What is the difference between Monte Carlo methods and TD learning?

Monte Carlo (MC) methods and Temporal Difference (TD) learning are two approaches in reinforcement learning for estimating value functions, but they differ in how and when they update these estimates. MC methods learn by averaging the total returns from complete episodes of experience. For example, if an agent navigates a maze, MC waits until the episode ends (e.g., reaching the goal or failing), calculates the cumulative reward from start to finish, and then updates the value of each state visited. In contrast, TD learning updates estimates incrementally, after each step, using a combination of observed rewards and current estimates of future rewards. For instance, TD might adjust the value of a state immediately after the agent moves to the next state, without waiting for the episode to conclude.

The key difference lies in their approach to bootstrapping and reliance on complete trajectories. MC does not bootstrap—it relies solely on actual returns from the entire episode. This makes MC unbiased but high-variance, as outcomes can vary widely between episodes. For example, in a game with stochastic rules, MC’s value estimates might fluctuate significantly due to random outcomes. TD, however, bootstraps by using its own predictions of future rewards to update values. A common TD method like TD(0) updates a state’s value using the immediate reward plus the discounted value of the next state. This introduces some bias (since predictions may be inaccurate) but reduces variance, as updates are based on shorter-term, more predictable steps.

The choice between MC and TD often depends on the problem’s structure and trade-offs between bias and variance. MC is suitable for episodic tasks with clear termination points, like board games, where full trajectories are available. However, it can be inefficient for long episodes or continuous tasks. TD is more flexible, working in both episodic and non-terminating environments (e.g., stock trading), and learns faster in many cases due to incremental updates. For example, TD can adapt to changing conditions in real-time control systems, while MC would require waiting for episodes to finish. Developers might prefer TD for online learning or when data is scarce, while MC could be better for offline batch processing where precise, unbiased estimates are critical.