Model-Free Reinforcement Learning

Learned world models are becoming essential to general-purpose agents: by predicting action consequences, they support planning and decision-making while reducing reliance on costly trial and error. This reliance creates a fundamental ambiguity: when a world-model-guided decision fails, the trajectory alone may not reveal whether the agent's decision rule or the world model caused the loss. We formalize this failure-attribution problem as a counterfactual decomposition of return loss and prove that its components are not identifiable from passive interaction, even for finite-horizon planners. This obstruction motivates Dual-Frontier, a learning principle that admits a world-model-guided decision only when its predicted advantage exceeds a certified bound on decision-relevant world-model error; otherwise, evidence is allocated to world-model verification. Action-conditioned value bounds and a closed-loop extension guarantee non-decreasing return for admitted decisions. Calibrated gates and simultaneous confidence sequences support adaptive evidence reuse, with sufficient and necessary verification bounds. Controlled learned-model experiments validate the predicted failure modes and certification behavior, while cross-backbone tool-use benchmarks instantiate the same verify-then-promote rule in realistic agent world-model pipelines, consistently improving decision quality and reliability.

Monte Carlo Tree Search (MCTS) is a powerful framework for solving complex decision-making problems, yet it often relies on the assumption that the simulator and the real-world dynamics are identical. Although this assumption helps achieve the success of MCTS in games like Chess, Go, and Shogi, the real-world scenarios incur ambiguity due to their modeling mismatches in low-fidelity simulators. In this work, we present a new robust variant of MCTS that mitigates dynamical model ambiguities. Our algorithm addresses transition dynamics and reward distribution ambiguities to bridge the gap between simulation-based planning and real-world deployment. We incorporate a robust power mean backup operator and carefully designed exploration bonuses to ensure finite-sample convergence at every node in the search tree. We show that our algorithm achieves a convergence rate of $\mathcal{O}(n^{-1/2})$ for the value estimation at the root node, comparable to that of standard MCTS. Finally, we provide empirical evidence that our method achieves robust performance in planning problems even under significant ambiguity in the underlying reward distribution and transition dynamics.

Solomonoff induction frames prediction as a mixture over computable hypotheses, typically leading to identification of the true environment. In a finite meta-reinforcement learning setting with nested constraint families, in our previous work, we observe a different regime: a value-mixture (VM) agent achieves near-optimal, zero-collision navigation without identifying the true environment, a phenomenon we call Free Inference. This regime persists up to a sharp density threshold, beyond which performance degrades and posterior-mode selection (PMS) becomes preferable. We formalize this behavior via the Free Inference dimension dFI(S,N), a combinatorial measure of the environmental complexity a VM agent can handle while preserving trajectory coherence. We prove dFI is strictly smaller than the VC-dimension and relates to the Natarajan dimension up to a path-length factor, capturing the cost of non-decomposable loss. A PAC-style relaxation yields generalization bounds driven by dFI^(epsilon,delta). We also define a complementary PMS identification dimension and show that a hybrid strategy---averaging until the first collision, then switching to selection---is optimal, with links to Littlestone-type dimensions supported by grid-world experiments.

Multimodal evaluations cannot say whether a vision-language model misread an image or misreasoned about it, because every existing method for separating the two places a second model in the loop. We introduce the render ceiling, a model-free reference for benchmarks built by rendering known objects: inverting the frozen cameras and re-solving cross-view correspondence recovers exactly the answer the images support. We prove the ceiling fails only through an enumerable set of projection coincidences and certify that set empty on 2,160 rendered crystal structures, so every point of a model's deficit belongs to the model. Across fourteen vision-language models, supplying exact geometry as text lifts every model yet closes under half the gap for thirteen, while a supervised vision model with no language component reads the same images at 0.8952, above every vision-language model. The instrument exposes extraction-stage fabrication that downstream accuracy would misattribute to reasoning, yields camera-placement rules for benchmark builders, and transfers to any benchmark with an invertible forward rendering.

Sample-efficient policy learning from pixels is a long-standing challenge in reinforcement learning (RL). Recent dynamics-based representation learning methods have significantly improved the sample efficiency of model-free visual RL by learning dynamics-aware representations through auxiliary prediction performed either in latent space (self-prediction) or observation space (observation prediction). However, state-of-the-art methods from both categories still struggle on challenging visual control tasks when training data is limited. We posit that relying on either predictive objective alone may be insufficient. In contrast, observation prediction grounds learned representations in observation-level dynamics, but does not directly regularize the temporal predictability of latent representations over extended horizons. In this paper, we propose Observation-Grounded Self-Predictive Representations (OG-SPR), a model-free visual RL algorithm for continuous control that learns representations that are both temporally predictive in latent space and grounded in observation-level dynamics. OG-SPR incorporates two core auxiliary objectives: multi-step latent self-prediction and next-observation prediction. We empirically show that directly imposing latent self-prediction on the shared representation may over-constrain it and does not necessarily improve performance. To address this issue, OG-SPR introduces two lightweight adapters for latent self-prediction, allowing the shared representation to benefit from temporally predictive signals without being forced to directly satisfy the self-prediction objective. Experiments on 28 visual control tasks from the DeepMind Control Suite show that OG-SPR improves aggregate performance over state-of-the-art self-predictive and observation-predictive RL methods, with particularly pronounced gains in challenging domains such as dog and humanoid.

This work studies model-free reinforcement learning for co-safe linear temporal logic (sc-LTL) objectives in finite Markov decision processes, which can be reduced to maximal reachability objectives via the standard product construction. For this problem, direct sample-based bootstrap methods (e.g., TD or Q-learning) may fail to converge to optimal policies due to the noncontractive nature and nonuniqueness of solutions to the Bellman equation. We develop a new two-step model-free reinforcement learning method that first uses a discounted surrogate to identify a clamp set that resolves this nonuniqueness, and then applies undiscounted policy evaluation and greedy policy improvement with guarantees of finding an optimal solution. We prove almost-sure convergence of the policy evaluation step and finite termination of the policy iteration algorithm at an optimal policy. These theoretical results are validated through numerical experiments on a stochastic grid world.

Contemporary model-free reinforcement learning algorithms can achieve very high performance, but have low sample efficiency and are not robust to changes in the environment. Model-based algorithms have much higher sample efficiency, but still fail when the environment shifts. This paper introduces Adaptive Topological Learning with Abstract Successors (ATLAS) to combat these challenges. ATLAS uses a Grow When Required network with Successor Features in order to achieve high sample efficiency while also robustly tackling catastrophic forgetting. We evaluate ATLAS in spatial navigation tasks, benchmarking its performance against common on-policy and off-policy algorithms. Our empirical results demonstrate that by structurally decoupling transition dynamics from the reward signal, ATLAS achieves near-instantaneous adaptation to new goals and can exhibit positive backward transfer, significantly outperforming baseline methods in non-stationary environments.

Designing effective reward functions for model-free reinforcement learning under non-holonomic constraints remains a persistent challenge, often resulting in severe local minima such as policy paralysis or over-conservative hazard avoidance. In this work, we present a parameterized reward shaping framework featuring coverage-gated alignment feedback, drive-direction switch regularization, and an aligned episode termination mechanism evaluated on an autonomous parallel parking task. Crucially, we show that environmental reward parameters and algorithmic hyperparameters are deeply co-dependent, requiring joint meta-optimization to achieve stable convergence. By employing surrogate-based Bayesian optimization, our co-optimized Deep Q-Network (DQN) agent resolves characteristic control failure modes, significantly outperforming uncalibrated baselines across both success rate and trajectory smoothness.

In multi-agent reinforcement learning (MARL), inter-agent communication is effective for improving performance under partial observability. Representation learning-based approaches enable decentralized agents to learn messages grounded in their own observations, but they rely only on current observations and cannot convey information accumulated over time. We propose Dreamer-CPC, a decentralized model-based MARL method that integrates message learning based on Collective Predictive Coding (CPC) into the world model of DreamerV3. Each agent independently maintains a world model and a message module, and infers and exchanges messages from the latent states of the world model that reflect the history of past observations and actions. We evaluated Dreamer-CPC in two environments: Observer, a non-cooperative information-sharing task, and CatchApple, a newly introduced task in which task-relevant observations are temporarily missing. In both environments, Dreamer-CPC outperformed IPPO-CPC, an existing CPC-based method that generates messages from current observations, as well as no-communication baselines. In particular, in CatchApple, Dreamer-CPC achieved 4 to 5 times the episode return of IPPO-CPC, demonstrating effective coordination where other methods fail due to missing observations. These results suggest that communication grounded in the latent dynamics of world models can support decentralized decision-making when current observations alone are insufficient.

Reinforcement learning is conventionally divided into model-based and model-free methods. In this taxonomy, model-based methods perform lookahead planning over a learned world model, whereas model-free methods learn a reactive state-action mapping. Recent work, however, has shown that planning can emerge from model-free reinforcement learning alone. The conditions under which this behavior emerges from a pure reward-maximization objective have so far remained unclear. In this paper, we present evidence that, in the observed cases, the hidden-state structure of the neural architecture is the deciding factor. We find that a network of relational hidden states, each anchored to an environment state and exchanging messages along learned relations, acquires a planning mechanism. These hidden states recover the environment's transition structure in their learned relations, and improve the policy at decision time by planning over the learned graph. In a matched control agent that must additionally discover which cells represent which states, no such binding arises, and no planning follows from it. We argue that this explains the observed phenomenon of emergent planning in model-free reinforcement learning and raises the question of how common such emergent planning might be more generally. Finally, we hypothesize that the discovered mechanism could describe how planning emerges from pure reward maximization in the human brain through a neural architectural prior.

The deployment of autonomous cyber-physical systems in safety-critical environments requires closed-loop control strategies (i.e., policies) that are not only performant but also provably safe and robust. While learning-based methodologies such as Reinforcement Learning offer flexible and scalable approaches to automatically synthesize such controllers, they typically lack the formal guarantees necessary for safe deployment. To bridge this gap, we propose a novel simulation-based methodology to automatically synthesize policies with formal guarantees regarding performance, safety, and robustness specifications. Specifically, given a set of properties to verify, a confidence parameter $δ$ and an allowable failure probability $\varepsilon$, our method guarantees that the synthesized policy comes with a certificate: with confidence at least $1 - δ$, the probability of encountering a scenario where the given properties are violated is at most $\varepsilon$. We demonstrate the feasibility of our approach by developing SMC-ES, an algorithm that integrates Evolutionary Strategies with Statistical Model Checking-based verification. We evaluate SMC-ES on a suite of continuous control tasks using Gymnasium and Safety Gymnasium testbeds. Results show that, at the price of a sustainable increase in computational cost, our algorithm provides formal guarantees regarding performance, safety, and robustness specifications, while performing competitively against leading model-free Deep Reinforcement Learning (DRL) and Safe-DRL baselines.

This paper develops a model-free reinforcement learning framework for continuous--time extended mean field control problems, where both the dynamics and reward may depend on the joint distribution of states and controls. We adopt deterministic feedback policies, under which the state--action distribution is induced directly as a push--forward of the state law. This avoids optimization over stochastic kernels and bypasses key limitations of existing approaches in extended mean field settings. We first establish a model--free sensitivity formula for parameterized McKean--Vlasov dynamics and use it to derive a deterministic policy gradient formula expressed through an advantage--rate function on the Wasserstein space. We then refine this formula by introducing local value and advantage--rate representations that depend on the state, action, and joint state--action distribution, yielding a policy gradient that includes both action derivatives and measure--derivative terms with respect to the control distribution. These characterizations lead to a martingale--based learning principle and motivate a continuous--time deep deterministic policy gradient algorithm combining particle approximations, measure--dependent neural networks, temporal--difference learning, and exploration in either action or parameter space. Numerical experiments on stochastic Cucker--Smale consensus control and optimal liquidation with trade crowding demonstrate the efficiency, stability, and robustness of the proposed method, including problems with explicit dependence on the control distribution.

In this paper, we investigate whether a model-free RL agent can identify and exploit price manipulation opportunities more effectively than a traditional model-based approach that assumes correct specification of the data-generating process but relies on noisy parameter estimates. We consider a single-asset market in which prices evolve according to an Almgren-Chriss framework with non-linear permanent impact and linear temporary impact. We first establish the existence of price-manipulative strategies in discrete time and compute the optimal benchmark strategy using Sequential Least Squares Quadratic Programming under full information. We then compare two finite-sample learning approaches: a model-based procedure that estimates impact parameters from simulated execution data and an agnostic RL approach based on Deep Deterministic Policy Gradient, trained directly on the same amount of data. For intermediate volatility, the RL agent successfully discovers profitable manipulative strategies without explicit knowledge of the underlying model, even when training data are quite limited. More importantly, RL consistently outperforms the model-based approach when parameter estimates are affected by sampling error, despite the latter benefiting from the correct model specification. For large volatility, all methods are unable to identify manipulation opportunities, while for small volatility, the model based approach outperforms RL. These findings highlight both the effectiveness of RL in complex control problems and the risks associated with deploying learning algorithms in financial markets without appropriate safeguards.

Due to the limited endurance of embedded energy sources such as lithium-polymer (LiPo) batteries, the flight duration and operational range of unmanned aerial vehicles (UAVs) are severely constrained. Although energy-efficient trajectory planning and control have been widely studied, most existing approaches rely on accurate system models and computationally expensive optimization procedures. This paper proposes a model-free online iterative learning (IL) framework to minimize energy consumption. Without requiring explicit models of UAV dynamics or energy consumption, the proposed method improves energy efficiency while maintaining a low computational cost. The per-iteration computational complexity is O(n), where n denotes the number of path points. In the tested cases, the proposed method is approximately 50--60 times faster than the model-based IPOPT benchmark. Simulation results and real-world flight experiments across multiple UAV platforms validate the effectiveness, computational efficiency, and practical applicability of the proposed approach.

This paper addresses model-free continuous-time mean-field control in a setting where the population dynamics evolve continuously according to an unknown McKean-Vlasov stochastic differential equation, while only discrete-time transition data are available. In the model-based formulation, policy evaluation is naturally described by a stationary Hamilton-Jacobi-Bellman equation on $\mathcal P_2(\mathbb R^d)$, but this equation involves the drift and diffusion coefficients of the controlled McKean-Vlasov dynamics, which are not identifiable when only discrete-time data are available. On the other hand, a direct reduction to a time-discrete Bellman equation avoids the non-identifiability issue but loses the differential equation structure. To bridge these two viewpoints, we introduce a Mean-Field-PhiBE (MF-PhiBE), which incorporates discrete-time transition information into a continuous-time PDE on the Wasserstein space. The MF-PhiBE replaces the unknown infinitesimal drift and covariance in the policy-evaluation equation by one-step estimators computed from data, while preserving the generator structure of the McKean-Vlasov HJB equation. We also derive a policy-gradient theorem for entropy-regularized randomized feedback policies, expressing the actor direction through an action-wise infinitesimal advantage and the score of the policy. Combining these two ingredients yields a model-free actor-critic method. We prove a first-order consistency estimate showing that the value induced by an optimal MF-PhiBE policy approximates the optimal continuous-time value with an error of order $Δt$. In the linear-quadratic case, we show our approximation achieves second-order accuracy with only one-step data. Numerical experiments on an LQR benchmark and a crowd-aversion problem illustrate the proposed framework.

Soft robots are challenging to control due to their nonlinear and time-varying dynamics. Data-enabled predictive control (DeePC) offers a model-free alternative by directly leveraging measured input-output trajectories to construct a predictive controller. However, its receding-horizon formulation requires solving a constrained optimization problem at every sampling instant, which can be computationally demanding for real-time deployment on resource-limited robotic platforms. To address this limitation, we propose an adaptive reinforcement-learning-based event-triggered DeePC (RL-ET-DeePC) framework for soft robotic control. A model-free RL policy is trained to determine when to invoke the DeePC optimizer based on the current system state representation, thereby reducing unnecessary optimization calls while preserving closed-loop performance. Simulation results show that RL-ET-DeePC reduces optimization frequency by up to 66% compared to periodic DeePC, while maintaining comparable tracking accuracy. Hardware experiments on a three-dimensional cable-driven soft robotic arm demonstrate zero-shot transfer, achieving a 34% reduction in optimization frequency with tracking accuracy comparable to periodic DeePC and more consistent performance than a static threshold-based event-triggered baseline.

In recent years, the Internet of Things (IoT) paradigm has been shifting toward batteryless, energy-harvesting architectures. Sustaining reliable operation in these systems requires intelligent management of highly volatile stored energy. As edge applications grow in complexity, traditional energy-aware schedulers struggle with unpredictable workloads due to their reliance on static execution thresholds or pre-measured, hardware-specific task profiles. To overcome this, we propose two novel, hardware-agnostic dynamic scheduling strategies treating applications as a "black box," requiring no prior energy information: a model-free Reinforcement Learning (RL) agent and an on-the-fly Approximated Prediction (AP) method. We evaluate these methods against an adaptive task rate approach (AsTAR) and optimized static thresholds using a custom-built, physically accurate simulation framework driven by real-world solar data and dynamic LoRa transmission profiles. Rather than claiming universal superiority, our analysis exposes the distinct operational trade-offs of each method: the AP approach delivers lightweight, near-oracle task throughput; the RL agent provides tunable survival-execution balancing; and AsTAR excels at execution pacing across long energy gaps. Finally, we demonstrate that while these advanced strategies provide critical resilience for severely constrained systems with small capacitors, devices with larger energy buffers can efficiently rely on simpler, less computationally expensive static policies.

Augmenting model-free reinforcement learning (RL) with representations learned through observation dynamics prediction (observation-predictive RL) can improve sample efficiency and performance, with minor modifications and limited additional computation. However, this approach still struggles in challenging tasks with low-dimensional observations. In this paper, we identify a key factor behind this problem: unbalanced reconstruction losses across observation dimensions, where dimensions with larger value ranges dominate the loss. This encourages the agent to neglect dimensions with relatively small ranges, leading to degraded performance. To address this issue, we propose a novel normalization method tailored to online RL, which normalizes low-dimensional observations and balances the resulting losses and gradients. Beyond balancing reconstruction losses, observation normalization enables dynamics prediction to be performed in a normalized observation space, thereby providing a unified treatment of low- and high-dimensional inputs (e.g., physical states and images). Building on this idea, we further introduce Normalized Observation Space Dynamics-Augmented Q-learning (NASDAQ), a framework for observation-predictive RL applicable across diverse domains. NASDAQ learns state-action representations by coupling value learning with two auxiliary tasks: short-term value prediction and next normalized observation prediction. Extensive experiments demonstrate that NASDAQ achieves competitive or superior performance compared with state-of-the-art model-based and self-predictive RL methods, while requiring significantly less training wall-time.

Model-based and model-free reinforcement learning are traditionally viewed as separate paradigms: instead of learning a model of the transition kernel $P$, model-free agents typically estimate value functions tied to a specific policy and reward. In this paper, we challenge this dichotomy by proving that value-based agents trained on a sufficiently rich set of reward functions, e.g. using goal-conditioned RL, implicitly encode a unique and accurate world model. To extract this model in practice, we introduce \textit{$P$-learning}, an inverse analogue to $Q$-learning that samples from an agent's $Q$-values, policies and rewards to decode its internal model of the environment. We then provide sufficient conditions on the type and number of goals for which agents encode the true kernel $P$, covering both stochastic and deterministic MDPs over finite or continuous state spaces. Even when our assumptions are violated, we empirically demonstrate that agents trained on a handful of reward functions encode accurate dynamics in $\texttt{Reacher}$, $\texttt{MountainCar}$ and stochastic variants of $\texttt{FourRooms}$. Surprisingly, we find that policies trained exclusively on a \texttt{Reacher} agent's implicit world model are quasi-optimal on out-of-distribution, velocity-based goals despite position-only training -- suggesting that agents contain hidden generalisation capabilities and providing a new lens into the connection between model-based, model-free, and goal-conditioned RL.

This paper compares the performance of model-free controllers on a nonlinear system under cyberattacks, including false data injection and denial-of-service attacks. Four RL reward types are analyzed for accuracy, cost, and resilience. Results show that the Lyapunov reward offers the best resilience with low tracking error. Exponential mode also provides good trade-offs with acceptable resilience under moderate training conditions. Progressive and linear rewards converge faster but are less robust. RL-MPCs show strong steady-state resilience but require longer training times; RL-PID controllers are faster with significantly less training time. Proximal Policy Optimization outperforms Deep Deterministic Policy Gradient with a significant reduction in KPI variance. This study serves to highlight how well-designed RL rewards can improve performance and resilience against cyber threats.

Navigation in partially observable environments presents a significant challenge for autonomous agents, requiring effective decision-making with limited sensory information in unknown environments. Belief-based methods, particularly those using neural networks to approximate the belief space, often fail to capture the inherent multimodality of belief spaces, especially in high-dimensional cases with perceptual aliasing. While generative models present a compelling alternative, they typically require substantial data or expert demonstrations and lack explicit mechanisms for long-term planning. In this paper, we introduce BeliefDiffusion, a novel framework that combines the benefits of both generation and planning. BeliefDiffusion leverages diffusion models to explicitly characterize multimodal belief distributions and utilizes Model Predictive Control (MPC) to simultaneously plan ahead. It consists of two steps: (1) Imagining plausible environment configurations based on observation history and (2) Planning efficient navigation strategies across an aggregated configurations. Through extensive experiments in synthetic map environments, we demonstrate that BeliefDiffusion significantly outperforms both model-free reinforcement learning baselines and other generative approaches in navigation success rate and path efficiency. Our results validate that explicitly incorporating multimodal belief representations into planning enables more robust navigation in partially observable settings.

While there is an extensive body of work characterizing the sample complexity of discounted cumulative-reward MDPs, finite sample analyses for average-reward MDPs have been limited, and most existing works rely on restrictive assumptions such as ergodicity or access to a generative model. In this work, we establish the first finite sample complexity guarantees from a single trajectory for weakly communicating average-reward MDPs. To this end, we study the dynamics of a single trajectory in weakly communicating MDPs and based on this analysis, we develop novel model-free methods. Notably, our value-based and policy-based methods provide finite sample complexity guarantees of $\widetilde{O}(1/\varepsilon^2)$ and $\widetilde{O}(1/\varepsilon^4)$ from a single trajectory in weakly communicating MDPs, respectively. Furthermore, we introduce the first model-free method that requires no prior knowledge of problem-dependent quantities for communicating MDPs.

This paper presents a hybrid model-based and model-free framework for active multi-view target recognition using forward-looking sonar. A convolutional neural network (CNN) provides data-driven observation likelihoods, while Radon-based orientation estimation enables viewpoint-aware sensing without requiring angle annotations. During training, an information-gain-based reward guides a Proximal Policy Optimization (PPO) agent to learn a belief-aware viewpoint selection policy offline. At deployment, the learned policy performs real-time viewpoint selection using only CNN-based belief updates, eliminating the need for computationally expensive online POMDP tree search. Experiments on a marine-debris forward-looking sonar dataset demonstrate that the proposed approach achieves competitive recognition accuracy while reducing sensing steps and motion cost compared to model-based baselines.

Designing high-performance legged robots requires jointly optimizing morphology and control. Model-free Reinforcement Learning (RL) offers an alternative to model-predictive control for developing robust controllers without explicitly specifying robot dynamics. Thus, we have seen theuse of RL to train controllers and evaluate designs for robot morphology optimization. While RL has shown success inlocomotion, using it in the co-design inner loop is expensive due to repeated policy training. Universal policies conditioned on morphology offer a promising alternative, but suffer from behavioral diversity collapse, converging to a single strategy that performs sub-optimally across designs. On the other hand, end-to-end Mixture-of-Experts (MoE) architectures fail due to a collapse in its representation. We propose Gaussian Evolutionary Specialists (GES), a framework that decouples design-space partitioning from policy learning to capture diverse behaviors explicitly. GES assigns specialist policies to evolving Gaussian regions and iteratively refines them via training, probing, and territory expansion. The resulting specialists are integrated into a design sampling loop, replacing costly re-training with direct evaluation. When tested on the Buoyancy-Assisted Light Legged Unit (BALLU), GES discovers designs with 5 - 25% higher performance than naive universal policies. On hardware, a GES optimized design overcomes a 24 cm tall obstacle - 3x improvement over the baseline BALLU design. Moreover, GES curtails design optimization time by 37%.

This paper addresses the problem of attack detection in cyber-physical systems without any knowledge of the plant model or its structure. A remotely located plant transmits sensor measurements to an operator over a network that is assumed to be under attack. We consider two classes of attacks: model-free replay attacks and model-based stealthy attacks. For the latter, we derive closed-form expressions for the optimal stealthy attack policy against a $χ^2$ detector, for both linear and nonlinear systems. We then propose a model-structure-free detector based on TimesFM, a time-series foundation model developed by Google Research, which serves as a surrogate residual generator operating in a zero-shot fashion. We show empirically that the TimesFM-based detector achieves a comparable or superior attack detection performance. The efficacy of the proposed approach is demonstrated numerically on the IEEE 14-bus power system. We also demonstrate that TimesFM predictions can serve as a substitute for corrupted measurements, a practical mitigation technique when classical redundancy assumptions fail.

Speculative decoding accelerates generation by verifying multiple drafted tokens in a single target-model forward pass, reducing sequential decoding iterations. Model-free variants avoid auxiliary draft models by reusing text and model states already available during generation, but their speedup depends on the reliability of the constructed drafts. We identify two limitations of existing reuse-based methods: lexically anchored retrieval has limited recall under surface-form variation, and deterministic span copying can be brittle when the retrieved context does not uniquely determine the continuation. We propose \emph{AdaPLD}, a training-free method that adaptively improves both retrieval and draft construction. AdaPLD preserves high-precision lexical reuse while using semantic similarity to recover additional reuse opportunities when lexical matching fails. It further constructs branched reuse hypotheses to account for continuation uncertainty, rather than relying on a single copied span. Across diverse benchmarks, AdaPLD reduces target-model forward passes and achieves up to $3.10\times$ decoding speedup.

It has been proposed that the brain integrates flexible, computationally expensive cortical processing with simpler, lower-cost subcortical mechanisms to achieve resource-efficient performance greater than that of either system alone. Despite the allure of this perspective, satisfying theoretical frameworks that explore this hypothesis are still limited. We extend existing frameworks in which a model-based module and model-free module learn in tandem by explicitly constraining the memory resources of the model-based module, and investigate the impact of this constraint in a simple decision-making setting. Memory constraints naturally give rise to strategies for allocating memory resources. We evaluate the performance of different strategies in different situations and demonstrate that when the rewarded states change often, it can be advantageous for the model-based module to focus its memory resources not on exploiting the current reward, but on capturing general structure of the environment. This work provides a theoretical foundation for a functional dissociation between cortical and subcortical systems during learning: the cortex supports general structure learning, while subcortical circuits specialize in reward-based learning. We further detail how these hypotheses can be tested on experimental data.

We study model-free Q-learning in finite-horizon episodic Markov Decision Processes (MDPs) with stationary dynamics across episodes. We identify a central issue in nascent model-free posterior-sampling works: the reliance on delayed learning in order to prove theoretical guarantees. In particular, we identify three opportunities for faster learning - (i) value-function update order, (ii) update frequencies, and (iii) value-function initialization. Using Wang et al.'s RandomizedQ as a basis, we illustrate these changes and their individual (as well as cumulative) impact in multiple empirical studies. We find that our combined modifications, termed ReversedQ, improve scaled mean cumulative reward compared to RandomizedQ, from 9.53% to 78.78% in the Bidirectional Diabolical Combination Lock (BDCL), and from 21.76% to 61.81% in a chain MDP.

Transfer Learning, a technique where a model/agent can use the knowledge/expertise that it gained from one task and exploit that to solve another closely-related task, is often used in tackling problems in deep learning. Through this project, we explore transfer learning in the purview of deep reinforcement learning. Specifically, we want to use transfer learning to achieve the fast lap times in OpenAI's Car racing environment by training the agent on one circuit, and racing it on other customized target environments by zero-shot transfer or by additional fine-tuning. In addition, we compare the performance of model-based and model-free approaches, and observe that model-based approaches dominate in performance and converge faster than model-free approaches in this environment. We observe that transfer learning in most setups not only boosts the performance on the target domain, but also shows high performance ability during learning.

We propose a model-free offline multi-step reinforcement learning (RL) algorithm, Conservative Peng's Q($λ$) (CPQL). Our algorithm adapts the Peng's Q($λ$) (PQL) operator for conservative value estimation as an alternative to the Bellman operator. To the best of our knowledge, this is the first work in offline RL to theoretically and empirically demonstrate the effectiveness of conservative value estimation with a \textit{multi-step} operator by fully leveraging offline trajectories. The fixed point of the PQL operator in offline RL lies closer to the value function of the behavior policy, thereby naturally inducing implicit behavior regularization. CPQL simultaneously mitigates over-pessimistic value estimation, achieves performance greater than (or equal to) that of the behavior policy, and provides near-optimal performance guarantees -- a milestone that previous conservative approaches could not achieve. Extensive numerical experiments on the D4RL benchmark demonstrate that CPQL consistently and significantly outperforms existing offline single-step baselines. In addition to the contributions of CPQL in offline RL, our proposed method also contributes to the offline-to-online learning framework. Using the Q-function pre-trained by CPQL in offline settings enables the online PQL agent to avoid the performance drop typically observed at the start of fine-tuning and to attain robust performance improvements. Our code is available at https://github.com/oh-lab/CPQL.

Dynamic Population Games (DPGs) provide a tractable framework for modeling strategic interactions in large populations of self-interested agents, and have been successfully applied to the design of Karma economies, a class of fair non-monetary resource allocation mechanisms. Despite their appealing theoretical properties, existing computational tools for DPGs assume full knowledge of the game model and operate in a centralized fashion, limiting their applicability in realistic settings where agents have access only to their own private experience. This paper takes a step towards addressing this gap by studying model-free equilibrium learning in Karma DPGs. First, we analyze the setting in which a novel agent joins a Karma DPG already at its Stationary Nash Equilibrium (SNE) and learns a policy via Deep Q-Networks (DQN) without knowledge of the game model. Leveraging recent convergence results for DQN, we establish a suboptimality bound consisting of a DQN approximation error of order $O(1/\sqrt{N_s})$ and a mean field perturbation error of order $O(1/N)$, where $N_s$ is the replay buffer size and $N$ is the population size. Second, we consider the challenging problem of learning the SNE from scratch. We show empirically that combining deep RL with fictitious play and smoothed policy iteration allows agents to converge, in a model-free fashion, to a configuration close to the centrally computed SNE. Together, these contributions support the vision of Karma economies as practical tools for fair resource allocation.

Designing model-free algorithms for distributionally robust reinforcement learning (DRRL) poses fundamental challenges. The robust Bellman operator is nonlinear in the transition kernel, which makes one-sample Bellman updates biased, while the adversarial optimization underlying robustness makes robust evaluation computationally demanding. To address these difficulties, we consider the natural small-ambiguity regime under Kullback--Leibler ambiguity sets and propose an approximate DRRL framework based on a first-order expansion of the relevant robust functional. This yields an approximate robust Bellman equation that removes the adversarial optimization while remaining first-order accurate in the ambiguity radius. To learn the fixed point of this approximate equation, we propose Mean-Variance Stochastic Approximation (MVSA), a model-free algorithm that uses only one-sample updates. This is achieved via a lifted stochastic approximation dynamics and a two-time-scale design. We then prove convergence and a central limit theorem for MVSA: its main iterate satisfies a central limit theorem at the canonical $n^{-1/2}$ scale, with explicitly characterized asymptotic covariances. Finally, we validate our theoretical findings with a numerical experiment.

Optimizing dynamic risk with stochastic policies is challenging in both policy updates and value learning. The former typically requires transition perturbation, while the latter may rely on model-based approaches. To address these challenges, we propose a surrogate policy gradient without transition perturbation under softmax policy parameterization. We further develop model-free value learning methods for dynamic expectile and conditional value-at-risk by leveraging elicitability. Finally, inspired by Expected SARSA and Expected Policy Gradient, a model-free off-policy actor-critic algorithm is constructed. Empirical results in domains with verifiable risk-averse behavior show that our algorithm can learn risk-averse policy and consistently outperforms other existing methods.

While reinforcement learning (RL) promises to revolutionize the control of complex nonlinear robotic systems, a profound gap persists between the heuristic success of model-free off-policy deep RL and the underlying theory, which remains largely confined to tabular or linearizable settings. We identify the cause of this gap as an emergent isolation of three traditions: (i) measure-theoretic MDP foundations on general spaces limit their analysis to exact dynamic programming and ignore all error sources of a learning process; (ii) deterministic error propagation analysis addresses the approximation error via concentrability coefficients without a finite-sample analysis of the estimation error; and (iii) PAC generalization bounds characterize the estimation errors of simplified topologies. We bridge these traditions with a unified theoretical framework for fitted Q-iteration (FQI) on general measurable Borel spaces. Our main result provides a finite-sample, adaptive-data performance bound by chaining measure-theoretic probability with Bellman-operator contraction in Banach spaces. We prove that sequential Rademacher complexity controls Bellman-regression generalization under policy-dependent data collection. We further extend this analysis to provide the first cumulative, pathwise online regret guarantee for FQI in continuous spaces. These results lay the necessary foundations for the formal analysis of many modern deep RL algorithms.

Middle-mile logistics describes the problem of routing parcels through a network of hubs linked by trucks with finite capacity. We rephrase this as a multi-object goal-conditioned MDP. Our method combines graph neural networks with model-free RL, extracting small feature graphs from the environment state.

We present a framework using Relative Entropy Inverse Reinforcement Learning (RE-IRL) to recover investor reward functions from observed investment actions and market conditions. Unlike traditional IRL algorithms, RE-IRL is employed to account for environments where transition probabilities are unknown or inaccessible. To address the challenge of data sparsity, we utilize a $K$-nearest neighbor approach to estimate the observed behavior policy. Furthermore, we propose a statistical testing framework to evaluate the validity and robustness of the estimated results.

Here, we explore the problem of error propagation mitigation in modular digital twins as a sequential decision process. Building on a companion study that used a Hidden Markov Model (HMM) to infer latent error regimes from surrogate-physics residuals, we develop a Markov Decision Process (MDP) in which the inferred regimes serve as states, corrective interventions serve as actions, and a scalar reward that takes into consideration the cost-benefit tradeoff between system fidelity and maintenance expense. The baseline transition matrix is extracted from the HMM-learned parameters. We then extend the formulation to a Partially Observable MDP (POMDP) that accounts for the imperfect nature of regime classification by maintaining a belief distribution updated via Bayesian filtering, with the HMM confusion matrix serving as the observation model. Both formulations are solved via dynamic programming and validated through Gillespie stochastic simulation. We then benchmark two model-free reinforcement learning algorithms, Q-learning and REINFORCE, to assess whether effective policies can be learned without explicit model knowledge. A systematic comparison of different intervention policies demonstrates that the MDP policy achieves the highest cumulative reward and fraction of time in nominal operation, while the POMDP recovers approximately 95% of MDP performance under realistic observation noise. Sensitivity analyses across observation quality, repair probability, and discount factor confirm the robustness of these conclusions, and the major gaps in the policy hierarchy are statistically significant at $p < 0.001$. The gap between MDP and POMDP performance quantifies the value of information providing a principled criterion for investing in improved classification accuracy.

We study model-free reinforcement learning (RL) in non-stationary finite-horizon episodic Markov decision processes (MDPs) without prior knowledge of the non-stationarity. We focus on the piecewise stationary (PS) setting, where both rewards and transition dynamics can change at unknown times. We first revisit existing state-of-the-art approaches and identify theoretical and practical limitations that change the current landscape of performance guarantees. To characterize the difficulty of the problem, we establish the first minimax lower bounds for PS-RL in tabular and linear MDPs. We then introduce Detection Augmented Reinforcement Learning (DARLING), a modular wrapper for PS-RL that applies to both tabular and linear MDPs, without knowledge of the changes. In tabular MDPs, under change-point separability and reachability conditions, DARLING improves the best known dynamic regret bounds and matches our minimax lower bound. In linear MDPs, DARLING matches the minimax lower bound when the relevant reachability parameters are known, and our analysis clarifies the structural obstacles that distinguish this setting from the tabular case. Finally, through extensive experimentation across diverse non-stationary benchmarks, we show that DARLING consistently surpasses the state-of-the-art methods.

Ad hoc wireless networks exhibit complex, innate and coupled dynamics: node mobility, energy depletion and topology change that are difficult to model analytically. Model-free deep reinforcement learning requires sustained online interaction whereas existing model based approaches use flat state representations that lose per node structure. Therefore we propose G-RSSM, a graph structured recurrent state space model that maintains per node latent states with cross node multi head attention to learn the dynamics jointly from offline trajectories. We apply the proposed method to the downstream task clustering where a cluster head selection policy trains entirely through imagined rollouts in the learned world model. Across 27 evaluation scenarios spanning MANET, VANET, FANET, WSN and tactical networks with N=30 to 1000 nodes, the learned policy maintains high connectivity with only trained for N=50. Herein, we propose the first multi physics graph structured world model applied to combinatorial per node decision making in size agnostic wireless ad hoc networks.

In general reinforcement learning, all established optimal agents, including AIXI, are model-based, explicitly maintaining and using environment models. This paper introduces Universal AI with Q-Induction (AIQI), the first model-free agent proven to be asymptotically $\varepsilon$-optimal in general RL. AIQI performs universal induction over distributional action-value functions, instead of policies or environments like previous works. Under a grain of truth condition, we prove that AIQI is strong asymptotically $\varepsilon$-optimal and asymptotically $\varepsilon$-Bayes-optimal. We also apply our novel proof techniques to show asymptotic $\varepsilon$-optimality of Self-AIXI without any ad-hoc assumptions. Our results significantly expand the diversity of known universal agents.

High-altitude balloons (HABs) are common in scientific research due to their wide range of applications and low cost. Because of their nonlinear, underactuated dynamics and the partial observability of wind fields, prior work has largely relied on model-free reinforcement learning (RL) methods to design near-optimal control schemes for station-keeping. These methods often compare only against hand-crafted heuristics, dismissing model-based approaches as impractical given the system complexity and uncertain wind forecasts. We revisit this assumption about the efficacy of model-based control for station-keeping by developing First-Order Model Predictive Control (FOMPC). By implementing the wind and balloon dynamics as differentiable functions in JAX, we enable gradient-based trajectory optimization for online planning. FOMPC outperforms a state-of-the-art RL policy, achieving a 24% improvement in time-within-radius (TWR) without requiring offline training, though at the cost of greater online computation per control step. Through systematic ablations of modeling assumptions and control factors, we show that online planning is effective across many configurations, including under simplified wind and dynamics models.

This paper focuses on dynamic origin-destination matrix estimation (DODE), a crucial calibration process necessary for the effective application of microscopic traffic simulations. The fundamental challenge of the DODE problem in microscopic simulations stems from the complex temporal dynamics and inherent uncertainty of individual vehicle dynamics. This makes it highly challenging to precisely determine which vehicle traverses which link at any given moment, resulting in intricate and often ambiguous relationships between origin-destination (OD) matrices and their contributions to resultant link flows. This phenomenon constitutes the credit assignment problem, a central challenge addressed in this study. We formulate the DODE problem as a Markov Decision Process (MDP) and propose a novel framework that applies model-free deep reinforcement learning (DRL). Within our proposed framework, the agent learns an optimal policy to sequentially generate OD matrices, refining its strategy through direct interaction with the simulation environment. This approach was evaluated through a toy experiment on the Nguyen-Dupuis network and a case study utilizing an actual highway subnetwork spanning Santa Clara and San Jose. Experimental results show that the proposed method consistently improves calibration performance relative to the strongest conventional baseline, reducing link-flow MSE by 23.7% in the toy experiment and by 59.2-88.3% in the real-world case study. By reframing DODE as a sequential decision-making problem, our approach addresses the credit assignment challenge through a learned policy and provides a novel framework for calibration of microscopic traffic simulations.

Distributionally robust reinforcement learning seeks policies that remain effective when the deployment environment differs from the one that generated the training data. We study model-free robust Q-learning with $χ^2$ uncertainty sets and linear function approximation, using data from a single trajectory of an unknown nominal MDP. Evaluating the $χ^2$ robust Bellman target introduces the square root of a conditional second moment, which cannot be estimated unbiasedly from one transition, while the projected robust Bellman operator need not be contractive. We address these obstacles through a variational reformulation of the robust Bellman target and a blockwise frozen-target scheme, and establish a finite-time error bound relative to the optimal robust Q-function for every $γ\in(0,1)$. A neural-network experiment illustrates how the variational target can be used in a continuous-state nonlinear-control task.

Multi-agent games in dynamic nonlinear settings are challenging due to the time-varying interactions among the agents and the non-stationarity of the (potential) Nash equilibria. In this paper we consider model-free games, where agent transitions and costs are observed without knowledge of the transition and cost functions that generate them. We propose a novel distributed policy structure that follows the communication constraints in multi-team games, with multiple agents per team, and learned through policy gradients. Our formulation is inspired by the structure of distributed policies in linear quadratic games, which take the form of time-varying linear feedback gains. In the nonlinear case, we model the policies as nonlinear feedback gains, parameterized by self-attention layers to account for the time-varying multi-agent communication topology. We demonstrate that our approach achieves strong performance in several settings, including distributed linear and nonlinear regulation, and simulated and real multi-robot pursuit-and-evasion games.

Robust reinforcement learning (RL) under the average-reward criterion is essential for long-term decision-making, particularly when the environment may differ from its training dynamics. However, most existing studies focus on model-based settings and provide only asymptotic guarantees, hindering their principled understanding and practical deployment, especially in data-limited scenarios. We aim to close this gap by proposing a model-free algorithm, \textbf{Robust Halpern Iteration (RHI)}. We first design our algorithm based on a black-box sampling oracle, which can estimate the worst-case performance accurately. We then derive the finite sample complexity of RHI under the generative model setting, assuming the sampling oracle. To concretely design such an oracle, we propose a $K$-order multi-level Monte-Carlo estimator, which is shown to have a lower bias compared to prior methods. We further instantiate our design for multiple uncertainty models, including KL and $χ^2$ divergence sets, and show that our RHI algorithm achieves an $\varepsilon$-optimal robust policy with a sample complexity of $\tilde{\mathcal{O}}\left( \frac{SA\mathcal{H}^2}{\varepsilon^{(2+o(1))}}\right)$, where $S,A$ are the number of states and actions, and $\mathcal{H}$ is the robust optimal span. Our result asymptotically matches the best complexity in robust average reward RL.

Packing objects efficiently is a fundamental problem in logistics, warehouse automation, and robotics. When dealing with highly diverse 3D objects (household or grocery items), closed-form solutions are infeasible, and heuristic or model-free Reinforcement Learning~(RL) methods tend to focus solely on geometric optimization, relying on exhaustive searches of the discretized solution space. This leads to long training times (for pure RL) and high latency (heuristics), limited transferability to robotic scenarios, and ultimately ignores object characteristics (fragility, deformability) and human preferences. We propose HERB, a human-augmented RL framework for packing irregular objects, the first to explore the potential of learning from human demonstrations to solve this complex task. It leverages human demonstrations of packing strategies, which inherently exhibit latent factors such as space optimization, stability, and object properties that are difficult to model explicitly. The human-expert data is combined with RL exploration to provide the placement of each object inside the container. Experimental results show that our method outperforms heuristic, purely RL-based, and imitation learning approaches in packing efficiency and latency. Qualitative results highlight that our packing strategy produces more stable, human-like arrangements, which we expect to be more appropriate and widely accepted. Finally, we demonstrate the real-world feasibility of our method on a robotic system.

Imagining potential outcomes of actions before execution helps agents make more informed decisions, a prospective thinking ability fundamental to human cognition. However, mainstream model-free Reinforcement Learning (RL) methods lack the ability to proactively envision future scenarios, plan, and guide strategies. These methods typically rely on trial and error to adjust policy functions, aiming to maximize cumulative rewards or long-term value, even if such high-reward decisions place the environment in extremely dangerous states. To address this, we propose the Prospective (ProSpec) RL method, which makes higher-value, lower-risk optimal decisions by imagining future n-stream trajectories. Specifically, ProSpec employs a dynamic model to predict future states (termed "imagined states") based on the current state and a series of sampled actions. Furthermore, we integrate the concept of Model Predictive Control and introduce a cycle consistency constraint that allows the agent to evaluate and select the optimal actions from these trajectories. Moreover, ProSpec employs cycle consistency to mitigate two fundamental issues in RL: augmenting state reversibility to avoid irreversible events (low risk) and augmenting actions to generate numerous virtual trajectories, thereby improving data efficiency. We validated the effectiveness of our method on the DMControl benchmarks, where our approach achieved significant performance improvements. Code will be open-sourced upon acceptance.

We study formal policy synthesis for continuous-state stochastic systems under linear temporal logic specifications. The product of the system with the automaton of the specification has a hybrid state space with sparse rewards. We introduce a generalized optimal backup order, defined in reverse to a topological order over automaton states, that guides value backups and provably preserves optimality. We further present a model-free actor-critic algorithm whose policy evaluation solves a constrained optimization problem by the augmented Lagrangian method, yielding hyperparameter self-tuning, and prove its optimality and convergence in the tabular case. Since integer encodings of automaton states impose a spurious ordinal relationship on functions learned by one network, we dedicate a value and a policy network to each automaton state (modular learning). The algorithm matches or outperforms PPO, DQN, and A2C on CartPole, and on a Dubins car under a temporal specification the topological order and modular learning raise the success rate from 26.0% to 71.5%.