Stochastic gradient descent

Policy Gradient Theorem Equation

The policy gradient theorem provides a way to optimize the parameters of a policy in reinforcement learning. It establishes a connection between the expected return and the gradient of the policy's parameters.

The policy gradient theorem states that the gradient of the expected return with respect to the policy parameters can be expressed as an expectation over the gradient of the log-probability of the taken actions. This gradient can be estimated using samples from the environment.

In reinforcement learning, this theorem allows for the optimization of a policy by adjusting its parameters in the direction that maximizes the expected return. This is done through stochastic gradient descent, which iteratively updates the policy parameters based on sampled gradients.

Example

Consider a reinforcement learning agent playing a game. The agent's policy determines the probability of taking certain actions given the current state. Using the policy gradient theorem, the agent can estimate the gradient of the expected return with respect to its policy parameters and update them to improve its performance in the game.

Understanding the policy gradient theorem is crucial for implementing and improving reinforcement learning algorithms that aim to optimize policies in complex environments.

Related concepts

Gradient descent

Gradient descent weight update equation: w := w - α * ∇J(w)

Write the Bellman equation for reinforcement learning

Bellman equation: V(s) = max_a [R(s,a) + γ Σ P(s'|s,a) V(s')]

Adam optimizer weight update with m and v terms

Adam optimizer weight update: w_t = w_{t-1} - α * m_t / (sqrt(v_t) + ε)

Variational autoencoder

ELBO formula in variational inference

Hessian matrix

The Hessian matrix is denoted by H or ∇²

natural gradient descent does: preconditions with inverse Fisher matrix

Natural gradient descent optimizes using the Fisher information matrix's inverse as the metric

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