To solve complex tasks under resource constraints, reinforcement learning (RL) agents need to be simple, efficient, and scalable, addressing (1) large state spaces and (2) the continuous accumulation of interaction data. We propose HyperAgent, an RL framework featuring the hypermodel and index sampling schemes that enable computation-efficient incremental approximation for the posteriors associated with general value functions without the need for conjugacy, and data-efficient action selection. Implementing HyperAgent is straightforward, requiring only one additional module beyond what is necessary for Double-DQN. HyperAgent stands out as the first method to offer robust performance in large-scale deep RL benchmarks while achieving provably scalable per-step computational complexity and attaining sublinear regret under tabular assumptions. HyperAgent can solve Deep Sea hard exploration problems with episodes that optimally scale with problem size and exhibits significant efficiency gains in both data and computation under the Atari benchmark. The core of our theoretical analysis is the sequential posterior approximation argument, enabled by the first analytical tool for sequential random projection -- a non-trivial martingale extension of the Johnson-Lindenstrauss. This work bridges the theoretical and practical realms of RL, establishing a new benchmark for RL algorithm design.

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