# A Reduction from Reinforcement Learning to No-Regret Online Learning

We present a reduction from reinforcement learning (RL) to no-regret online learning based on the saddle-point formulation of RL, by which "any" online algorithm with sublinear regret can generate policies with provable performance guarantees. This new perspective decouples the RL problem into two parts: regret minimization and function approximation. The first part admits a standard online-learning analysis, and the second part can be quantified independently of the learning algorithm. Therefore, the proposed reduction can be used as a tool to systematically design new RL algorithms. We demonstrate this idea by devising a simple RL algorithm based on mirror descent and the generative-model oracle. For any $\gamma$-discounted tabular RL problem, with probability at least $1-\delta$, it learns an $\epsilon$-optimal policy using at most $\tilde{O}\left(\frac{|\mathcal{S}||\mathcal{A}|\log(\frac{1}{\delta})}{(1-\gamma)^4\epsilon^2}\right)$ samples. Furthermore, this algorithm admits a direct extension to linearly parameterized function approximators for large-scale applications, with computation and sample complexities independent of $|\mathcal{S}|$,$|\mathcal{A}|$, though at the cost of potential approximation bias.

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