  We study risk-sensitive Reinforcement Learning (RL), where we aim to maximize
the Conditional Value at Risk (CVaR) with a fixed risk tolerance $\tau$. Prior
theoretical work studying risk-sensitive RL focuses on the tabular Markov
Decision Processes (MDPs) setting. To extend CVaR RL to settings where state
space is large, function approximation must be deployed. We study CVaR RL in
low-rank MDPs with nonlinear function approximation. Low-rank MDPs assume the
underlying transition kernel admits a low-rank decomposition, but unlike prior
linear models, low-rank MDPs do not assume the feature or state-action
representation is known. We propose a novel Upper Confidence Bound (UCB)
bonus-driven algorithm to carefully balance the interplay between exploration,
exploitation, and representation learning in CVaR RL. We prove that our
algorithm achieves a sample complexity of $\tilde{O}\left(\frac{H^7 A^2
d^4}{\tau^2 \epsilon^2}\right)$ to yield an $\epsilon$-optimal CVaR, where $H$
is the length of each episode, $A$ is the capacity of action space, and $d$ is
the dimension of representations. Computational-wise, we design a novel
discretized Least-Squares Value Iteration (LSVI) algorithm for the CVaR
objective as the planning oracle and show that we can find the near-optimal
policy in a polynomial running time with a Maximum Likelihood Estimation
oracle. To our knowledge, this is the first provably efficient CVaR RL
algorithm in low-rank MDPs.
