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.
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.
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.
We propose a novel distributionally robust $Q$-learning algorithm for the non-tabular case accounting for continuous state spaces where the state transition of the underlying Markov decision process is subject to model uncertainty. The uncertainty is taken into account by considering the worst-case transition from a ball around a reference probability measure. To determine the optimal policy under the worst-case state transition, we solve the associated non-linear Bellman equation by dualising and regularising the Bellman operator with the Sinkhorn distance, which is then parameterized with deep neural networks. This approach allows us to modify the Deep Q-Network algorithm to optimise for the worst case state transition. We illustrate the tractability and effectiveness of our approach through several applications, including a portfolio optimisation task based on S\&{P}~500 data.
Navigating in a fluid flow while being carried by it, using only information accessible from on-board sensors, is a problem commonly faced by small planktonic organisms. It is also directly relevant to autonomous robots deployed in the oceans. In the last ten years, the fluid mechanics community has widely adopted reinforcement learning, often in the form of its simplest implementations, to address this challenge. But it is unclear how good are the strategies learned by these algorithms. In this paper, we perform a quantitative assessment of reinforcement learning methods applied to navigation in partially observable flows. We first introduce a well-posed problem of directional navigation for which a quasi-optimal policy is known analytically. We then report on the poor performance and robustness of commonly used algorithms (Q-Learning, Advantage Actor Critic) in flows regularly encountered in the literature: Taylor-Green vortices, Arnold-Beltrami-Childress flow, and two-dimensional turbulence. We show that they are vastly surpassed by PPO (Proximal Policy Optimization), a more advanced algorithm that has established dominance across a wide range of benchmarks in the reinforcement learning community. In particular, our custom implementation of PPO matches the theoretical quasi-optimal performance in turbulent flow and does so in a robust manner. Reaching this result required the use of several additional techniques, such as vectorized environments and generalized advantage estimation, as well as hyperparameter optimization. This study demonstrates the importance of algorithm selection, implementation details, and fine-tuning for discovering truly smart autonomous navigation strategies in complex flows.
Recent progress in Meta-Black-Box-Optimization (MetaBBO) has demonstrated that using RL to learn a meta-level policy for dynamic algorithm configuration (DAC) over an optimization task distribution could significantly enhance the performance of the low-level BBO algorithm. However, the online learning paradigms in existing works makes the efficiency of MetaBBO problematic. To address this, we propose an offline learning-based MetaBBO framework in this paper, termed Q-Mamba, to attain both effectiveness and efficiency in MetaBBO. Specifically, we first transform DAC task into long-sequence decision process. This allows us further introduce an effective Q-function decomposition mechanism to reduce the learning difficulty within the intricate algorithm configuration space. Under this setting, we propose three novel designs to meta-learn DAC policy from offline data: we first propose a novel collection strategy for constructing offline DAC experiences dataset with balanced exploration and exploitation. We then establish a decomposition-based Q-loss that incorporates conservative Q-learning to promote stable offline learning from the offline dataset. To further improve the offline learning efficiency, we equip our work with a Mamba architecture which helps long-sequence learning effectiveness and efficiency by selective state model and hardware-aware parallel scan respectively. Through extensive benchmarking, we observe that Q-Mamba achieves competitive or even superior performance to prior online/offline baselines, while significantly improving the training efficiency of existing online baselines. We provide sourcecodes of Q-Mamba at https://github.com/MetaEvo/Q-Mamba.
Dynamic hedging is a financial strategy that consists in periodically transacting one or multiple financial assets to offset the risk associated with a correlated liability. Deep Reinforcement Learning (DRL) algorithms have been used to find optimal solutions to dynamic hedging problems by framing them as sequential decision-making problems. However, most previous work assesses the performance of only one or two DRL algorithms, making an objective comparison across algorithms difficult. In this paper, we compare the performance of eight DRL algorithms in the context of dynamic hedging; Monte Carlo Policy Gradient (MCPG), Proximal Policy Optimization (PPO), along with four variants of Deep Q-Learning (DQL) and two variants of Deep Deterministic Policy Gradient (DDPG). Two of these variants represent a novel application to the task of dynamic hedging. In our experiments, we use the Black-Scholes delta hedge as a baseline and simulate the dataset using a GJR-GARCH(1,1) model. Results show that MCPG, followed by PPO, obtain the best performance in terms of the root semi-quadratic penalty. Moreover, MCPG is the only algorithm to outperform the Black-Scholes delta hedge baseline with the allotted computational budget, possibly due to the sparsity of rewards in our environment.
Extending deep Q-learning to cooperative multi-agent settings is challenging due to the exponential growth of the joint action space, the non-stationary environment, and the credit assignment problem. Value decomposition allows deep Q-learning to be applied at the joint agent level, at the cost of reduced expressivity. Building on past work in this direction, our paper proposes PairVDN, a novel method for decomposing the value function into a collection of pair-wise, rather than per-agent, functions, improving expressivity at the cost of requiring a more complex (but still efficient) dynamic programming maximisation algorithm. Our method enables the representation of value functions which cannot be expressed as a monotonic combination of per-agent functions, unlike past approaches such as VDN and QMIX. We implement a novel many-agent cooperative environment, Box Jump, and demonstrate improved performance over these baselines in this setting. We open-source our code and environment at https://github.com/zzbuzzard/PairVDN.
We present the POPGym Arcade, a collection of hardware-accelerated, pixel-based environments with shared observation and action spaces. Each environment includes fully and partially observable variants, enabling counterfactual studies on partial observability. We also introduce mathematical tools for analyzing policies under partial observability, which reveal how agents recall past information to make decisions. Our analysis shows (1) that controlling for partial observability is critical and (2) that agents with long-term memory learn brittle policies that struggle to generalize. Finally, we demonstrate that recurrent policies can be "poisoned" by old, out-of-distribution observations, with implications for sim-to-real transfer, imitation learning, and offline reinforcement learning.
While a number of existing approaches for building foundation model agents rely on prompting or fine-tuning with human demonstrations, it is not sufficient in dynamic environments (e.g., mobile device control). On-policy reinforcement learning (RL) should address these limitations, but collecting actual rollouts in an environment is often undesirable in truly open-ended agentic problems such as mobile device control or interacting with humans, where each unit of interaction is associated with a cost. In such scenarios, a method for policy learning that can utilize off-policy experience by learning a trained action-value function is much more effective. In this paper, we develop an approach, called Digi-Q, to train VLM-based action-value Q-functions which are then used to extract the agent policy. We study our approach in the mobile device control setting. Digi-Q trains the Q-function using offline temporal-difference (TD) learning, on top of frozen, intermediate-layer features of a VLM. Compared to fine-tuning the whole VLM, this approach saves us compute and enhances scalability. To make the VLM features amenable for representing the Q-function, we need to employ an initial phase of fine-tuning to amplify coverage over actionable information needed for value function. Once trained, we use this Q-function via a Best-of-N policy extraction operator that imitates the best action out of multiple candidate actions from the current policy as ranked by the value function, enabling policy improvement without environment interaction. Digi-Q outperforms several prior methods on user-scale device control tasks in Android-in-the-Wild, attaining 21.2% improvement over prior best-performing method. In some cases, our Digi-Q approach already matches state-of-the-art RL methods that require interaction. The project is open-sourced at https://github.com/DigiRL-agent/digiq
Extensive behavioral experiments reveal that conditional cooperation is a prevalent phenomenon. Previous game-theoretical studies have predominantly relied on hard-manner models, where cooperation is triggered only upon reaching a specific threshold. However, this approach contrasts with the observed flexibility of human behaviors, where individuals adapt their strategies dynamically based on their surroundings. To capture this adaptability, we introduce a soft form of conditional cooperation by integrating the Q-learning algorithm from reinforcement learning. In this form, players not only reciprocate mutual cooperation but may also defect in highly cooperative environments or cooperate in less cooperative settings to maximize rewards. To explore the effects of hard and soft conditional cooperators, we examine their interactions in two scenarios: structural mixture (SM) and probabilistic mixture (PM), where the two behavioral modes are fixed and probabilistically adopted, respectively. In SM, hard conditional cooperators enhance cooperation when the threshold is low but hinder it otherwise. Surprisingly, in PM, the cooperation prevalence exhibits two first-order phase transitions as the probability is varied, leading to high, low, and vanishing levels of cooperation. Analysis of Q-tables offers insights into the "psychological shifts" of soft conditional cooperators and the overall evolutionary dynamics. Model extensions confirm the robustness of our findings. These results highlight the novel complexities arising from the diversity of conditional cooperators.
Vision-Language-Action (VLA) models have shown substantial potential in real-world robotic manipulation. However, fine-tuning these models through supervised learning struggles to achieve robust performance due to limited, inconsistent demonstrations, especially in contact-rich environments. In this paper, we propose a reinforced fine-tuning approach for VLA models, named ConRFT, which consists of offline and online fine-tuning with a unified consistency-based training objective, to address these challenges. In the offline stage, our method integrates behavior cloning and Q-learning to effectively extract policy from a small set of demonstrations and stabilize value estimating. In the online stage, the VLA model is further fine-tuned via consistency policy, with human interventions to ensure safe exploration and high sample efficiency. We evaluate our approach on eight diverse real-world manipulation tasks. It achieves an average success rate of 96.3% within 45-90 minutes of online fine-tuning, outperforming prior supervised methods with a 144% improvement in success rate and 1.9x shorter episode length. This work highlights the potential of integrating reinforcement learning to enhance the performance of VLA models for real-world robotic applications. Videos and code are available at our project website https://cccedric.github.io/conrft/.
We present flow Q-learning (FQL), a simple and performant offline reinforcement learning (RL) method that leverages an expressive flow-matching policy to model arbitrarily complex action distributions in data. Training a flow policy with RL is a tricky problem, due to the iterative nature of the action generation process. We address this challenge by training an expressive one-step policy with RL, rather than directly guiding an iterative flow policy to maximize values. This way, we can completely avoid unstable recursive backpropagation, eliminate costly iterative action generation at test time, yet still mostly maintain expressivity. We experimentally show that FQL leads to strong performance across 73 challenging state- and pixel-based OGBench and D4RL tasks in offline RL and offline-to-online RL. Project page: https://seohong.me/projects/fql/
Overestimation in single-agent reinforcement learning has been extensively studied. In contrast, overestimation in the multiagent setting has received comparatively little attention although it increases with the number of agents and leads to severe learning instability. Previous works concentrate on reducing overestimation in the estimation process of target Q-value. They ignore the follow-up optimization process of online Q-network, thus making it hard to fully address the complex multiagent overestimation problem. To solve this challenge, in this study, we first establish an iterative estimation-optimization analysis framework for multiagent value-mixing Q-learning. Our analysis reveals that multiagent overestimation not only comes from the computation of target Q-value but also accumulates in the online Q-network's optimization. Motivated by it, we propose the Dual Ensembled Multiagent Q-Learning with Hypernet Regularizer algorithm to tackle multiagent overestimation from two aspects. First, we extend the random ensemble technique into the estimation of target individual and global Q-values to derive a lower update target. Second, we propose a novel hypernet regularizer on hypernetwork weights and biases to constrain the optimization of online global Q-network to prevent overestimation accumulation. Extensive experiments in MPE and SMAC show that the proposed method successfully addresses overestimation across various tasks.
In reinforcement learning (RL), continuing tasks refer to tasks where the agent-environment interaction is ongoing and can not be broken down into episodes. These tasks are suitable when environment resets are unavailable, agent-controlled, or predefined but where all rewards-including those beyond resets-are critical. These scenarios frequently occur in real-world applications and can not be modeled by episodic tasks. While modern deep RL algorithms have been extensively studied and well understood in episodic tasks, their behavior in continuing tasks remains underexplored. To address this gap, we provide an empirical study of several well-known deep RL algorithms using a suite of continuing task testbeds based on Mujoco and Atari environments, highlighting several key insights concerning continuing tasks. Using these testbeds, we also investigate the effectiveness of a method for improving temporal-difference-based RL algorithms in continuing tasks by centering rewards, as introduced by Naik et al. (2024). While their work primarily focused on this method in conjunction with Q-learning, our results extend their findings by demonstrating that this method is effective across a broader range of algorithms, scales to larger tasks, and outperforms two other reward-centering approaches.
Behavioral experiments on the ultimatum game (UG) reveal that we humans prefer fair acts, which contradicts the prediction made in orthodox Economics. Existing explanations, however, are mostly attributed to exogenous factors within the imitation learning framework. Here, we adopt the reinforcement learning paradigm, where individuals make their moves aiming to maximize their accumulated rewards. Specifically, we apply Q-learning to UG, where each player is assigned two Q-tables to guide decisions for the roles of proposer and responder. In a two-player scenario, fairness emerges prominently when both experiences and future rewards are appreciated. In particular, the probability of successful deals increases with higher offers, which aligns with observations in behavioral experiments. Our mechanism analysis reveals that the system undergoes two phases, eventually stabilizing into fair or rational strategies. These results are robust when the rotating role assignment is replaced by a random or fixed manner, or the scenario is extended to a latticed population. Our findings thus conclude that the endogenous factor is sufficient to explain the emergence of fairness, exogenous factors are not needed.
Reinforcement learning methods have proposed promising traffic signal control policy that can be trained on large road networks. Current SOTA methods model road networks as topological graph structures, incorporate graph attention into deep Q-learning, and merge local and global embeddings to improve policy. However, graph-based methods are difficult to parallelize, resulting in huge time overhead. Moreover, none of the current peer studies have deployed dynamic traffic systems for experiments, which is far from the actual situation. In this context, we propose Multi-Scene Aggregation Convolutional Learning for traffic signal control (MacLight), which offers faster training speeds and more stable performance. Our approach consists of two main components. The first is the global representation, where we utilize variational autoencoders to compactly compress and extract the global representation. The second component employs the proximal policy optimization algorithm as the backbone, allowing value evaluation to consider both local features and global embedding representations. This backbone model significantly reduces time overhead and ensures stability in policy updates. We validated our method across multiple traffic scenarios under both static and dynamic traffic systems. Experimental results demonstrate that, compared to general and domian SOTA methods, our approach achieves superior stability, optimized convergence levels and the highest time efficiency. The code is under https://github.com/Aegis1863/MacLight.
In Location-Based Services (LBS), such as food delivery, a fundamental task is segmenting Areas of Interest (AOIs), aiming at partitioning the urban geographical spaces into non-overlapping regions. Traditional AOI segmentation algorithms primarily rely on road networks to partition urban areas. While promising in modeling the geo-semantics, road network-based models overlooked the service-semantic goals (e.g., workload equality) in LBS service. In this paper, we point out that the AOI segmentation problem can be naturally formulated as a Markov Decision Process (MDP), which gradually chooses a nearby AOI for each grid in the current AOI's border. Based on the MDP, we present the first attempt to generalize Deep Reinforcement Learning (DRL) for AOI segmentation, leading to a novel DRL-based framework called DRL4AOI. The DRL4AOI framework introduces different service-semantic goals in a flexible way by treating them as rewards that guide the AOI generation. To evaluate the effectiveness of DRL4AOI, we develop and release an AOI segmentation system. We also present a representative implementation of DRL4AOI - TrajRL4AOI - for AOI segmentation in the logistics service. It introduces a Double Deep Q-learning Network (DDQN) to gradually optimize the AOI generation for two specific semantic goals: i) trajectory modularity, i.e., maximize tightness of the trajectory connections within an AOI and the sparsity of connections between AOIs, ii) matchness with the road network, i.e., maximizing the matchness between AOIs and the road network. Quantitative and qualitative experiments conducted on synthetic and real-world data demonstrate the effectiveness and superiority of our method. The code and system is publicly available at https://github.com/Kogler7/AoiOpt.
Developing effective quantitative trading strategies using reinforcement learning (RL) is challenging due to the high risks associated with online interaction with live financial markets. Consequently, offline RL, which leverages historical market data without additional exploration, becomes essential. However, existing offline RL methods often struggle to capture the complex temporal dependencies inherent in financial time series and may overfit to historical patterns. To address these challenges, we introduce a Decision Transformer (DT) initialized with pre-trained GPT-2 weights and fine-tuned using Low-Rank Adaptation (LoRA). This architecture leverages the generalization capabilities of pre-trained language models and the efficiency of LoRA to learn effective trading policies from expert trajectories solely from historical data. Our model performs competitively with established offline RL algorithms, including Conservative Q-Learning (CQL), Implicit Q-Learning (IQL), and Behavior Cloning (BC), as well as a baseline Decision Transformer with randomly initialized GPT-2 weights and LoRA. Empirical results demonstrate that our approach effectively learns from expert trajectories and secures superior rewards in certain trading scenarios, highlighting the effectiveness of integrating pre-trained language models and parameter-efficient fine-tuning in offline RL for quantitative trading. Replication code for our experiments is publicly available at https://github.com/syyunn/finrl-dt