Improving Reinforcement Learning Sample-Efficiency using Local Approximation
This work addresses sample efficiency in RL, which is crucial for applications like robotics and gaming, but it is incremental as it builds on existing MDP frameworks with a specific improvement.
The paper tackles the problem of high sample complexity in reinforcement learning by deriving sharper PAC bounds and proposing a method that reduces sample complexity to O(SA log A) timesteps, achieving a logarithmic factor improvement over prior work.
In this study, we derive Probably Approximately Correct (PAC) bounds on the asymptotic sample-complexity for RL within the infinite-horizon Markov Decision Process (MDP) setting that are sharper than those in existing literature. The premise of our study is twofold: firstly, the further two states are from each other, transition-wise, the less relevant the value of the first state is when learning the $ε$-optimal value of the second; secondly, the amount of 'effort', sample-complexity-wise, expended in learning the $ε$-optimal value of a state is independent of the number of samples required to learn the $ε$-optimal value of a second state that is a sufficient number of transitions away from the first. Inversely, states within each other's vicinity have values that are dependent on each other and will require a similar number of samples to learn. By approximating the original MDP using smaller MDPs constructed using subsets of the original's state-space, we are able to reduce the sample-complexity by a logarithmic factor to $O(SA \log A)$ timesteps, where $S$ and $A$ are the state and action space sizes. We are able to extend these results to an infinite-horizon, model-free setting by constructing a PAC-MDP algorithm with the aforementioned sample-complexity. We conclude with showing how significant the improvement is by comparing our algorithm against prior work in an experimental setting.