value Estimation)
Policy Update Signal	Full Return $G_t$ (often with baseline)	Advantage Estimate $A(s, a)$ (e.g., TD Advantage)
Variance	High (due to $G_t$)	Lower (due to TD-based value estimates)
Bias	Unbiased (estimate of $Q^{\pi_\theta}$)	Biased (due to approximate $V_\phi$)
Sample Efficiency	Lower (updates per episode)	Higher (updates per step or batch)
Architecture	Policy Network (optional Baseline Network)	Actor Network + Critic Network (can share layers)
Stability	Can be unstable	Generally more stable

Visualizing Learning Stability

The difference in variance often manifests in the smoothness of the learning curves. While highly dependent on implementation details and hyperparameters, we might expect A2C/A3C to show steadier improvement compared to the potentially more erratic progress of REINFORCE.

Comparison of reward accumulation during training. A2C often exhibits smoother and potentially faster convergence due to lower gradient variance compared to REINFORCE.

Choosing Between REINFORCE and A2C/A3C

• Choose REINFORCE (especially with a baseline) if:
  • Simplicity is a high priority.
  • Episodes are relatively short and non-terminal states are not critical.
  • You need an unbiased gradient estimate (though the high variance might negate this benefit in practice).
• Choose A2C/A3C if:
  • You need more stable and faster convergence.
  • Sample efficiency is important.
  • You are working with environments where learning from incomplete episodes is beneficial (e.g., long or continuous tasks).
  • You have the computational resources to handle the slightly more complex architecture and update rules (especially for A3C's parallelism).

In practice, Actor-Critic methods like A2C and A3C (and their successors) have largely superseded basic REINFORCE in many applications due to their improved stability and efficiency derived from the bias-variance trade-off offered by the Critic. They represent a significant step in combining the strengths of both value-based and policy-based approaches.