The two most common perspectives on Reinforcement learning (RL) are optimization and dynamic programming. Methods that compute the gradients of the non-differentiable expected reward objective, such as the REINFORCE trick are commonly grouped into the optimization perspective, whereas methods that employ TD-learning or Q-learning are dynamic programming methods. While these methods have shown considerable success in recent years, these methods are still quite challenging to apply to new problems. In contrast deep supervised learning has been extremely successful and we may hence ask: Can we use supervised learning to perform RL? In this blog post we discuss a mental model for RL, based on the idea that RL can be viewed as doing supervised learning on the "good data".

The two most common perspectives on Reinforcement learning (RL) are optimization and dynamic programming. Methods that compute the gradients of the non-differentiable expected reward objective, such as the REINFORCE trick are commonly grouped into the optimization perspective, whereas methods that employ TD-learning or Q-learning are dynamic programming methods. While these methods have shown considerable success in recent years, these methods are still quite challenging to apply to new problems. In contrast deep supervised learning has been extremely successful and we may hence ask: Can we use supervised learning to perform RL? In this blog post we discuss a mental model for RL, based on the idea that RL can be viewed as doing supervised learning on the "good data".

In high-dimensional and/or non-parametric regression problems, regularization (or penalization) is used to control model complexity and induce desired structure. Each penalty has a weight parameter that indicates how strongly the structure corresponding to that penalty should be enforced. Typically the parameters are chosen to minimize the error on a separate validation set using a simple grid search or a gradient-free optimization method. It is more efficient to tune parameters if the gradient can be determined, but this is often difficult for problems with non-smooth penalty functions. Here we show that for many penalized regression problems, the validation loss is actually smooth almost-everywhere with respect to the penalty parameters. We can therefore apply a modified gradient descent algorithm to tune parameters. Through simulation studies on example regression problems, we find that increasing the number of penalty parameters and tuning them using our method can decrease the generalization error.