Trust Region Policy Optimization (TRPO) is a method used in reinforcement learning to update a policy gradient without changing it too much. TRPO uses a KL divergence constraint on the size of the policy update to ensure that the policy is updated within a specific range.
Off-Policy Reinforcement Learning
In off-policy reinforcement learning, the policy for collecting trajectories on rollout workers may be different from the policy that is optimized for. The objective function in an off-policy model measures the total advantage over the state visitation distribution and actions, while the mismatch between the training data distribution and the true policy state distribution is compensated with an importance sampling estimator. The objective function becomes:
$$ J\left(\theta\right) = \mathbb{E}\_{s\sim{p}^{\pi\_{\theta\_{old}}}, a\sim{\pi\_{\theta\_{old}}}} \left(\frac{\pi\_{\theta}\left(a\mid{s}\right)}{\pi\_{\theta\_{old}}\left(a\mid{s}\right)}\hat{A}\_{\theta\_{old}}\left(s, a\right)\right)$$
When rollout workers and optimizers are running in parallel asynchronously, the policy for collecting data may become stale, and TRPO considers this subtle difference.
Maximizing the Objective Function Subject to a Trust Region Constraint
TRPO aims to maximize the objective function $J\left(\theta\right)$ while also enforcing a trust region constraint. The trust region constraint ensures that the distance between the old and new policies, measured by KL-divergence, is small enough. The constraint is within a parameter $\delta$:
$$ \mathbb{E}\_{s\sim{p}^{\pi\_{\theta\_{old}}}} \left[D\_{KL}\left(\pi\_{\theta\_{old}}\left(.\mid{s}\right)\mid\mid\pi\_{\theta}\left(.\mid{s}\right)\right)\right] \leq \delta$$
By restricting the policy update to a small range, TRPO is able to prevent the policy from changing too much at each iteration. This leads to more stable updates and better overall performance.
Benefits of TRPO
TRPO offers several benefits over other reinforcement learning algorithms. For one, it is able to achieve better performance with fewer iterations. Additionally, TRPO is less sensitive to the choice of hyperparameters than other methods, which can be a major advantage for those without extensive experience in deep learning. Finally, TRPO is able to handle continuous and high-dimensional action spaces effectively, which is important in real-world applications.
Applications of TRPO
TRPO is applicable in a wide range of industries and scenarios. It has been used in robotics to improve control policies in complex systems, in finance to optimize trading strategies and minimize risk, and in healthcare to enhance patient outcomes and optimize resource allocation.
Trust Region Policy Optimization is a powerful method in reinforcement learning that is able to achieve better performance with fewer iterations. TRPO is less sensitive to the choice of hyperparameters than other methods, and is able to handle continuous and high-dimensional action spaces effectively. As such, it has many practical applications in industries ranging from robotics to finance to healthcare.
