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In real-world reinforcement learning (RL) systems, various forms of {\itimpaired observability} can complicate matters. These situations arise when anagent is unable to observe the most recent state of the system due to latencyor lossy channels, yet the agent must still make real-time decisions. Thispaper introduces a theoretical investigation into efficient RL in controlsystems where agents must act with delayed and missing state observations. Wepresent algorithms and establish near-optimal regret upper and lower bounds, ofthe form $\tilde{\mathcal{O}}(\sqrt{{\rm poly}(H) SAK})$, for RL in the delayedand missing observation settings. Here $S$ and $A$ are the sizes of state andaction spaces, $H$ is the time horizon and $K$ is the number of episodes.Despite impaired observability posing significant challenges to the policyclass and planning, our results demonstrate that learning remains efficient,with the regret bound optimally depending on the state-action size of theoriginal system. Additionally, we provide a characterization of the performanceof the optimal policy under impaired observability, comparing it to the optimalvalue obtained with full observability. Numerical results are provided tosupport our theory.

Efficient Reinforcement Learning with Impaired Observability: Learning to Act with Delayed and Missing State Observations