We propose a robust Q-learning algorithm for Markov decision processes under model uncertainty when each state--action pair is associated with a finite ambiguity set of candidate transition kernels. This finite-measure framework enables user-designed uncertainty models, including competing fitted models and stress scenarios. {The learner observes successor states and their deterministic rewards from every candidate simulator, without requiring explicit knowledge of the transition probabilities or the reward function.} We establish almost sure convergence of the learned Q-function to the robust optimum, and derive a time-uniform high-probability error certificate that separates an observable empirical Bellman residual from transition-kernel estimation error. We also give quantitative finite-ambiguity approximation results for Wasserstein and parametric uncertainty models on finite state spaces. Numerical examples illustrate the effect of scenario selection and compare the tabular algorithm with robust value iteration.
There is growing experimental evidence that $Q$-learning agents can learn to charge supracompetitive prices. We ask when such behavior persists, whether it emerges, and which strategies support it. In a repeated pricing game in which firms condition on the previous period's price profile, we give conditions on the learned action values under which supracompetitive prices become an absorbing state once experimentation ends. We then show that under softmax exploration these conditions are reached with positive and explicitly bounded probability, both from a random and from an all-zero initial $Q$-table. In the latter case firms lock in supracompetitive prices because they never learn that undercutting pays; the same mechanism can lock in the competitive price, so the long-run outcome is selected by the exploration path. Finally, we give sufficient conditions on the learned table under which the induced strategy is naive collusion, a grim trigger strategy or an increasing-price strategy; grim trigger strategies are subgame perfect under a standard discounting condition, whereas naive collusion is generally not an equilibrium.
Robots are increasingly integrated across industries, particularly in healthcare. However, many valuable applications for quadrupedal robots remain overlooked. This research explores the effectiveness of three reinforcement learning algorithms in training a simulated quadruped robot for autonomous navigation and obstacle avoidance. The goal is to develop a robotic guide dog simulation capable of path following and obstacle avoidance, with long-term potential for real-world assistance to guide dogs and visually impaired individuals. It also seeks to expand research into medical 'pets', including robotic guide and alert dogs. A comparative analysis of thirteen related research papers shaped key evaluation criteria, including collision detection, pathfinding algorithms, sensor usage, robot type, and simulation platforms. The study focuses on sensor inputs, collision frequency, reward signals, and learning progression to determine which algorithm best supports robotic navigation in complex environments. Custom-made environments were used to ensure fair evaluation of all three algorithms under controlled conditions, allowing consistent data collection. Results show that Proximal Policy Optimization (PPO) outperformed Deep Q-Network (DQN) and Q-learning across all metrics, particularly in average and median steps to goal per episode. By analysing these results, this study contributes to robotic navigation, AI and medical robotics, offering insights into the feasibility of AI-driven quadruped mobility and its role in assistive robotics.
This paper presents a sample-efficient, data-driven control framework for finite-horizon linear quadratic (LQ) control of linear time-varying (LTV) systems. In contrast to the time-invariant case, the time-varying LQ problem involves a differential Riccati equation (DRE) with time-dependent parameters and terminal boundary constraints. We formulate the LQ problem as a nonconvex optimization problem and conduct a rigorous analysis of its dual structure. By exploiting the inherent convexity of the dual problem and analyzing the KKT conditions, we derive an explicit relationship between the optimal dual solution and the parameters of the associated Q-function in time-varying case. This theoretical insight supports the development of a novel, sample-efficient, non-iterative semidefinite programming (SDP) algorithm that directly computes the optimal sequence of feedback gains from an ensemble of input-state data sequences without model identification. The resulting convex, data-dependent framework provides global optimality guarantees for completely unknown LTV systems. As a special case, the method also applies to finite-horizon LQ control of linear time-invariant (LTI) systems. In this setting, a single input-state trajectory suffices to identify the optimal LQ feedback policy, improving significantly over existing Q-learning approaches for finite horizon LTI systems that typically require data from multiple episodes. The approach provides a new optimization-based perspective on Q-learning in time-varying settings and contributes to the broader understanding of data-driven control in non-stationary environments. Simulation results show that, compared to recent methods, the proposed approach achieves superior optimality and sample efficiency on LTV systems, and indicates potential for stabilizing and optimal control of nonlinear systems.
We introduce ExRec, a general framework for personalized exercise recommendation with semantically-grounded knowledge tracing. Our method builds on the observation that existing exercise recommendation approaches simulate student performance via knowledge tracing (KT) but they often overlook two key aspects: (a) the semantic content of questions and (b) the sequential, structured progression of student learning. To address this, our ExRec presents an end-to-end pipeline, from annotating the KCs of questions and learning their semantic representations to training KT models and optimizing several reinforcement learning (RL) methods. Moreover, we improve standard Q-learning-based continuous RL methods via a tailored model-based value estimation (MVE) approach that directly leverages the components of KT model in estimating cumulative knowledge improvement. We validate the effectiveness of our ExRec using various RL methods across four real-world tasks with different educational goals in online math learning. We further show that ExRec generalizes robustly to new, unseen questions and that it produces interpretable student learning trajectories. Together, our findings highlight the promise of KT-guided RL for effective personalization in education.
Bias problems in the estimation of $Q$-values are a well-known obstacle that slows down convergence of $Q$-learning and actor-critic methods. One of the reasons of the success of modern RL algorithms is partially a direct or indirect overestimation reduction mechanism. We propose an easy to implement method built on top of distributional reinforcement learning (DRL) algorithms to deal with the overestimation in a locally adaptive way. Our framework is simple to implement, existing distributional algorithms can be improved with a few lines of code. We provide theoretical evidence and use double $Q$-learning to show how to include locally adaptive overestimation control in existing algorithms. Experiments are provided for tabular, Atari, and MuJoCo environments.
Flexible and efficient wireless resource sharing across heterogeneous services is a key objective for future wireless networks. In this context, we investigate the performance of a system where latency-constrained internet-of-things (IoT) devices coexist with a broadband user. The base station adopts a grant-free access framework to manage resource allocation, either through orthogonal radio access network (RAN) slicing or by allowing shared access between services. For the IoT users, we propose a reinforcement learning (RL) approach based on double Q-Learning (QL) to optimise their repetition-based transmission strategy, allowing them to adapt to varying levels of interference and meet a predefined latency target. We evaluate the system's performance in terms of the cumulative distribution function of IoT users' latency, as well as the broadband user's throughput and energy efficiency (EE). Our results show that the proposed RL-based access policies significantly enhance the latency performance of IoT users in both RAN Slicing and RAN Sharing scenarios, while preserving desirable broadband throughput and EE. Furthermore, the proposed policies enable RAN Sharing to be energy-efficient at low IoT traffic levels, and RAN Slicing to be favourable under high IoT traffic.
Offline reinforcement learning promises policy improvement from logged interaction data alone, yet state-of-the-art algorithms remain vulnerable to value over-estimation and to violations of domain knowledge such as monotonicity or smoothness. We introduce implicit constraint-aware off-policy correction, a framework that embeds structural priors directly inside every Bellman update. The key idea is to compose the optimal Bellman operator with a proximal projection on a convex constraint set, which produces a new operator that (i) remains a $\gamma$-contraction, (ii) possesses a unique fixed point, and (iii) enforces the prescribed structure exactly. A differentiable optimization layer solves the projection; implicit differentiation supplies gradients for deep function approximators at a cost comparable to implicit Q-learning. On a synthetic Bid-Click auction -- where the true value is provably monotone in the bid -- our method eliminates all monotonicity violations and outperforms conservative Q-learning and implicit Q-learning in return, regret, and sample efficiency.
To empower precision agriculture through distributed machine learning (DML), split learning (SL) has emerged as a promising paradigm, partitioning deep neural networks (DNNs) between edge devices and servers to reduce computational burdens and preserve data privacy. However, conventional SL frameworks' one-split-fits-all strategy is a critical limitation in agricultural ecosystems where edge insect monitoring devices exhibit vast heterogeneity in computational power, energy constraints, and connectivity. This leads to straggler bottlenecks, inefficient resource utilization, and compromised model performance. Bridging this gap, we introduce ReinDSplit, a novel reinforcement learning (RL)-driven framework that dynamically tailors DNN split points for each device, optimizing efficiency without sacrificing accuracy. Specifically, a Q-learning agent acts as an adaptive orchestrator, balancing workloads and latency thresholds across devices to mitigate computational starvation or overload. By framing split layer selection as a finite-state Markov decision process, ReinDSplit convergence ensures that highly constrained devices contribute meaningfully to model training over time. Evaluated on three insect classification datasets using ResNet18, GoogleNet, and MobileNetV2, ReinDSplit achieves 94.31% accuracy with MobileNetV2. Beyond agriculture, ReinDSplit pioneers a paradigm shift in SL by harmonizing RL for resource efficiency, privacy, and scalability in heterogeneous environments.
In this paper we analyze the sample complexities of learning the optimal state-action value function $Q^*$ and an optimal policy $\pi^*$ in a discounted Markov decision process (MDP) where the agent has recursive entropic risk-preferences with risk-parameter $\beta\neq 0$ and where a generative model of the MDP is available. We provide and analyze a simple model based approach which we call model-based risk-sensitive $Q$-value-iteration (MB-RS-QVI) which leads to $(\epsilon,\delta)$-PAC-bounds on $\|Q^*-Q^k\|$, and $\|V^*-V^{\pi_k}\|$ where $Q_k$ is the output of MB-RS-QVI after k iterations and $\pi_k$ is the greedy policy with respect to $Q_k$. Both PAC-bounds have exponential dependence on the effective horizon $\frac{1}{1-\gamma}$ and the strength of this dependence grows with the learners risk-sensitivity $|\beta|$. We also provide two lower bounds which shows that exponential dependence on $|\beta|\frac{1}{1-\gamma}$ is unavoidable in both cases. The lower bounds reveal that the PAC-bounds are both tight in $\varepsilon$ and $\delta$ and that the PAC-bound on $Q$-learning is tight in the number of actions $A$, and that the PAC-bound on policy-learning is nearly tight in $A$.
The steelmaking continuous casting scheduling problem (SCCSP) is a critical and complex challenge in modern steel production, requiring the coordinated assignment and sequencing of steel charges across multiple production stages. Efficient scheduling not only enhances productivity but also significantly reduces energy consumption. However, both traditional heuristics (e.g., two-stage local search) and recent metaheuristics often struggle to adapt to the dynamic characteristics of practical SCCSP instances. To address these limitations, this paper introduces a novel Q learning based hierarchical cooperative local search framework, termed HierC_Q, aimed at minimizing the weighted sum of the maximum completion time and the average waiting time in SCCSP. The core contributions of HierC_Q are twofold. First, considering the intrinsic coupling properties of the SCCSP, a dedicated reward function is proposed based on a novel coupling measure (CM), guiding the exploration process towards promising regions of the solution space. Second, a hierarchical architecture is devised, comprising two distinct tiers: the learn to improve (L2I) tier and the "disturb to renovate" (D2R) tier. The L2I tier performs deep exploitation within promising regions using two independent Q-learning-based local search frameworks (QLSFs) tailored for subproblems, along with a synergy QLSF designed for the main problem. To enhance the effectiveness of local search, a validity evaluation approach and a speed-up evaluation method are also intro-duced, grounded in a detailed study of the problem's structure. Meanwhile, the D2R tier incorporates a perturbation and construction based solution renewal strategy to mitigate the risk of premature convergence. The superiority and effectiveness of HierC_Q are demonstrated through extensive comparisons with eleven local search frameworks and nine state-of-the-art algorithms.
In this work, we provide an extended discussion of a new approach to explainable Reinforcement Learning called Diverse Near-Optimal Alternatives (DNA), first proposed at L4DC 2025. DNA seeks a set of reasonable "options" for trajectory-planning agents, optimizing policies to produce qualitatively diverse trajectories in Euclidean space. In the spirit of explainability, these distinct policies are used to "explain" an agent's options in terms of available trajectory shapes from which a human user may choose. In particular, DNA applies to value function-based policies on Markov decision processes where agents are limited to continuous trajectories. Here, we describe DNA, which uses reward shaping in local, modified Q-learning problems to solve for distinct policies with guaranteed epsilon-optimality. We show that it successfully returns qualitatively different policies that constitute meaningfully different "options" in simulation, including a brief comparison to related approaches in the stochastic optimization field of Quality Diversity. Beyond the explanatory motivation, this work opens new possibilities for exploration and adaptive planning in RL.
In value-based reinforcement learning, removing the target network is tempting as the boostrapped target would be built from up-to-date estimates, and the spared memory occupied by the target network could be reallocated to expand the capacity of the online network. However, eliminating the target network introduces instability, leading to a decline in performance. Removing the target network also means we cannot leverage the literature developed around target networks. In this work, we propose to use a copy of the last linear layer of the online network as a target network, while sharing the remaining parameters with the up-to-date online network, hence stepping out of the binary choice between target-based and target-free methods. It enables us to leverage the concept of iterated Q-learning, which consists of learning consecutive Bellman iterations in parallel, to reduce the performance gap between target-free and target-based approaches. Our findings demonstrate that this novel method, termed iterated Shared Q-Learning (iS-QL), improves the sample efficiency of target-free approaches across various settings. Importantly, iS-QL requires a smaller memory footprint and comparable training time to classical target-based algorithms, highlighting its potential to scale reinforcement learning research.
Motivated by real-world settings where data collection and policy deployment -- whether for a single agent or across multiple agents -- are costly, we study the problem of on-policy single-agent reinforcement learning (RL) and federated RL (FRL) with a focus on minimizing burn-in costs (the sample sizes needed to reach near-optimal regret) and policy switching or communication costs. In parallel finite-horizon episodic Markov Decision Processes (MDPs) with $S$ states and $A$ actions, existing methods either require superlinear burn-in costs in $S$ and $A$ or fail to achieve logarithmic switching or communication costs. We propose two novel model-free RL algorithms -- Q-EarlySettled-LowCost and FedQ-EarlySettled-LowCost -- that are the first in the literature to simultaneously achieve: (i) the best near-optimal regret among all known model-free RL or FRL algorithms, (ii) low burn-in cost that scales linearly with $S$ and $A$, and (iii) logarithmic policy switching cost for single-agent RL or communication cost for FRL. Additionally, we establish gap-dependent theoretical guarantees for both regret and switching/communication costs, improving or matching the best-known gap-dependent bounds.
Hanabi has become a popular game for research when it comes to reinforcement learning (RL) as it is one of the few cooperative card games where you have incomplete knowledge of the entire environment, thus presenting a challenge for a RL agent. We explored different tabular and deep reinforcement learning algorithms to see which had the best performance both against an agent of the same type and also against other types of agents. We establish that certain agents played their highest scoring games against specific agents while others exhibited higher scores on average by adapting to the opposing agent's behavior. We attempted to quantify the conditions under which each algorithm provides the best advantage and identified the most interesting interactions between agents of different types. In the end, we found that temporal difference (TD) algorithms had better overall performance and balancing of play types compared to tabular agents. Specifically, tabular Expected SARSA and deep Q-Learning agents showed the best performance.
We propose a new ternary spiking neuron model to improve the representation capacity of binary spiking neurons in deep Q-learning. Although a ternary neuron model has recently been introduced to overcome the limited representation capacity offered by the binary spiking neurons, we show that its performance is worse than that of binary models in deep Q-learning tasks. We hypothesize gradient estimation bias during the training process as the underlying potential cause through mathematical and empirical analysis. We propose a novel ternary spiking neuron model to mitigate this issue by reducing the estimation bias. We use the proposed ternary spiking neuron as the fundamental computing unit in a deep spiking Q-learning network (DSQN) and evaluate the network's performance in seven Atari games from the Gym environment. Results show that the proposed ternary spiking neuron mitigates the drastic performance degradation of ternary neurons in Q-learning tasks and improves the network performance compared to the existing binary neurons, making DSQN a more practical solution for on-board autonomous decision-making tasks.
Ensuring convergence of policy gradient methods in federated reinforcement learning (FRL) under environment heterogeneity remains a major challenge. In this work, we first establish that heterogeneity, perhaps counter-intuitively, can necessitate optimal policies to be non-deterministic or even time-varying, even in tabular environments. Subsequently, we prove global convergence results for federated policy gradient (FedPG) algorithms employing local updates, under a {\L}ojasiewicz condition that holds only for each individual agent, in both entropy-regularized and non-regularized scenarios. Crucially, our theoretical analysis shows that FedPG attains linear speed-up with respect to the number of agents, a property central to efficient federated learning. Leveraging insights from our theoretical findings, we introduce b-RS-FedPG, a novel policy gradient method that employs a carefully constructed softmax-inspired parameterization coupled with an appropriate regularization scheme. We further demonstrate explicit convergence rates for b-RS-FedPG toward near-optimal stationary policies. Finally, we demonstrate that empirically both FedPG and b-RS-FedPG consistently outperform federated Q-learning on heterogeneous settings.
Polyak-Ruppert averaging is a widely used technique to achieve the optimal asymptotic variance of stochastic approximation (SA) algorithms, yet its high-probability performance guarantees remain underexplored in general settings. In this paper, we present a general framework for establishing non-asymptotic concentration bounds for the error of averaged SA iterates. Our approach assumes access to individual concentration bounds for the unaveraged iterates and yields a sharp bound on the averaged iterates. We also construct an example, showing the tightness of our result up to constant multiplicative factors. As direct applications, we derive tight concentration bounds for contractive SA algorithms and for algorithms such as temporal difference learning and Q-learning with averaging, obtaining new bounds in settings where traditional analysis is challenging.
Bayesian optimization (BO) offers an efficient pipeline for optimizing black-box functions with the help of a Gaussian process prior and an acquisition function (AF). Recently, in the context of single-objective BO, learning-based AFs witnessed promising empirical results given its favorable non-myopic nature. Despite this, the direct extension of these approaches to multi-objective Bayesian optimization (MOBO) suffer from the \textit{hypervolume identifiability issue}, which results from the non-Markovian nature of MOBO problems. To tackle this, inspired by the non-Markovian RL literature and the success of Transformers in language modeling, we present a generalized deep Q-learning framework and propose \textit{BOFormer}, which substantiates this framework for MOBO via sequence modeling. Through extensive evaluation, we demonstrate that BOFormer constantly outperforms the benchmark rule-based and learning-based algorithms in various synthetic MOBO and real-world multi-objective hyperparameter optimization problems. We have made the source code publicly available to encourage further research in this direction.
We study the problem of offline imitation learning in Markov decision processes (MDPs), where the goal is to learn a well-performing policy given a dataset of state-action pairs generated by an expert policy. Complementing a recent line of work on this topic that assumes the expert belongs to a tractable class of known policies, we approach this problem from a new angle and leverage a different type of structural assumption about the environment. Specifically, for the class of linear $Q^\pi$-realizable MDPs, we introduce a new algorithm called saddle-point offline imitation learning (\SPOIL), which is guaranteed to match the performance of any expert up to an additive error $\varepsilon$ with access to $\mathcal{O}(\varepsilon^{-2})$ samples. Moreover, we extend this result to possibly non-linear $Q^\pi$-realizable MDPs at the cost of a worse sample complexity of order $\mathcal{O}(\varepsilon^{-4})$. Finally, our analysis suggests a new loss function for training critic networks from expert data in deep imitation learning. Empirical evaluations on standard benchmarks demonstrate that the neural net implementation of \SPOIL is superior to behavior cloning and competitive with state-of-the-art algorithms.