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Week 7

Chapter 7: Policy Gradient Methods

Optimize the policy directly instead of deriving it from values: why value-based methods fail on continuous actions, the policy gradient theorem, REINFORCE, baselines and variance reduction, and Gaussian policies for continuous control.

Chapter Overview

Every method so far learned a value function and derived a policy from it by maximization. That indirection has three costs. It cannot handle continuous actions, because the arg-max becomes an optimization problem at every step. It cannot represent a genuinely stochastic optimum, which is required whenever the environment is partially observable or adversarial. And small changes in value estimates can flip the arg-max, making the policy change discontinuously.

Policy gradient methods remove the indirection: parameterize the policy itself and ascend the gradient of expected return. The obstacle is that the objective depends on the distribution of trajectories, which depends on the policy in a way that seems to require differentiating through the environment. The policy gradient theorem shows that it does not — the gradient can be written as an expectation over trajectories the agent can simply sample. That result is what makes the whole family possible, and it leads directly to the actor-critic and PPO algorithms of Chapter 8.

Chapter Roadmap

Click any topic to jump in

1
Why Policy Gradients

Continuous actions, genuinely stochastic optima, and smooth policy changes are all out of reach for arg-max methods.

From identity to algorithm
2
Policy Gradient Theorem

The gradient of expected return is an expectation you can sample — no derivative of the environment required.

The naive estimator is too noisy to use

Baselines and causality reduce variance by orders of magnitude at no cost in bias.

3
REINFORCE

The theorem turned into an algorithm: weight the log-probability gradient of each action by the return that followed.

4
Baselines & Variance

Subtracting a state-dependent baseline cuts variance dramatically without introducing bias.

The payoff is continuous control
5
Continuous Actions

Output the parameters of a distribution rather than a choice — the setting where policy gradients are not merely better but necessary.

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