Asymptotic Bias of Stochastic Gradient Search in Reinforcement Learning

In this article, we propose a new method called Score-aware gradient estimator (SAGE) to help artificial intelligence agents learn the best actions to take in complex, changing environments. The key insight behind SAGE is that instead of trying to directly estimate the gradient of the reward function, which can be difficult and lead to slow learning, we focus on estimating a simpler quantity called the score function.
Think of the score function as a sort of "proxy" for the gradient. By estimating the score function accurately, we can then use it to approximate the gradient, which makes the learning process faster and more stable. SAGE is particularly useful in situations where the environment is dynamic and the agent needs to adapt quickly, such as in robotics or autonomous driving applications.
The basic idea of SAGE is to maintain a set of "histories" – short sequences of states, actions, and rewards – and use these histories to estimate the score function. We update our estimates of the score function using a simple recursion equation that involves the gradient of the reward function, which allows us to incorporate information from the current state and action into our estimates.
To make things more concrete, imagine you’re playing a game of chess. In this case, the states are the positions on the board, the actions are the moves you can make, and the rewards are the points you score for winning the game. If you want to learn the best moves to play, you need to estimate the gradients of the reward function as quickly and accurately as possible. SAGE provides a way to do this by focusing on estimating the simpler quantity of the score function, which can then be used to approximate the gradient.
One advantage of SAGE is that it can handle problems with high-variance rewards, which can make learning much harder. This is because the score function has lower variance than the reward function, so we can use it to estimate the gradient more accurately. Additionally, SAGE can be used in both model-based and model-free settings, making it a versatile tool for solving complex problems.
Overall, SAGE provides a powerful new method for learning optimal policies in dynamic environments, and has the potential to make a significant impact in fields such as robotics, autonomous driving, and game playing. By focusing on estimating the simpler quantity of the score function, SAGE can help artificial intelligence agents learn faster and more efficiently, even in the most challenging situations.