Model-Free Reinforcement Learning with the Decision-Estimation Coefficient
This work provides incremental improvements in regret guarantees for model-free reinforcement learning with value function approximation, benefiting researchers in statistical learning and decision theory.
The paper tackles the problem of interactive decision making in reinforcement learning by improving regret bounds through a combination of the Estimation-to-Decisions reduction and optimistic estimation, achieving more lenient error accommodations compared to prior work.
We consider the problem of interactive decision making, encompassing structured bandits and reinforcement learning with general function approximation. Recently, Foster et al. (2021) introduced the Decision-Estimation Coefficient, a measure of statistical complexity that lower bounds the optimal regret for interactive decision making, as well as a meta-algorithm, Estimation-to-Decisions, which achieves upper bounds in terms of the same quantity. Estimation-to-Decisions is a reduction, which lifts algorithms for (supervised) online estimation into algorithms for decision making. In this paper, we show that by combining Estimation-to-Decisions with a specialized form of optimistic estimation introduced by Zhang (2022), it is possible to obtain guarantees that improve upon those of Foster et al. (2021) by accommodating more lenient notions of estimation error. We use this approach to derive regret bounds for model-free reinforcement learning with value function approximation, and give structural results showing when it can and cannot help more generally.