In this paper, we derive rates of convergence in the high-dimensional central limit theorem for Polyak--Ruppert averaged iterates generated by entropy-regularized asynchronous Q-learning with linear function approximation and a polynomial stepsize $k^{-ω}$, $ω\in (1/2,1)$. Assuming that the sequence of observed triples $(s_k,a_k,s_{k+1})_{k \geq 0}$ forms a uniformly geometrically ergodic Markov chain, and under suitable regularity conditions for the projected soft Bellman equation, we establish a Gaussian approximation bound in the convex distance with rate of order $n^{-1/4}$, up to polylogarithmic factors in $n$, where $n$ is the number of samples used by the algorithm. To obtain this result, we combine a linearization of the soft Bellman recursion with a Gaussian approximation for the leading martingale term. Finally, we derive high-order moment bounds for the algorithm's last iterate, which might be of independent interest.

This paper proposes a deep reinforcement learning (DRL)-based event-triggered controller design for networked artificial pancreas (AP) systems. Although existing DRL-based AP controllers typically assume periodic control updates, networked control systems (NCSs) require a reduction in communication frequency to achieve energy-efficient operation, which is directly tied to control updates. However, jointly learning both insulin dosing and update timing significantly increases the complexity of the learning problem. To alleviate this complexity, we develop a practical DRL-based controller design that avoids explicitly learning update timing by introducing a rule-based criterion defined by changes in blood glucose. As a result, decision-making occurs at irregular intervals, and the problem is naturally formulated as a semi-Markov decision process (SMDP), for which we extend a standard DRL algorithm. Numerical experiments demonstrate that the proposed method improves communication efficiency while maintaining control performance.

We study episodic reinforcement learning with fixed reward and transition functions, but with episode-dependent admissible action sets that are observed at the start of each episode. Performance is measured by cumulative regret against the episode-wise optimal value, $\sum_{k=1}^K [V^{*,M^k} - V^{π^k,M^k}]$, where $M^k$ represents the action context in the $k$-th episode. We show that the MVP algorithm naturally extends to this framework and enjoys strong theoretical guarantees. In particular, we establish a minimax regret bound of $\widetilde{O}(\sqrt{SAH^3K\log L})$ for adversarial contexts, where $L$ denotes the number of possible contexts. This result implies a regret bound of $\widetilde{O}(\sqrt{SAH^3K})$ for stochastic contexts. We further translate the stochastic regret guarantee into a sample complexity bound of $\widetilde{O}(SAH^3/ε^2)$ for a fixed context distribution. In addition, we derive a gap-dependent regret bound of \[ \widetilde O\left( \inf_{p\in [0,1)} \left( \frac{1}{Δ_{\min}^{p}} + pKΔ_{\min}^{p} \right)\log K \cdot \mathrm{poly}(S,A,H) \right), \] where $Δ_{\min}^{p}$ is the global $p$-trimmed positive-gap floor over suboptimal $(h,s,a)$ triples. This bound can substantially improve upon the minimax rate when the relevant suboptimality gaps are large.

We study reinforcement learning in hybrid discrete-continuous action spaces, such as settings where the discrete component selects a regime (or index) and the continuous component optimizes within it -- a structure common in robotics, control, and operations problems. Standard model-free policy gradient methods rely on score-function (SF) estimators and suffer from severe credit-assignment issues in high-dimensional settings, leading to poor gradient quality. On the other hand, differentiable simulation largely sidesteps these issues by backpropagating through a simulator, but the presence of discrete actions or non-smooth dynamics yields biased or uninformative gradients. To address this, we propose Hybrid Policy Optimization (HPO), which backpropagates through the simulator wherever smoothness permits, using a mixed gradient estimator that combines pathwise and SF gradients while maintaining unbiasedness. We also show how problems with action discontinuities can be reformulated in hybrid form, further broadening its applicability. Empirically, HPO substantially outperforms PPO on inventory control and switched linear-quadratic regulator problems, with performance gaps increasing as the continuous action dimension grows. Finally, we characterize the structure of the mixed gradient, showing that its cross term -- which captures how continuous actions influence future discrete decisions -- becomes negligible near a discrete best response, thereby enabling approximate decentralized updates of the continuous and discrete components and reducing variance near optimality.

We establish novel structural and statistical results for entropy-regularized min-max inverse reinforcement learning (Min-Max-IRL) with linear reward classes in finite-horizon MDPs with Borel state and action spaces. On the structural side, we show that maximum likelihood estimation (MLE) and Min-Max-IRL are equivalent at the population level, and at the empirical level under deterministic dynamics. On the statistical side, exploiting pseudo-self-concordance of the Min-Max-IRL loss, we prove that both the trajectory-level KL divergence and the squared parameter error in the Hessian norm decay at the fast rate $\mathcal{O}(n^{-1})$, where $n$ is the number of expert trajectories. Our guarantees apply under misspecification and require no exploration assumptions. We further extend reward-identifiability results to general Borel spaces and derive novel results on the derivatives of the soft-optimal value function with respect to reward parameters.

Every adaptive learning system must alternate between two operations: consolidating what it already knows and expanding into new evidence. We propose \emph{Consolidation-Expansion Operator Mechanics} (OpMech), a framework that makes this structure precise. The central object is the \emph{order-gap} $\Ogap(θ; e)$, the degree to which a consolidation operator~$Q$ and an expansion operator~$P_e$ fail to commute at a given knowledge state. Because the order-gap is computable from the system's own trajectory, it serves as a real-time control signal: large values indicate that the system is still sensitive to the ordering of consolidation and expansion; once the order-gap falls and stays small, further processing is unlikely to change the outcome. Three results give the signal precise meaning: the order-gap decays along convergent trajectories; a persistently large order-gap implies the system is far from its settled state; and an order-gap-based stopping rule terminates with provable guarantees in both noiseless and bounded-noise settings. The framework applies across five domains: bandits, reinforcement learning, stochastic optimization, continual learning, and recursive language models. We give conditions under which the order-gap reliably tracks convergence in three representative cases. We develop the recursive language model application in detail, showing how OpMech replaces heuristic stopping rules and fixed recursion budgets with principled, evidence-driven alternatives.

Reinforcement learning agents for portfolio management are typically trained and deployed as static policies, with no mechanism for using price forecasts at inference time. We propose $\text{FPILOT}$ (**Fin**ancial **P**lugin **I**nference-time **L**earning for **O**ptimal **T**rading), a plugin inference-time optimization framework inspired by Model Predictive Control (MPC). Our key structural insight is that future prices mostly do not depend on one agent's portfolio allocation, so a suitable predictive model can produce a multi-step price trajectory without iterative action-conditioned rollouts as in typical reinforcement learning. At each decision step, we use the forecaster's predicted price trajectory to construct an allocation-based imagined return objective, and optimize the policy at inference-time before executing one step of the trade. Our framework is compatible with any pre-trained agent and adapts the policy to the forecaster's predictions without any retraining. Evaluated across five policy learning algorithms on the TradeMaster DJ30 benchmark, $\text{FPILOT}$ produces consistent improvements in total return and return-based risk-adjusted metrics (Sharpe, Sortino, Calmar), with stochastic policies benefiting more than deterministic ones. Further, using synthetic forecasts at calibrated quality levels, we show that gains consistently improve with forecaster quality, suggesting that our performance will improve based on advances in financial forecasting.

We propose a data augmentation method for offline reinforcement learning, motivated by active positioning problems. Particularly, our approach enables the training of off-policy models from a limited number of suboptimal trajectories. We introduce a trajectory-based augmentation technique that exploits task structure and the geometric relationship between rewards, value functions, and mathematical properties of logging policies. During data collection, our augmentation supports suboptimal logging policies, leading to higher data quality and improved offline reinforcement learning performance. We provide theoretical justification for these strategies and validate them empirically across positioning tasks of varying dimensionality and under partial observability.

In this paper, we establish last-iterate convergence rates for off-policy actor--critic methods in reinforcement learning. In particular, under a single-loop, single-timescale implementation and a broad class of policy updates, including approximate policy iteration and natural policy gradient methods, we prove the first $\tilde{\mathcal{O}}(ε^{-2})$ sample complexity guarantee for finding an $ε$-optimal policy under minimal assumptions, namely, the existence of a policy that induces an irreducible Markov chain. This stands in stark contrast to the existing literature, where an $\tilde{\mathcal{O}}(ε^{-2})$ sample complexity is achieved only through nested-loop updates and/or under strong, algorithm-dependent assumptions on the policies, such as uniform mixing and uniform exploration. Technically, to address the challenges posed by the coupled update equations arising from the single-loop implementation, as well as the potentially unbounded iterates induced by off-policy learning, our analysis is based on a coupled Lyapunov drift framework. Specifically, we establish a geometric convergence rate for the actor and an $\tilde{\mathcal{O}}(1/T)$ convergence rate for the critic, and combine the two Lyapunov drift inequalities through a cross-domination property. We believe this analytical framework is of independent interest and may be applicable to other coupled iterative algorithms with unbounded

We study best-policy identification for finite-horizon risk-sensitive reinforcement learning under the entropic risk measure. Recent work established a constant gap in the exponential horizon dependence between lower and upper bounds on the number of samples required to identify an approximately optimal policy. Precisely, known lower bounds scale in Ωpe|β|Hq where H is the horizon of the MDP, while the state-of-the-art upper bound achieves at best Ope2|β|Hq (Mortensen and Talebi, 2025) using a generative model. We show that this extra exponential factor can be traced to overly loose concentration control for exponential utilities. To close this open gap, we revisit the analysis of this problem through a forward-model based algorithm building on KL-based exploration bonuses that we adapt to the entropic criterion. The improvement we get is due to two main novel technical innovations. We leverage the smoothness properties of the exponential utility to derive sharper concentration bounds, and we propose a new stopping rule that exploits further this tightness to obtain a sample complexity that matches the lower bound.