A Free Lunch from the Noise: Provable and Practical Exploration for Representation Learning

Reinforcement learning (RL) dedicates to solve the sequential decision making problem, where an agent is interacting with an unknown environment to find the best policy that maximizes the expected cumulative rewards (Sutton & Barto, 2018). It is known that the tabular algorithms direct controlling over the original state and action achieve the minimax-optimal regret depending on the cardinality of the state and action space (Jaksch et al., 2010; Osband & Van Roy, 2016; Azar et al., 2017; Jin et al., 2018). However, these algorithms become intractable for the real-world problems with an enormous number of states, due to the curse of dimensionality. Learning with function approximation upon good representation is a natural idea to tackle the curse and serving as the key for the success of deep learning (Bengio et al., 2013). In fact, representation learning lies at the heart of the empirical successes of deep RL in video games (Mnih et al., 2013), robotics (Levine et al., 2016), Go (Silver et al., 2017), dialogue systems (Jiang et al., 2021) to name a few. Meanwhile, the importance and benefits of the representation in RL is rigorously justified (Jin et al.,