In shared autonomy, user input is combined with semi-autonomous control to achieve a common goal. The goal is often unknown ex-ante, so prior work enables agents to infer the goal from user input and assist with the task. Such methods tend to assume some combination of knowledge of the dynamics of the environment, the user's policy given their goal, and the set of possible goals the user might target, which limits their application to real-world scenarios. We propose a deep reinforcement learning framework for model-free shared autonomy that lifts these assumptions. We use human-in-the-loop reinforcement learning with neural network function approximation to learn an end-to-end mapping from environmental observation and user input to agent action values, with task reward as the only form of supervision. This approach poses the challenge of following user commands closely enough to provide the user with real-time action feedback and thereby ensure high-quality user input, but also deviating from the user's actions when they are suboptimal. We balance these two needs by discarding actions whose values fall below some threshold, then selecting the remaining action closest to the user's input. Controlled studies with users (n = 12) and synthetic pilots playing a video game, and a pilot study with users (n = 4) flying a real quadrotor, demonstrate the ability of our algorithm to assist users with real-time control tasks in which the agent cannot directly access the user's private information through observations, but receives a reward signal and user input that both depend on the user's intent. The agent learns to assist the user without access to this private information, implicitly inferring it from the user's input. This paper is a proof of concept that illustrates the potential for deep reinforcement learning to enable flexible and practical assistive systems.