Tabular RL

rl_rob is an open-source Python library for teaching reinforcement learning. It implements the arc of a modern course, from tabular temporal-difference learning through linear function approximation to deep value-based and policy-gradient methods, with every algorithm written from first principles so that its update rule is visible in a few lines of code. All agents share one interface, so learners can compare methods directly across stages and trace a deep reinforcement learning update from the temporal-difference error to the weight change. The library supports teaching and assessment in which students implement, modify and explain update rules, rather than only produce working code.

Simulation is a fundamental computational primitive in reinforcement learning (RL), yet conventional simulation explicitly generates individual trajectories even when downstream procedures use only aggregate statistics. To address this, we develop an exact fast-simulation framework for finite-horizon tabular Markov decision processes. Our framework has two complementary modes. In direct batch simulation, a batch is represented by its aggregate Markov flow. With sufficient parallel simulation resources, this flow can be obtained by trajectory aggregation; when such simulation is unavailable or costly but the initial state and transition distributions are directly accessible, we instead generate an identically distributed flow through forward Markov-flow sampling without materializing individual trajectories. The latter reduces the simulator-side computational dependence on batch size $m$ from $O(m)$ to $O(1)$. In adaptive batch simulation, when batch length is determined by a data-dependent condition, exact multivariate-hypergeometric splitting recursively refines a candidate Markov flow while preserving the conditional law, reducing the cost dependence on $m$ from $O(m)$ to $O(\log m)$. Together, these modes accelerate simulation by keeping trajectories aggregated whenever possible and refining flows only when required to locate data-dependent boundaries. The framework applies broadly across simulator-based, offline, and online batch or stage-based RL, as illustrated with representative algorithms from each setting.

Offline policy evaluation (OPE) is crucial in high-stakes reinforcement learning applications, where new policies must be assessed reliably before deployment. In such settings, point estimates alone are insufficient; principled uncertainty quantification, such as confidence intervals and variance estimates, is essential for safe and risk-aware decision-making. A comprehensive way to unify these tasks is to estimate the sampling distribution of the evaluation error. Existing approaches, however, often suffer from limited robustness, scalability, or finite-sample validity. In this paper, we propose a model-based bootstrap framework for uncertainty quantification of OPE in finite-horizon, time-inhomogeneous Markov decision processes (MDPs). Unlike classical bootstrap methods that rely on resampling complete episodes, the proposed method regenerates trajectories from an estimated MDP and can therefore accommodate a much broader range of offline data formats, including complete trajectories, transition-level observations, and trajectory fragments. This flexibility further improves finite-sample statistical efficiency. We establish bootstrap distributional consistency, asymptotically valid confidence intervals, and consistent variance estimation for the target policy value. Extensive simulations show that the proposed method accurately captures the sampling distribution of the OPE estimator, yielding tighter confidence intervals and more accurate variance estimates in most settings.

Reinforcement learning (RL) is an exciting concept as well as a remarkable success story worth sharing. However, RL builds on rather complex interactions between different objects that play out over several cycles. Such dynamics are often best explained with an easily accessible implementation. We present RLLBC-Lib, a carefully crafted code library with the goal of lowering the entry barrier for students and other learners of RL in the context of learning-based control. At its heart, RLLBC-Lib comprises a comprehensive library of tabular RL approaches to enforce a clear understanding of the theoretical foundations. A deep RL library follows the same design principles, underscoring the parallels between simple tabular and state-of-the-art deep RL approaches. Additionally, RLLBC-Lib provides a collection of implementations illustrating core RL principles and contrasting RL to other learning-based control approaches. Finally, RLLBC-Lib provides an ideal basis for creating programming assignments with automated grading.

We study horizon-free regret minimization for finite-horizon time-homogeneous tabular Markov decision processes with $S$ states, $A$ actions, horizon $H$, and per-trajectory total reward bounded by $1$. We propose a new algorithm and prove a regret upper bound $$\tilde O(\sqrt{SAK}+S^8A^3)$$ with failure probability $δ$, where $K$ is the number of episodes and $\tilde O(\cdot)$ hides $\mathsf{poly}\log(S,A,K,1/δ)$. Thus, the regret is $H$-free and asymptotically optimal, matching the contextual-bandit lower bound $Ω(\sqrt{SAK})$ up to logarithmic factors. This completely removes the $\log H$ dependence from the previous $\tilde O(\sqrt{SAK\log H}+S^2A\log H)$ guarantee of Zhang et al. (2021), and drastically improves the prior best horizon-free regret $\tilde O(\sqrt{S^9A^3K})$ of Zhang et al. (2022) asymptotically. The main technical difficulty is that the optimal value functions $\{V_h^*\}_{h=1}^H$ are time-inhomogeneous even though the transition kernel is time-homogeneous. A direct union bound over all value functions typically incurs an additional $\min\{\log H,S\}$ factor. We avoid this factor by (i) exploiting the monotonicity of $V_h^*$ in $h$ and (ii) non-trivially projecting the value functions onto an $S$-dimensional grid. Our analysis relies on three additional ingredients. First, we introduce a horizon-truncation argument that enables reward-based exploration and removes the cost of a separate reward-free exploration phase. Second, we design a cutting bonus that preserves both optimism and the monotonicity needed for planning. Third, we prove a new bound on total deviation for time-homogeneous MDPs, which controls the clipped variance terms in the cutting bonus with adjustable polynomial dependence on $S$ and without any dependence on $H$. Together, these tools yield an asymptotically optimal horizon-free regret guarantee.

Reinforcement learning is usually introduced through the Bellman update, yet the equation often remains abstract to undergraduates: they watch policy arrows converge but rarely observe how each value is computed or why an action is chosen. We present Q-Learning Lab, a single-file, browser-based, bilingual (Thai/English) tool for teaching tabular Q-learning that requires no installation. Beyond the usual gridworld visualization - color-coded Q-values and policy arrows on a $5 \times 5$ world - the tool exposes a live Bellman-substitution panel showing the numeric update at every step, and logs each transition, including the full pre-action Q-row, the greedy-versus-random decision under $\varepsilon$-greedy exploration, and wall-collision events, into an exportable trace. The central contribution is a learn-export-analyze loop: learners run their own agent, export the complete trace as CSV, and analyze it themselves, producing learning curves, value heatmaps, and visitation maps, turning a passive demonstration into a source of learner-generated data for reflective inquiry. We validate the tool without human-subject data through three complementary evaluations: (i) correctness of the learned values and policy against a value-iteration ground truth on the identical MDP; (ii) hyperparameter sweeps over $α$, $γ$, and $\varepsilon$ showing that every pedagogical claim the tool makes is reproducible; and (iii) a reward-editing study that uses the ground-truth optimal policy to separate two behaviorally identical but diagnostically opposite failure modes - an exploration failure versus genuine reward misspecification - that a single edited reward can produce. We also compare the tool against existing gridworld visualizers, describe its grounding in learning-by-doing pedagogy, and include a 50-minute lesson plan. The tool and all experiment code are openly available.

Foundation models for language and vision are powered by internet-scale data, while structured domains such as tabular prediction are powered by synthetic data. This substitute shifts the challenge from collection to prior design. Such priors already exist for many structured tasks: TabPFN and its successors solve tabular classification with a transformer pretrained on a synthetic Bayesian prior. We make two points. First, reinforcement learning is the conspicuous gap: sampling a synthetic MDP is as feasible as sampling a synthetic tabular dataset, yet no in-context RL work treats prior design as a primary objective. Second, MDPs admit a fixed-size sufficient statistic, independent of the episodes observed and tabular in shape, which makes them directly amenable to the attention-based architectures used for tabular foundation models, with a policy head replacing the supervised target. Together these define the agenda for an RL foundation model. As a proof of concept, we train a Graph Attention Network entirely on synthetic MDPs and show that, with no task-specific tuning, it solves held-out tabular benchmarks in context, both online and offline: online, in far fewer episodes than UCB-VI and tabular Q-learning, and offline, competitively with VI-LCB.

We formulate the problem of exact unlearning in reinforcement learning, where the goal is to design an efficient framework that enables the removal of any user's data upon deletion request, i.e., the online learner's output after unlearning is indistinguishable from what would have been produced had the deleted user never interacted with the learner. For any $ρ>0$, we show that there exists a reinforcement learning (RL) algorithm that is $ρ$-TV-stable and supports an exact unlearning procedure whose expected computational cost is only a $ρ\sqrt{\ln T}$ fraction of the computational cost of retraining from scratch. We construct such a $ρ$-TV-stable RL algorithm for tabular Markov decision processes (MDPs), which achieves a regret bound of $\mathcal{O}(H^2 \sqrt{SAT} + H^3 S^2 A + {H^{2.5} S^2 A}/ρ)$, where $S, A, H$, and $T$ denote the number of states, the number of actions, the episode horizon, and the number of episodes, respectively. We also establish a lower bound of $Ω(H\sqrt{\!SAT}\! +\! {SAH}/ρ)$ for $ρ$-TV-stable RL algorithms, showing that our algorithm is nearly minimax optimal.

We tackle the Metro Network Expansion Problem (MNEP), a subset of the Transport Network Design Problem (TNDP), which focuses on expanding metro systems to satisfy travel demand. Traditional methods rely on exact and heuristic approaches that require expert-defined constraints to reduce the search space. Recently, deep reinforcement learning (Deep RL) has emerged due to its effectiveness in complex sequential decision-making processes-it remains, however, computationally expensive, environmentally costly, and requires additional engineering to interpret. We show that MNEP problems are small enough to not require Deep RL methods. Reformulating the MNEP as a Non-Markovian Rewards Decision Process (NMRDP), we use tabular RL to achieve similar performance with significantly fewer training episodes, additionally offering greater interpretability. Additionally, we incorporate social equity criteria into the reward functions, focusing on efficiency and fairness, highlighting the versatility of our method. Evaluated in real-world settings-Xi'an and Amsterdam-our method reduces total episodes by a factor of 18 and total carbon emissions by a factor of 12 on average, while remaining competitive with Deep RL. This approach offers a replicable, modular, interpretable, and resource-efficient solution with potential applications to other combinatorial optimization problems.