Instance-Dependent Continuous-Time Reinforcement Learning via Maximum Likelihood Estimation

The paper proposes a model-based continuous-time reinforcement learning algorithm using maximum likelihood estimation to achieve instance-dependent regret guarantees. It resides in the Finite-Horizon Episodic LQ Learning leaf, which contains three papers including this work. This leaf sits within the Linear-Quadratic Control Problems branch, representing a moderately populated research direction where tractable dynamics enable sharp theoretical analysis. The focus on instance-dependent bounds through MLE distinguishes this work from sibling papers that pursue either logarithmic regret under strong assumptions or sublinear rates with broader applicability.

The taxonomy reveals that Linear-Quadratic Control Problems form the most developed branch, with three distinct learning paradigms: episodic, single-trajectory, and actor-critic approaches. Neighboring leaves address average-reward continuous-time MDPs and ODE-based model learning in the General Continuous-Time MDP Frameworks branch, which handles nonlinear dynamics and broader state spaces. The paper's episodic LQ setting connects naturally to these general frameworks but exploits quadratic structure for tighter guarantees. The Specialized Application Domains branch shows extensions to finance and jump-diffusion processes, indicating how core LQ insights scale to richer environments beyond the paper's finite-horizon regime.

Among 19 candidates examined across three contributions, no clearly refuting prior work was identified. The CT-MLE algorithm examined 3 candidates with none refutable; the instance-dependent regret bound examined 7 candidates with none refutable; the randomized measurement strategy examined 9 candidates with none refutable. This suggests that within the limited search scope, the specific combination of state marginal density estimation, variance-adaptive measurement, and randomized scheduling appears relatively unexplored. However, the search examined only top-K semantic matches and citations, not an exhaustive literature review, so stronger overlap may exist beyond these 19 papers.

Based on the limited search scope of 19 papers, the work appears to occupy a distinct position within episodic LQ learning by emphasizing measurement-adaptive strategies and state marginal density estimation rather than direct dynamics estimation. The absence of refuting candidates across all contributions suggests novelty in the specific technical approach, though the episodic LQ setting itself is well-established. The analysis cannot rule out substantial prior work outside the examined candidates, particularly in adjacent areas like adaptive sampling or variance-dependent bounds in discrete-time settings.