Lecture 4: Model-Free Prediction | Highlights and Annotations by Gistr.

Reinforcement learning's model-free prediction uses Monte Carlo (MC) and Temporal Difference (TD) learning to estimate value functions. MC uses complete episode returns (unbiased, high variance), while TD uses bootstrapping (biased, low variance). TD(λ) unifies both, offering a flexible trade-off via a weighted average of n-step returns. This segment provides a concise review of dynamic programming in the context of solving known MDPs, contrasting it with the model-free approach. It clearly outlines the shift from solving known MDPs to tackling scenarios where the environment's dynamics are unknown, setting the stage for the introduction of model-free methods. This segment introduces Monte Carlo learning as a model-free method for policy evaluation. It explains the core idea of learning directly from complete episodes of experience, emphasizing its simplicity and wide applicability despite its limitations for non-episodic tasks. The explanation of using sample returns to estimate the value function is particularly valuable. This segment uses the game of Blackjack as a practical example to illustrate the application of Monte Carlo methods. It details how the game can be represented as an MDP, focusing on the state representation (card sum, dealer's showing card) and the actions (stick or twist), making the abstract concepts more concrete and relatable. This segment explains the concept of incremental mean computations, demonstrating how to update the mean iteratively without storing the entire sum of elements. The speaker derives the formula for incremental mean updates and relates it to the general form of many reinforcement learning algorithms. It lays the groundwork for understanding how online algorithms update estimates step-by-step, improving efficiency and adaptability. This segment details the application of Monte Carlo policy evaluation to a simplified Blackjack game, highlighting a naive policy of sticking only at 20 or 21 and always twisting otherwise. The discussion covers the use of state variables (player sum, usable ace, dealer's showing card), the simulation of 10,000 and 500,000 episodes, and the resulting value function which reveals insights into the game's dynamics and the effectiveness of the naive policy. The impact of the number of episodes on the accuracy of the value function estimate is also discussed. This segment uses a relatable driving scenario to illustrate the key difference between TD and Monte Carlo learning. It highlights TD learning's ability to update value functions immediately based on perceived risks (like a near-miss accident), unlike Monte Carlo, which waits for the final outcome. This emphasizes TD's advantage in learning from incomplete sequences or continuous environments. This segment introduces Temporal Difference (TD) learning, contrasting it with Monte Carlo methods. The key difference highlighted is TD's use of incomplete episodes and bootstrapping—using an estimate of future rewards instead of waiting for the complete episode to finish. The concept of bootstrapping is explained clearly, emphasizing its role in updating value function estimates incrementally without waiting for the end of an episode. This segment delves into the bias-variance tradeoff inherent in TD and Monte Carlo methods. It explains how Monte Carlo provides unbiased estimates but suffers from high variance due to the reliance on complete episode data, while TD introduces bias by using estimated values but significantly reduces variance by focusing on single-step updates. This analysis provides a deeper understanding of the tradeoffs involved in choosing between the two approaches. This segment uses a simple random walk problem to concretely demonstrate the efficiency difference between TD and Monte Carlo learning. By visualizing learning curves, it shows how TD learning converges to the true value function faster than Monte Carlo, highlighting the practical advantage of TD's lower variance in many situations. The visual representation reinforces the theoretical concepts discussed earlier. This segment presents a detailed example of a commute to work, comparing how Monte Carlo and TD learning would update value estimations (time taken) at each step of the journey. The comparison clearly shows how TD learning updates incrementally based on immediate observations, while Monte Carlo waits until the end of the journey to perform a single update. This strengthens the understanding of the core difference between the two approaches. This segment compares Monte Carlo and TD methods, focusing on their efficiency in Markov and non-Markov environments. It explains how TD exploits the Markov property by implicitly building an MDP model and solving for it, making it more efficient in Markov environments. Conversely, Monte Carlo performs better in non-Markov or partially observed environments because it doesn't rely on the Markov assumption. The discussion clarifies the trade-offs between these methods based on the environment's characteristics.This segment provides a visual representation of the algorithm space for policy evaluation, categorizing methods based on two dimensions: bootstrapping and full-width backups. It contrasts Monte Carlo, which samples and doesn't bootstrap, with TD and dynamic programming, which both bootstrap. The explanation clarifies the differences in how these methods utilize sampled versus exhaustive look-ahead in their updates and how this affects their efficiency and accuracy.This segment introduces TD-Lambda as a unifying algorithm that bridges the gap between shallow backups (like TD) and deep backups (like Monte Carlo). It explains how the lambda parameter controls the depth of the backup, allowing for a spectrum of methods between the two extremes. The discussion provides a comprehensive overview of the algorithm space and how TD-Lambda offers flexibility in choosing the appropriate backup depth. This segment analyzes the convergence behavior of Monte Carlo and Temporal Difference (TD) methods when training is stopped after a finite number of episodes. It uses a simple example to illustrate how Monte Carlo minimizes mean squared error to fit observed returns, while TD0 converges to the solution of the MDP that best explains the observed data. The discussion highlights the different approaches to value function estimation and their implications for learning in finite data settings. This segment explains the concept of n-step TD returns, showing how they bridge the gap between TD(0) and Monte Carlo methods. It highlights that by varying 'n', we can control the balance between short-term and long-term reward estimations, impacting the bias-variance trade-off. The discussion leads to the question of finding the optimal 'n' value.This segment presents an empirical study comparing the performance of n-step TD learning across different values of 'n'. The results reveal a "sweet spot" for 'n', indicating that intermediate values often outperform both TD(0) and Monte Carlo methods. However, the optimal 'n' value is shown to be sensitive to environmental parameters, motivating the need for a more robust approach.This segment introduces the core idea behind TD(λ): averaging n-step returns to create a more robust and less sensitive estimator. This approach combines the benefits of different n-step methods, avoiding the need to select a single optimal 'n'. The discussion sets the stage for a more efficient algorithm that considers all 'n' simultaneously. This segment introduces eligibility traces as a mechanism for combining frequency and recency heuristics in credit assignment. The explanation uses an intuitive example of a rat learning from rewards and punishments, illustrating how eligibility traces allow for more efficient learning by weighting the importance of past states based on their frequency and recency. This leads to the backward view of TD(λ). This segment addresses a fundamental question about TD learning: why updates are forward-looking (from earlier states to later states) and not backward-looking. It explains that forward updates are more accurate because they incorporate one step of real-world dynamics and rewards, grounding the estimates in reality. The segment offers an intuitive explanation and hints at the mathematical justification for this crucial aspect of TD learning.