How do you incorporate exploration and exploitation trade-offs in TRPO?

1 Policy gradient methods

TRPO belongs to the class of policy gradient methods, which directly optimize the policy by estimating the gradient of the expected return with respect to the policy parameters. Policy gradient methods can be seen as a form of exploration, as they allow the agent to update its policy based on the feedback from the environment. However, policy gradient methods also face some challenges, such as high variance, poor sample efficiency, and policy degradation.

2 Trust regions

To overcome these challenges, TRPO introduces the concept of trust regions, which are regions in the policy space where the policy improvement is guaranteed. Trust regions are defined by a constraint on the KL divergence between the old and new policies, which measures how much the policy distribution changes after an update. By limiting the KL divergence, TRPO ensures that the policy update is not too large or too small, and that it does not violate the monotonic improvement property.

3 Natural gradient

To optimize the policy within the trust region, TRPO uses the natural gradient, which is a gradient that takes into account the curvature of the policy space. The natural gradient is computed by multiplying the ordinary gradient by the inverse of the Fisher information matrix, which is a matrix that captures the sensitivity of the policy to the parameter changes. The natural gradient has some desirable properties, such as being invariant to the parameterization of the policy and being aligned with the steepest direction of improvement.

4 Conjugate gradient and line search

However, computing the natural gradient requires inverting the Fisher information matrix, which can be costly and impractical for high-dimensional policies. To avoid this, TRPO uses the conjugate gradient algorithm, which is an iterative method that can approximate the natural gradient by solving a system of linear equations. The conjugate gradient algorithm only requires matrix-vector products, which can be efficiently computed using the policy gradient samples. To ensure that the policy update satisfies the trust region constraint, TRPO also performs a line search along the natural gradient direction, which adjusts the step size according to the KL divergence and the expected return.

5 Exploration strategies

Besides using the policy gradient as a form of exploration, TRPO can also incorporate other exploration strategies, such as adding noise to the policy or using entropy regularization. Adding noise to the policy can increase the diversity of the actions and prevent premature convergence to suboptimal policies. Entropy regularization can encourage the policy to be more stochastic and explore more options, by adding a term to the objective function that penalizes low-entropy policies. Both noise and entropy regularization can be combined with TRPO by modifying the policy gradient estimator or the trust region constraint.

6 Here’s what else to consider

This is a space to share examples, stories, or insights that don’t fit into any of the previous sections. What else would you like to add?