Exploiting Exogenous Structure for Sample-Efficient Reinforcement Learning

We study reinforcement learning for episodic Markov Decision Processes (MDPs) whose transitions are modelled by a multinomial logistic (MNL) model. Existing algorithms for MNL mixture MDPs yield a regret of $\smash{\tilde{O}(dH^2\sqrt{T})}$ (Li et al., 2024), where $d$ is the feature dimension, $H$ the episode length, and $T$ the number of episodes. Inspired by the logistic bandit literature (Abeille et al., 2021; Faury et al., 2022; Boudart et al., 2026), we introduce a problem-dependent constant $\barσ\_T \leq 1/2$, measuring the normalised average variance of the optimal downstream value function along the learner's trajectory. We propose an algorithm achieving a regret of $\smash{\tilde{O}(dH^2\barσ\_T\sqrt{T})}$, which recovers the existing bound in the worst case and improves upon it for structured MDPs. For instance, for KL-constrained robust MDPs, $\barσ\_T = O(H^{-1})$, reducing the horizon dependence by a factor $H$. We further establish a matching $\smash{Ω(dH^2\barσ\_T\sqrt{T})}$ lower bound, proving minimax optimality (up to logarithmic factors) and fully characterising the regret complexity of MNL mixture MDPs for the first time.

We study PAC learning in tabular discounted Markov decision processes with exogenous i.i.d. contexts, with discount factor $γ$, finite state space $\mathcal X$, action space $\mathcal A$, and context space $\mathcal Z$. At each time step, a context is drawn independently from an unknown distribution $μ$ and revealed before the agent acts. This context may affect both rewards and transitions, while remaining uncontrolled by the agent. Depending on the regime, the learner has access either to a sampling oracle for $μ$, to a sampling oracle for the transition kernel conditioned on state-context-action tuples, or to both. Oracles can be accessed before and during policy execution. The sample complexity is measured by a couple $(n,m)$, where $n$ is the number of calls to the sampling oracles before execution and $m$ is the number of calls to the sampling oracles during execution. When rewards and transitions are known and only the context distribution $μ$ is sampled, we give a variance-reduced algorithm that solves policy evaluation (PE), best-value estimation (BVE), and best-policy extraction (BPE) with $\left(\widetilde O\left(1/((1-γ)^3\varepsilon^2)\right), 0 \right)$ sample complexity. The rate is independent of $|\mathcal Z|$ and minimax optimal up to logarithmic factors. As a corollary, we also obtain tight rates in the case of one-step perfect look-ahead, improving upon the existing guarantees. In the fully unknown regime, where both $μ$ and P must be learned, we show that PE remains $|\mathcal Z|$-free, with matching upper and lower bounds $\bigl(\widetilde O(|\mathcal X|/((1-γ)^3\varepsilon^2)),\, \widetilde O(1/((1-γ)^2\varepsilon^2))\bigr)$.

The exploration-exploitation dilemma in reinforcement learning (RL) is a fundamental challenge to efficient RL algorithms. Existing algorithms for finite state and action discounted RL problems address this by assuming sufficient exploration over both state and action spaces. However, this yields non-implementable algorithms and sub-optimal performance. To resolve these limitations, we introduce a new class of methods with auto-exploration, or methods that automatically explore both state and action spaces. Auto-exploration can be applied in both the tabular and linear function approximation setting. Under algorithm-independent assumptions on the existence of an exploring optimal policy, both settings attain $O(ε^{-2})$ sample complexity to solve to $ε$ error. These complexities are novel since they avoid algorithm-dependent parameters seen in prior works, which may be arbitrarily large. The methods are also simple to implement because they are parameter-free. We achieve these results by integrating auto-exploration into policy mirror descent to avoid the (unknown) stationary distribution seen in prior art. In the tabular setting, we introduce a dynamic exploration time with a data-driven stopping time, while for linear function approximation we propose a new sampling distribution based on the discounted visitation distribution that covers a more general class of Markov chains.