# Simple Reinforcement Learning Algorithms for Continuous States and Action Space Systems

Rahul Jain (University of Southern California)

Reinforcement Learning (RL) problems for continuous state and action space systems is quite challenging. Recently, deep reinforcement learning methods have been shown to be quite effective for certain RL problems in settings of very large/continuous state and action spaces. But such methods require extensive hyper-parameter tuning, huge amount of data, and come with no performance guarantees. We note that such methods are mostly trained `offline’ on experience replay buffers. In this talk, I will describe a series of simple reinforcement learning schemes for various settings. Our premise is that we have access to a generative model that can give us simulated samples of the next state. We will start with finite state and action space MDPs. An `empirical value learning’ (EVL) algorithm can be derived quite simply by replacing the expectation in the Bellman operator with an empirical estimate. We note that the EVL algorithm has remarkably good numerical performance for practical purposes. We next extend this to continuous state spaces by considering randomized function approximation on a reproducible kernel Hilbert space (RKHS). This allows for arbitrarily good approximation with high probability for any problem due to its universal function approximation property. Next, we consider continuous action spaces. In each iteration of EVL, we sample actions from the continuous action space, and take a supremum over the sampled actions. Under mild assumptions on the MDP, we show that this performs quite well numerically, with provable performance guarantees. Finally, we consider the `Online-EVL’ algorithm that learns from a trajectory of state-action-reward sequence. Under mild mixing conditions on the trajectory, we can provide performance bounds and also show that it has competitive (and in fact slightly superior) performance as compared to the Deep Q-Network algorithm on a benchmark RL problem. I will conclude by a brief overview of the framework of probabilistic contraction analysis of iterated random operators that underpins the theoretical analysis.

This talk is based on work with a number of people that includes Hiteshi Sharma, William Haskell, and Dileep Kalathil.

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