Okay, we are about to enter the final chapter of this tutorial, and also the most technically advanced one. In this chapter, we will learn a powerful statistical tool that "unlocks" off-policy learning capabilities in reinforcement learning, greatly enhancing the sample efficiency of our algorithms.
Introduction to this Chapter:
Hello, brave explorer! Prior to this, most of the algorithms we've learned, such as Sarsa, REINFORCE, and A2C, belong to On-Policy methods. This means they are like "forgetful" students: after taking an exam and updating their notes, they discard all previous drafts 🗑️, and for the next learning session, they must use entirely new exam questions (experiences). While this approach is straightforward, it is extremely sample inefficient, especially in real-world scenarios where acquiring experience is costly (e.g., robot training).
Can we make the agent "smarter," capable of repeatedly utilizing past experiences ("old mistake notebooks") to learn and optimize the current new policy? This is the goal of Off-Policy learning. And the key "magic" to achieving this goal is Importance Sampling (IS).
💡Let's clarify the setup for off-policy learning:
β) 🏃: This is a policy used for exploration and data collection. It's usually more "adventurous," like an ε-greedy policy, to ensure broad coverage of states and actions.π) 🎯: This is the policy we genuinely want to learn and optimize. It's typically the "greedy" or ultimately optimal policy we aim for.Core Problem: How do we use data (s, a, r, ...) generated by policy β to evaluate and improve a completely different policy π? Directly using it won't work, because the data itself carries the "behavioral bias" of β.
Imagine you want to estimate the average weight of all fish in a large lake (π), but you can only fish in a small harbor (β). There are many small fish in this harbor.
If you directly calculate the average weight of the fish caught in the harbor, the result will certainly be biased low and will not represent the entire large lake.
Importance Sampling Solution ✨:
"Assign a correction weight to every fish you catch! If a fish is common in the harbor but rare in the big lake, decrease its weight; conversely, if it's rare in the harbor (like a big fish) but common in the big lake, increase its weight."
This correction weight is called the Importance Weight or Importance Ratio.