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.
Much research has been done to analyze the stock market. After all, if one can determine a pattern in the chaotic frenzy of transactions, then they could make a hefty profit from capitalizing on these insights. As such, the goal of our project was to apply reinforcement learning (RL) to determine the best time to buy a stock within a given time frame. With only a few adjustments, our model can be extended to identify the best time to sell a stock as well. In order to use the format of free, real-world data to train the model, we define our own Markov Decision Process (MDP) problem. These two papers [5] [6] helped us in formulating the state space and the reward system of our MDP problem. We train a series of agents using Q-Learning, Q-Learning with linear function approximation, and deep Q-Learning. In addition, we try to predict the stock prices using machine learning regression and classification models. We then compare our agents to see if they converge on a policy, and if so, which one learned the best policy to maximize profit on the stock market.
When applying offline reinforcement learning (RL) in healthcare scenarios, the out-of-distribution (OOD) issues pose significant risks, as inappropriate generalization beyond clinical expertise can result in potentially harmful recommendations. While existing methods like conservative Q-learning (CQL) attempt to address the OOD issue, their effectiveness is limited by only constraining action selection by suppressing uncertain actions. This action-only regularization imitates clinician actions that prioritize short-term rewards, but it fails to regulate downstream state trajectories, thereby limiting the discovery of improved long-term treatment strategies. To safely improve policy beyond clinician recommendations while ensuring that state-action trajectories remain in-distribution, we propose \textit{Offline Guarded Safe Reinforcement Learning} ($\mathsf{OGSRL}$), a theoretically grounded model-based offline RL framework. $\mathsf{OGSRL}$ introduces a novel dual constraint mechanism for improving policy with reliability and safety. First, the OOD guardian is established to specify clinically validated regions for safe policy exploration. By constraining optimization within these regions, it enables the reliable exploration of treatment strategies that outperform clinician behavior by leveraging the full patient state history, without drifting into unsupported state-action trajectories. Second, we introduce a safety cost constraint that encodes medical knowledge about physiological safety boundaries, providing domain-specific safeguards even in areas where training data might contain potentially unsafe interventions. Notably, we provide theoretical guarantees on safety and near-optimality: policies that satisfy these constraints remain in safe and reliable regions and achieve performance close to the best possible policy supported by the data.
This paper presents a novel reinforcement learning (RL) framework for dynamically optimizing numerical precision in the preconditioned conjugate gradient (CG) method. By modeling precision selection as a Markov Decision Process (MDP), we employ Q-learning to adaptively assign precision levels to key operations, striking an optimal balance between computational efficiency and numerical accuracy, while ensuring stability through double-precision scalar computations and residual computing. In practice, the algorithm is trained on a set of data and subsequently performs inference for precision selection on out-of-sample data, without requiring re-analysis or retraining for new datasets. This enables the method to adapt seamlessly to new problem instances without the computational overhead of recalibration. Our results demonstrate the effectiveness of RL in enhancing solver's performance, marking the first application of RL to mixed-precision numerical methods. The findings highlight the approach's practical advantages, robustness, and scalability, providing valuable insights into its integration with iterative solvers and paving the way for AI-driven advancements in scientific computing.
Offline reinforcement learning seeks to derive improved policies entirely from historical data but often struggles with over-optimistic value estimates for out-of-distribution (OOD) actions. This issue is typically mitigated via policy constraint or conservative value regularization methods. However, these approaches may impose overly constraints or biased value estimates, potentially limiting performance improvements. To balance exploitation and restriction, we propose an Imagination-Limited Q-learning (ILQ) method, which aims to maintain the optimism that OOD actions deserve within appropriate limits. Specifically, we utilize the dynamics model to imagine OOD action-values, and then clip the imagined values with the maximum behavior values. Such design maintains reasonable evaluation of OOD actions to the furthest extent, while avoiding its over-optimism. Theoretically, we prove the convergence of the proposed ILQ under tabular Markov decision processes. Particularly, we demonstrate that the error bound between estimated values and optimality values of OOD state-actions possesses the same magnitude as that of in-distribution ones, thereby indicating that the bias in value estimates is effectively mitigated. Empirically, our method achieves state-of-the-art performance on a wide range of tasks in the D4RL benchmark.
An AI agent might surprisingly find she has reached an unknown state which she has never been aware of -- an unknown unknown. We mathematically ground this scenario in reinforcement learning: an agent, after taking an action calculated from value functions $Q$ and $V$ defined on the {\it {aware domain}}, reaches a state out of the domain. To enable the agent to handle this scenario, we propose an {\it episodic Markov decision {process} with growing awareness} (EMDP-GA) model, taking a new {\it noninformative value expansion} (NIVE) approach to expand value functions to newly aware areas: when an agent arrives at an unknown unknown, value functions $Q$ and $V$ whereon are initialised by noninformative beliefs -- the averaged values on the aware domain. This design is out of respect for the complete absence of knowledge in the newly discovered state. The upper confidence bound momentum Q-learning is then adapted to the growing awareness for training the EMDP-GA model. We prove that (1) the regret of our approach is asymptotically consistent with the state of the art (SOTA) without exposure to unknown unknowns in an extremely uncertain environment, and (2) our computational complexity and space complexity are comparable with the SOTA -- these collectively suggest that though an unknown unknown is surprising, it will be asymptotically properly discovered with decent speed and an affordable cost.
A key task in Artificial Intelligence is learning effective policies for controlling agents in unknown environments to optimize performance measures. Off-policy learning methods, like Q-learning, allow learners to make optimal decisions based on past experiences. This paper studies off-policy learning from biased data in complex and high-dimensional domains where \emph{unobserved confounding} cannot be ruled out a priori. Building on the well-celebrated Deep Q-Network (DQN), we propose a novel deep reinforcement learning algorithm robust to confounding biases in observed data. Specifically, our algorithm attempts to find a safe policy for the worst-case environment compatible with the observations. We apply our method to twelve confounded Atari games, and find that it consistently dominates the standard DQN in all games where the observed input to the behavioral and target policies mismatch and unobserved confounders exist.
The fine-tuning of pre-trained large language models (LLMs) using reinforcement learning (RL) is generally formulated as direct policy optimization. This approach was naturally favored as it efficiently improves a pretrained LLM, seen as an initial policy. Another RL paradigm, Q-learning methods, has received far less attention in the LLM community while demonstrating major success in various non-LLM RL tasks. In particular, Q-learning effectiveness comes from its sample efficiency and ability to learn offline, which is particularly valuable given the high computational cost of sampling with LLMs. However, naively applying a Q-learning-style update to the model's logits is ineffective due to the specificity of LLMs. Our core contribution is to derive theoretically grounded loss functions from Bellman equations to adapt Q-learning methods to LLMs. To do so, we carefully adapt insights from the RL literature to account for LLM-specific characteristics, ensuring that the logits become reliable Q-value estimates. We then use this loss to build a practical algorithm, ShiQ for Shifted-Q, that supports off-policy, token-wise learning while remaining simple to implement. Finally, we evaluate ShiQ on both synthetic data and real-world benchmarks, e.g., UltraFeedback and BFCL-V3, demonstrating its effectiveness in both single-turn and multi-turn LLM settings
Recent studies claim that human behavior in a two-armed Bernoulli bandit (TABB) task is described by positivity and confirmation biases, implying that humans do not integrate new information objectively. However, we find that even if the agent updates its belief via objective Bayesian inference, fitting the standard Q-learning model with asymmetric learning rates still recovers both biases. Bayesian inference cast as an effective Q-learning algorithm has symmetric, though decreasing, learning rates. We explain this by analyzing the stochastic dynamics of these learning systems using master equations. We find that both confirmation bias and unbiased but decreasing learning rates yield the same behavioral signatures. Finally, we propose experimental protocols to disentangle true cognitive biases from artifacts of decreasing learning rates.
Emotional support conversation (ESC) aims to alleviate the emotional distress of individuals through effective conversations. Although large language models (LLMs) have obtained remarkable progress on ESC, most of these studies might not define the diagram from the state model perspective, therefore providing a suboptimal solution for long-term satisfaction. To address such an issue, we leverage the Q-learning on LLMs, and propose a framework called straQ*. Our framework allows a plug-and-play LLM to bootstrap the planning during ESC, determine the optimal strategy based on long-term returns, and finally guide the LLM to response. Substantial experiments on ESC datasets suggest that straQ* outperforms many baselines, including direct inference, self-refine, chain of thought, finetuning, and finite state machines.
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.
The Capacitated Vehicle Routing Problem with Time Windows (CVRPTW) is a classic NP-hard combinatorial optimization problem widely applied in logistics distribution and transportation management. Its complexity stems from the constraints of vehicle capacity and time windows, which pose significant challenges to traditional approaches. Advances in Large Language Models (LLMs) provide new possibilities for finding approximate solutions to CVRPTW. This paper proposes a novel LLM-enhanced Q-learning framework to address the CVRPTW with real-time emergency constraints. Our solution introduces an adaptive two-phase training mechanism that transitions from the LLM-guided exploration phase to the autonomous optimization phase of Q-network. To ensure reliability, we design a three-tier self-correction mechanism based on the Chain-of-Thought (CoT) for LLMs: syntactic validation, semantic verification, and physical constraint enforcement. In addition, we also prioritized replay of the experience generated by LLMs to amplify the regulatory role of LLMs in the architecture. Experimental results demonstrate that our framework achieves a 7.3\% average reduction in cost compared to traditional Q-learning, with fewer training steps required for convergence.
The approximation capabilities of Deep Q-Networks (DQNs) are commonly justified by general Universal Approximation Theorems (UATs) that do not leverage the intrinsic structural properties of the optimal Q-function, the solution to a Bellman equation. This paper establishes a UAT for a class of DQNs whose architecture is designed to emulate the iterative refinement process inherent in Bellman updates. A central element of our analysis is the propagation of regularity: while the transformation induced by a single Bellman operator application exhibits regularity, for which Backward Stochastic Differential Equations (BSDEs) theory provides analytical tools, the uniform regularity of the entire sequence of value iteration iterates--specifically, their uniform Lipschitz continuity on compact domains under standard Lipschitz assumptions on the problem data--is derived from finite-horizon dynamic programming principles. We demonstrate that layers of a deep residual network, conceived as neural operators acting on function spaces, can approximate the action of the Bellman operator. The resulting approximation theorem is thus intrinsically linked to the control problem's structure, offering a proof technique wherein network depth directly corresponds to iterations of value function refinement, accompanied by controlled error propagation. This perspective reveals a dynamic systems view of the network's operation on a space of value functions.
Vision is well-known for its use in manipulation, especially using visual servoing. To make it robust, multiple cameras are needed to expand the field of view. That is computationally challenging. Merging multiple views and using Q-learning allows the design of more effective representations and optimization of sample efficiency. Such a solution might be expensive to deploy. To mitigate this, we introduce a Merge And Disentanglement (MAD) algorithm that efficiently merges views to increase sample efficiency while augmenting with single-view features to allow lightweight deployment and ensure robust policies. We demonstrate the efficiency and robustness of our approach using Meta-World and ManiSkill3. For project website and code, see https://aalmuzairee.github.io/mad
Precise assembly of composite fuselages is critical for aircraft assembly to meet the ultra-high precision requirements. Due to dimensional variations, there is a gap when two fuselage assemble. In practice, actuators are required to adjust fuselage dimensions by applying forces to specific points on fuselage edge through pulling or pushing force actions. The positioning and force settings of these actuators significantly influence the efficiency of the shape adjustments. The current literature usually predetermines the fixed number of actuators, which is not optimal in terms of overall quality and corresponding actuator costs. However, optimal placement of actuators in terms of both locations and number is challenging due to compliant structures, complex material properties, and dimensional variabilities of incoming fuselages. To address these challenges, this paper introduces a reinforcement learning (RL) framework that enables sequential decision-making for actuator placement selection and optimal force computation. Specifically, our methodology employs the Dueling Double Deep Q-Learning (D3QN) algorithm to refine the decision-making capabilities of sequential actuator placements. The environment is meticulously crafted to enable sequential and incremental selection of an actuator based on system states. We formulate the actuator selection problem as a submodular function optimization problem, where the sub-modularity properties can be adopted to efficiently achieve near-optimal solutions. The proposed methodology has been comprehensively evaluated through numerical studies and comparison studies, demonstrating its effectiveness and outstanding performance in enhancing assembly precision with limited actuator numbers.
This work presents the first finite-time analysis for the last-iterate convergence of average-reward Q-learning with an asynchronous implementation. A key feature of the algorithm we study is the use of adaptive stepsizes, which serve as local clocks for each state-action pair. We show that the iterates generated by this Q-learning algorithm converge at a rate of $O(1/k)$ (in the mean-square sense) to the optimal relative Q-function in the span seminorm. Moreover, by adding a centering step to the algorithm, we further establish pointwise mean-square convergence to a centered optimal relative Q-function, also at a rate of $O(1/k)$. To prove these results, we show that adaptive stepsizes are necessary, as without them, the algorithm fails to converge to the correct target. In addition, adaptive stepsizes can be interpreted as a form of implicit importance sampling that counteracts the effects of asynchronous updates. Technically, the use of adaptive stepsizes makes each Q-learning update depend on the entire sample history, introducing strong correlations and making the algorithm a non-Markovian stochastic approximation (SA) scheme. Our approach to overcoming this challenge involves (1) a time-inhomogeneous Markovian reformulation of non-Markovian SA, and (2) a combination of almost-sure time-varying bounds, conditioning arguments, and Markov chain concentration inequalities to break the strong correlations between the adaptive stepsizes and the iterates. The tools developed in this work are likely to be broadly applicable to the analysis of general SA algorithms with adaptive stepsizes.
A clustered adaptive intervention (cAI) is a pre-specified sequence of decision rules that guides practitioners on how best - and based on which measures - to tailor cluster-level intervention to improve outcomes at the level of individuals within the clusters. A clustered sequential multiple assignment randomized trial (cSMART) is a type of trial that is used to inform the empirical development of a cAI. The most common type of secondary aim in a cSMART focuses on assessing causal effect moderation by candidate tailoring variables. We introduce a clustered Q-learning framework with the M-out-of-N Cluster Bootstrap using data from a cSMART to evaluate whether a set of candidate tailoring variables may be useful in defining an optimal cAI. This approach could construct confidence intervals (CI) with near-nominal coverage to assess parameters indexing the causal effect moderation function. Specifically, it allows reliable inferences concerning the utility of candidate tailoring variables in constructing a cAI that maximizes a mean end-of-study outcome even when "non-regularity", a well-known challenge exists. Simulations demonstrate the numerical performance of the proposed method across varying non-regularity conditions and investigate the impact of varying number of clusters and intra-cluster correlation coefficient on CI coverage. Methods are applied on ADEPT dataset to inform the construction of a clinic-level cAI for improving evidence-based practice in treating mood disorders.
Integrating human expertise with machine learning is crucial for applications demanding high accuracy and safety, such as autonomous driving. This study introduces Interactive Double Deep Q-network (iDDQN), a Human-in-the-Loop (HITL) approach that enhances Reinforcement Learning (RL) by merging human insights directly into the RL training process, improving model performance. Our proposed iDDQN method modifies the Q-value update equation to integrate human and agent actions, establishing a collaborative approach for policy development. Additionally, we present an offline evaluative framework that simulates the agent's trajectory as if no human intervention had occurred, to assess the effectiveness of human interventions. Empirical results in simulated autonomous driving scenarios demonstrate that iDDQN outperforms established approaches, including Behavioral Cloning (BC), HG-DAgger, Deep Q-Learning from Demonstrations (DQfD), and vanilla DRL in leveraging human expertise for improving performance and adaptability.
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.