A Provably Efficient Sample Collection Strategy for Reinforcement Learning

One of the challenges in online reinforcement learning (RL) is that the agent needs to trade off the exploration of the environment and the exploitation of the samples to optimize its behavior. Whether we optimize for regret, sample complexity, state-space coverage or model estimation, we need to strike a different exploration-exploitation trade-off. In this paper, we propose to tackle the exploration-exploitation problem following a decoupled approach composed of: 1) An "objective-specific" algorithm that (adaptively) prescribes how many samples to collect at which states, as if it has access to a generative model (i.e., a simulator of the environment); 2) An "objective-agnostic" sample collection exploration strategy responsible for generating the prescribed samples as fast as possible. Building on recent methods for exploration in the stochastic shortest path problem, we first provide an algorithm that, given as input the number of samples b(s, a) needed in each state-action pair, requires O BD + D 3/2 S 2 A time steps to collect the B = s,a b(s, a) desired samples, in any unknown communicating MDP with S states, A actions and diameter D. Then we show how this general-purpose exploration algorithm can be paired with "objective-specific" strategies that prescribe the sample requirements to tackle a variety of settings -e.g., model estimation, sparse reward discovery, goal-free cost-free exploration in communicating MDPs -for which we obtain improved or novel sample complexity guarantees. Recent works on reward-free exploration (RFE) in the finite-horizon setting [e.g., 30, 31, 39, 64] provide sufficient exploration so that an ε-optimal policy for any reward function can be computed. Our proposed solution shares high-level algorithmic principles with RFE approaches which incentivize the agent to visit insufficiently visited states via intrinsic reward. Nonetheless, our contribution significantly differs from existing RFE literature in two dimensions: 1) While we study the performance of GOSPRL in one goal-conditioned RFE problem (Sect. 4.3), our framework is much broader and it allows us to tackle a wider and diverse set of problems (Sect. 4 and App. I); 2) Our setting is horizon-agnostic and reset-free, which prevents from directly using any method or technical analysis in RFE designed for problems with an imposed planning horizon (e.g., finite-horizon or discounted). Finally, GOSPRL draws inspiration from the SSP formalism and solutions of [50, 45] , but our approach critically differs from these works in three main ways: 1) we are interested in sample 1 Alternatively, we can view it as a general approach to take any SO-based algorithm and convert it into an online RL algorithm.